The evidence presented in the previous chapter indicated that estimates of hospital impacts in the evaluation, based on the Medicare sample, are not biased by attrition. The evidence for other outcomes and analysis samples, while suggesting that attrition did not lead to biased estimates of impacts, was less direct, however. Hence, in this chapter we employ the statistical procedures described in Chapter III to provide additional evidence on whether restriction of the analysis of channeling impacts to the nursing home, followup, and incommunity samples produces biased estimates of channeling impacts.
In Section A below we present the model of attrition estimated for the nursing home, followup, and incommunity samples. Because of the central importance of the interviews in defining all of these samples, the discussion is focused on attrition from the followup sample. In Section B, estimates of channeling impacts corrected for potential attrition bias, using the methods of Chapter III, are compared to impact estimates unadjusted for bias. In Section C, the approach developed in Chapter III is extended to make it more general, and these more general results are compared to those obtained from the simpler model.

A. A Model of Attrition

Models of the response to survey interviews are recent in origin and few attempts to estimate models of the response mechanism are present in the literature (Madow et al., 1983). Fortunately, knowledge of some aspects of the channeling demonstration evaluation assist in the specification of a model of response.
As discussed in Chapter II, a major finding about attrition was the fact that a substantially higher proportion of controls than treatment group members refused the baseline (often giving their assignment to the control group as the reason for their refusal). That difference in baseline nonresponse led to treatment/control differences in rates of followup interview nonresponse, simply because a followup interview was not attempted if the baseline was not completed. This difference also carried over to the other (Medicare, nursing home, incommunity) analysis samples. Thus, experimental status is an important determinant of whether observations are included in the analysis samples. Two binary variables for treatment status were included in the model, one for treatments in the basic model and one for treatments in the financial control model, to account for the known difference between models in data availability for treatment group members. Site binary variables were also included in the model to capture differences in response rates by site that could arise due to site differences in interviewer quality or supervision, or in the types of persons referred to channeling.
Another major cause of followup interview nonresponse is death. This suggests that variables related to health status and other factors that may affect mortality should be included in the general response model. Such factors include the following:
 Impairments on activities of daily living
 Age
 Whether referred to channeling by a hospital or nursing home
 Unmet needs
 Whether received help with various household tasks or personal care
 Whether on a waiting list for a nursing home
Reasons given by those refusing the baseline suggest another reason why such health status variables are potentially important predictors of response: those who are severely impaired may simply be unable to complete the interviews. Even if proxy respondents are present, they often are too busy caring for the impaired sample member to be interviewed.
Besides these indicators of impairment, more indirect measures of the willingness and ability to complete an interview include:
 Cognitive impairment
 Whether a proxy assisted the sample member with the screen questions
 Whether living alone (if someone lives alone, a proxy is less likely to he available to answer questions if the sample member is unable to do so)
 The number of contacts required to complete the screen
 Whether the screen interviewer felt the sample member would require help with the baseline
 The number of missing items on the screen.
The last three variables use the experience with the screen interview as predictors of the sample member's willingness or ability to cooperate with followups.
Finally, there are socioeconomic variables that may have little direct bearing on attrition, but may affect outcome measures which in turn affect the probability of response. Since outcome measures cannot be used to predict response (because they are not observed for nonrespondents), we include these screen determinants of outcomes in the response equation. These factors include sex, ethnicity, Medicaid coverage, and income.
Probit models for the likelihood of being in the 6, 12, and 18month followup samples as a function of the characteristics discussed above were estimated, and the results are presented in Table V.1. Unfortunately, probit coefficients do not have the same interpretation as regression coefficients, which indicate, for a given predictor variable, the effect of a unit change in the predictor variable on the dependent variable. A rough approximation of the effect of a given predictor on the probability of being in the sample is obtained by multiplying the probit coefficient by 0.4.^{24} Thus, sample members in the treatment group of the basic model are (.134 * 0.4) * 100 = 5 percentage points more likely than otherwise identical control group members in the same site to be in the 6 month followup sample.
TABLE V.1: Probit Coefficients for a Model of Being in the 6, 12, and 18 Month Followup Samples Screen Variable 6Month 12Month 18Month Coefficient tvalue Coefficient tvalue Coefficient tvalue TREATMENT STATUS Basic model 0.134** (2.81) 0.200** (4.28) 0.126 (1.94) Financial control 0.419** (8.67) 0.331** (7.03) 0.319** (4.69) SITE Basic Model Baltimore 0.118 (1.23) 0.012 (0.13) 0.154 (1.13) E. Kentucky 0.097 (0.96) 0.210* (2.17) 0.136 (0.94) Houston 0.089 (0.89) 0.038 (0.38) 0.194 (1.33) Middlesex County 0.396** (4.28) 0.217* (2.40) 0.214 (1.59) S. Maine 0.188 (1.94) 0.44 (0.47) 0.118 (0.86) Financial Control Cleveland 0.206* (2.22) 0.052 (0.58) 0.012 (0.09) Greater Lynn 0.129 (1.43) 0.135 (1.56) 0.110 (0.87) Miami 0.419** (4.77) 0.170* (2.01) 0.260* (2.05) Philadelphia 0.147 (1.70) 0.041 (0.49) 0.049 (0.40) (Rensselaer) IMPAIRMENT OF ABILITY TO PERFORM ACTIVITY OF DAILY LIVING (ADL)^{a} Extremely severe 0.171** (2.76) 0.241** (4.00) 0.162 (1.92) Highly severe 0.056 (1.04) 0.066 (1.28) 0.036 (0.49) Moderately severe 0.019 (0.34) 0.040 (0.76) 0.004 (0.06) (Mild or none) CONTINENCE^{a} Colostomy bag, device, need help 0.305** (5.05) 0.304** (5.04) 0.229** (2.65) Incontinent 0.065 (1.77) 0.131** (3.68) 0.137** (2.75) (Continent) REFERRAL SOURCE Hospital or nursing home 0.190** (4.10) 0.163** (3.58) 0.095 (1.44) Home health agency 0.072 (1.43) 0.145** (2.97) 0.079 (1.12) (Other) ETHNICITY Black 0.060 (1.24) 0.003 (0.06) 0.065 (0.97) Hispanic 0.526** (4.86) 0.497** (4.83) 0.486** (3.71) (White) MALE 0.218** (5.50) 0.275** (7.06) 0.324** (5.84) AGE (in years) 0.004 (1.82) 0.008** (3.62) 0.009** (2.92) COGNITIVE IMPAIRMENT^{b} Severe 0.064 (1.18) 0.021 (0.39) 0.062 (0.85) Moderate 0.035 (0.79) 0.056 (1.31) 0.085 (1.41) (Mild, none) INTERVIEWER ASSESSED UNMET NEEDS^{b} High 0.024 (0.53) 0.005 (0.11) 0.039 (0.61) Medium 0.015 (0.34) 0.024 (0.57) 0.003 (0.05) (Low) MEDICAID INSURANCE 0.055 (1.20) 0.041 (0.94) 0.089 (1.49) PROXY USE AT SCREEN 0.075 (1.47) 0.042 (0.86) 0.092 (1.37) REGULAR HELP RECEIVED WITH Meal preparation 0.063 (1.03) 0.055 (0.94) 0.036 (0.46) Housework, shopping 0.149* (2.36) 0.065 (1.08) 0.169* (2.07) Taking medicine 0.045 (0.89) 0.037 (0.75) 0.046 (0.67) Medical treatments at home 0.069 (1.56) 0.059 (1.39) 0.088 (1.45) Personal care 0.049 (0.86) 0.042 (0.75) 0.129 (1.70) INCOME <$500/mo. 0.040 (0.54) 0.041 (0.57) 0.012 (0.12) $500$999/mo. 0.007 (0.11) 0.003 (0.05) 0.052 (0.54) (>$1,000/mo.) ON WAITING LIST (or applied for) NURSING HOME 0.007 (0.12) 0.002 (0.03) 0.104 (1.34) NUMBER OF CONTACTS TO OBTAIN SCREEN INTERVIEW 0.048** (2.98) 0.044** (2.82) 0.041 (1.93) NUMBER OF MISSING ITEMS ON SCREEN 0.016 (1.82) 0.027** (3.16) 0.024 (1.76) EXPECTED TO NEED HELP TO COMPLETE BASELINE 0.016 (0.34) 0.014 (0.31) 0.040 (0.64) LIVING ARRANGEMENT^{b} With child 0.046 (0.85) 0.053 (0.99) 0.129 (1.70) With other (no spouse or child) 0.116 (1.65) 0.075 (1.09) 0.114 (1.19) Alone 0.111* (2.15) 0.032 (0.64) 0.136 (1.88) (With spouse, not with child) CONSTANT 1.23** (5.91) 1.20** (5.87) 1.06** (3.62) PERCENT IN SAMPLE 66 57 44 SAMPLE SIZE 6,326 6,326 3,165 2 LOG LIKELIHOOD RATIO 415.05 468.96 233.34 DEGREES OF FREEDOM 45 45 45 NOTE: For categorical variables the names of omitted categories are enclosed in parentheses, except where it is obvious (e.g., male).  Missing values for this variable were replaced by the mean.
 A missing value indicator was included for this variable in the model (coefficient not reported).
* Statistically significant at the 5 percent level for a twotailed test.
** Statistically significant at the 1 percent level for a twotailed test.The likelihood ratio statistics reported at the bottom of Table V.1 are for tests of whether all probit coefficients (except the intercept) are simultaneously zero. The large values of these test statistics indicate that this hypothesis is strongly rejected and suggest that the screen variables as a group do lead to significantly improved predictions of whether specific sample members respond. Furthermore, we can determine from the tvalues which of the factors are important determinants of being in the samples. Consistent with the response rates discussed in Chapter II, treatment group members are significantly more likely to respond than are controls, except in the basic model at 18 months. There are significant betweensite differences in the probability of response , but only those in the Miami site are consistently less likely (relative to Rensselaer) to respond at all three interviews. As expected, extremely severe ADL impairments at screen reduces the likelihood of response (less so at 18 months), and so do continence problems. Another indicator of poor health status, whether referred to channeling by a hospital or nursing home, also substantially reduces the likelihood of being in the 6 and 12month followup samples. On the other hand, no explanation is apparent for why hispanics are substantially more likely to he included in all three followup samples, as compared to blacks and whites (note, however, that only about 2 percent of the sample members are hispanic in the basic sites and 5 percent in the financial control sites). Furthermore, males are consistently less likely than females to respond; those who receive regular help with housework and shopping are more likely to respond at the 6 and 18 month interviews. Those living alone are less likely to respond at 6 months, although living arrangement does not seem to affect the likelihood of responding to the later interviews. Finally, the more contacts it took to obtain a screen interview from a given sample member, the less likely it was that a followup interview was obtained. This variable is apparently a good proxy for the tendency to cooperate with interviews.
We also estimated models of the probability that sample members were included in the other analysis samples. Probit models analogous to the ones presented in Table V.1 were estimated for the probability that the sample member was included in the nursing home and incommunity samples at 6 and 12 months.^{25} The results are generally quite similar to those obtained for the followup samples in terms of what factors are related to attrition. This is not surprising, given the relatively small number of cases that are included in the other samples but excluded from the followup samples. The primary differences between the other analysis samples and the followup sample in the factors affecting whether observations are available for analysis are:

Medicaid eligibility is a highly significant predictor of inclusion in the nursing home samples, but not in the followup or incommunity samples.

ADL is not a significant predictor of inclusion in the nursing home samples, but the severely impaired are significantly less likely to be included in the other analysis samples.

Older individuals are significantly less likely to be in the community samples but no less likely to be in the followup or nursing home samples.
The fact that Medicaid eligibles are much more likely to be in the nursing home samples than noneligibles, but no more likely to be in the other samples, is not surprising, given that the nursing home samples are defined to include all individuals known to be on Medicaid throughout a period, even if no followup interviews were completed. The significance of age in predicting inclusion in the incommunity sample reflects the fact that the oldest individuals are more likely to be in hospitals or nursing homes, even though they are no less likely to complete (or have a proxy complete) the interview. It is unclear why severe ADL impairments does not significantly decrease the likelihood of being in the nursing home analysis samples, unless the severely impaired tend to he Medicaideligible and are therefore automatically included in the nursing home samples, despite the fact that they were less likely to complete the interviews necessary to be included in the other samples.
The finding that about half of the screen variables appear to have significant effects on the probability that observations are available for analysis suggests that, as expected, attrition is not entirely random. Nevertheless, it does not appear to be strongly related to the set of screen factors at our disposal. This is clear from Table V.2, which displays the distribution of predicted probabilities obtained from the model for both responders and nonresponders. Although there is some difference between these two distributions, as evidenced by the Chisquare test showing that they differ significantly more than would be expected by chance, it is clear that the model does not discriminate well between responders and nonresponders. Responders tend to have only slightly higher predicted probabilities of response than nonresponclers. A goodness of fit measure, analogous to the R^{2} statistic produced for regressions, was quite low for all of the models.
It is important that this lack of predictive power be properly interpreted, however. What it shows is that attrition is not closely tied to the fairly extensive set of screen characteristics, but rather occurs for a wide variety of unknown reasons. This should be viewed as evidence that those who drop out of the sample are not strikingly different from those that remain in, i.e., that attrition bias is relatively unlikely. This is especially so since much of the attrition occurs at baseline, which is only a short time after the screen interview was conducted. Any relationship between personal characteristics and attrition at baseline, therefore, should not be masked by drastic changes in the characteristics between the time of measurement (screen) and the time the response decision was made.
It is true that if the attrition correction term (M) is actually affected by personal characteristics, but none of these characteristics appear in the attrition equation, that the attrition model will produce poor estimates of M and the Heckman procedure described in Chapter III will erroneously indicate that there is no bias. However, this typically occurs because very few characteristics of nonresponders are available for inclusion in the response model in most applications of this procedure. In this analysis, however, the screen provides a great deal of information on sample members, and these data are used in the attrition model. The relevant criteria in assessing the ability of the model to control for attrition is not how well it fits (since attrition may be totally or largely random) but rather that important variables that might affect attrition and whose coefficients in the outcome equation we are most interested in appear in the model of response. In this study, treatment status clearly affects attrition. That relationship is reflected in the estimated response model; hence, the model, despite low predictive power, produces a very adequate instrument for M. Attrition bias, if it exists, should be identified by a significant coefficient on M.
TABLE V.2: Measures of the Predictive Accuracy of the Response Models and Distribution of Responders and Nonresponders at the Followup Interviews by Predicted Probability of Response
(percent)Sample & Sample Member Response Status Predicted Probability of Response Total Number of
ObservationsR^{2a} Chi
square^{b}
(df)0 0.10 0.11 0.20 0.21 0.30 0.31 0.40 0.41 0.50 0.51 0.60 0.61 0.70 0.71 0.80 0.81 0.90 0.91 1.0 FOLLOWUP SAMPLE (%) 6Months Nonresponders 0 0 1 5 13 25 30 22 5 0 100.0 (2,149) 0.065 399.9**
(7)Responders 0 0 0 1 6 17 28 33 14 0 100.0 (4,177) 12Months Nonresponders 0 1 4 13 24 27 21 10 1 0 100.0 (2,703) 0.072 435.8**
(8)Responders 0 0 1 6 15 25 31 19 3 0 100.0 (3,623) 18Months Nonresponders 0 5 17 27 26 18 7 1 0 0 100.0 (1,760) 0.071 213.4** Responders 0 1 8 19 29 25 15 3 0 0 100.0 (1405) NOTE: Percent ages do not always sum to 100 due to rounding. Predicted probabilities were obtained from the estimated probit models presented in Table V.1.  The R^{2} measure is Efrons R^{2} for qualitative response models (see Amemlya, 1981), the analogue to the R^{2} statistic for linear regression.
 These Chisquare statistics test whether the distribution of the predicted probabilities of response for respondents differ from the distribution for nonrespondents by more than might be expected by chance. All these statistics strongly reject the hypothesis that the distributions are equal for respondents and nonrespondents, which implies that the model does discriminate to some degree between respondents and nonrespondents.
** Statistically significant at the 5 percent level.
Another very important feature of the attrition model used here is that it includes several factors that are unlikely to affect outcomes. Chief among these factors is the number of contacts required to complete the screen, which has a statistically significant effect on the probability of response. Even some of the variables that do appear in both the attrition and outcome equations are not exactly the same because they come from different sources and take different forms in the two equations. Having some nonoverlapping variables in the attrition model and outcome model greatly increases the validity of the attrition bias correction procedure. Thus, we proceed in the next section to use the attrition model estimated here to control for attrition bias in estimates of program impacts.


B. Impact Estimates Adjusted for Attrition

The probit estimates in Table V.1 and those for the other analysis samples were used to construct for each sample member a correction term (M) specific to each of the analysis samples, as defined in Chapter III. This term, when included as an additional control variable in the outcome regression, will control for the effects of attrition on the impact estimate and the other coefficients. The set of auxiliary control variables (X_{1}) used in the outcome equation, in some cases taken from the baseline interview and from the screen in others,^{26} is the set that were used in the final reports on channeling impacts and includes:
 Site
 Impairments on activities of daily living (ADL)
 Incontinence
 Medicaid coverage
 Living arrangement/availability of informal support
 Whether on a waiting list for a nursing home
 Cognitive impairment
 Interviewerassessed unmet needs
 Whether referred to channeling by hospital or nursing home
 Age
 Ethnicity
 Marital status
 Homeownership
 Life satisfaction
 Stressful life events within the past year (death of person close to respondent; change in health condition)
 Number of physician visits during past 2 months
 Number of hours per week visiting informal caregiver spends in residence
 Whether formal care received
 Number of hours per week formal caregiver spends in residence
 Proxy or self response at baseline
 Sex
For some of these variables, means have been imputed for missing values, whereas for variables with a substantial number of missing values a separate missing value indicator is included.
In total, the X_{1}vector consists of 51 separate variables, including the constant. A number of these variables are included in the set of variables used to predict attrition. Others, including informal support, homeownership, life satisfaction, stressful life events, number of physician visits, whether formal care was received, and the number of hours of formal and informal care received were obtained from the baseline and, therefore, were not available for use in predicting response. Still other variables were excluded from the list of auxiliary control variables, but were used to predict attrition (e.g., number of contacts required to complete the screen), as pointed out in the previous section. The appendix contains a comparison of the variables used in the two equations and indicates for the auxiliary control variables whether they were drawn from screen or baseline.
We examine the effects of attrition by estimating channeling impacts on a set of the key outcome measures, with and without adjustment for possible attrition bias. The key outcomes examined (and the analysis samples on which they were estimated) were:

Nursing home outcomes (nursing homes samples)
 whether admitted during months 16, 713, 1318
 number of days in nursing homes in each period
 nursing home expenditures in each period

Wellbeing outcomes (followup samples)
 number of unmet needs at'6, 12, and 18 months after randomization
 number of impairments on activities of daily living at each followup
 whether dissatisfied with life at each followup

Formal and informal care (incommunity samples)
 whether received care from visiting formal caregiver during reference weeks at 6, 12, and 18 months
 hours of formal inhome care received during reference weeks
 number of visits from formal caregiver
 whether received care from visiting informal caregiver during reference week at 6 and 12 months
 hours of care received from visiting informal caregiver
 number of visits from visiting informal caregiver
The unadjusted and adjusted impact estimates for the basic and financial control models are presented in Table V.3, Table V.4 and Table V.5. The results are summarized below.
TABLE V.3: Estimates of Channeling Impacts on Nursing Home Outcomes With and Without Correction for Effects of Attrition: 6, 12, and 18Month Nursing Home Samples Basic Model Financial Control Model Rho^{a} Sample
SizeUncorrected
EstimateCorrected
EstimateUncorrected
EstimateCorrected
EstimateAny Nursing Home Admission Last 6 Months (percent) Months 1 to 6 0.52
(0.37)0.34
(0.23)0.37
(0.27)0.08
(0.05)0.07
(0.37)4593 Months 7 to 12 2.23
(1.88)3.03*
(2.20)0.29
(0.25)1.24
(0.70)0.27
(1.17)4752 Months 13 to 18 0.26
(0.13)0.21
(0.10)0.89
(0.43)0.59
(0.21)0.04
(0.16)2248 Number of Nursing Home Days Last 6 Months Months 1 to 6 2.36
(1.93)1.98
(1.54)1.14
(0.94)0.17
(0.10)0.18
(0.89)4593 Months 7 to 12 1.19
(0.63)2.61
(1.19)2.19
(1.15)4.94
(1.75)0.31
(1.32)4752 Months 13 to 18 1.12
(0.36)0.94
(0.30)0.18
(0.05)1.05
(0.24)0.11
(0.42)2248 Total Nursing Home Expenditures Last 6 Months^{b} Months 1 to 6 165*
(2.15)136
(1.67)8
(0.11)68
(0.66)0.22
(1.11)4593 Months 7 to 12 58
(0.56)144
(1.20)103
(0.99)270
(1.74)0.34
(1.46)4752 NOTE: Tvalues are reported in parentheses. For the corrected estimates, these are computed from standard errors which have been adjusted for heteroskedasticity using methods developed by Heckman (1979) and Greene (1981).  Rho is the estimated correlation between the disturbance terms in the impact regression (u_{1}) and the attrition equation (u_{2}), obtained by dividing the estimated coefficient on the attrition correction term by the estimated standard error of the disturbance term in the outcome equation. The tvalue in this column is the tvalue of the coefficient on the correction term in the outcome equation.
 Data on nursing home expenditures were not collected for months 13 to 18.
* Statistically significant at the 5 percent level for a twotailed test.
** Statistically significant at the 1 percent level for a twotailed test.1. Nursing Home Outcomes
Impact estimates for nursing home admissions, days, and expenditures before adjustment for possible attrition bias provide little evidence that channeling had any such effects. From Table V.3 we see that in no time period and in neither model were estimates statistically significant, except for nursing home expenditures at 6 months in the basic model (costs reduced by an average of 165 dollars per treatment group member by channeling). Adding the attrition correction term did little to change the overall interpretation of the results. The estimated correlation between unobserved factors affecting attrition and nursing home outcomes was generally small, sometimes positive and sometimes negative, and in all cases statistically insignificant, implying that there was no attrition bias. This finding is also reflected in the general similarity of the impact estimates before and after the attrition correction. There are two instances where the statistical significance of the estimates changes after the attrition correction, both occurring in the basic model. The estimated impact on nursing home admissions at 12 months goes from 2.2 percentage points before correction to 3.0 after correction. The tstatistic of the former is slightly below the critical value for a 5 percent level test while the tstatistic for the latter is slightly above the critical value. However, the point estimates are quite similar. The other instance of a change in significance after controlling for potential bias is similar but reversed: the estimated impact on expenditures at 6 months went from a significant effect of minus 165 dollars to an insignificant estimate of minus 136 dollars.
TABLE V.4: Estimates of Channeling Impacts on WellBeing Outcomes With and Without Correction for Effects of Attrition: 6, 12 and 18Month Followup Samples
(tvalues in parentheses)Basic Model Financial Control Model Rho^{a} Sample
SizeUncorrected
EstimateCorrected
EstimateUncorrected
EstimateCorrected
EstimateNumber of Unmet Needs 6 months 0.17*
(1.96)0.19*
(1.99)0.25**
(2.83)0.31*
(2.01)0.16
(0.45)4075 12 months 0.31**
(3.52)0.38**
(3.56)0.31**
(3.52)0.43**
(3.21)0.36
(1.20)3532 18 months 0.11
(0.82)0.12
(0.81)0.08
(0.55)0.09
(0.46)0.03
(0.07)1377 Number of Impairments on Activities of Daily Living 6 months 0.04
(0.66)0.08
(1.10)0.22**
(3.30)0.34**
(2.85)0.38
(1.22)4094 12 months 0.06
(0.76)1.16
(1.73)0.21**
(2.90)0.39**
(3.37)0.59*
(2.05)3539 18 months 0.08
(0.66)0.02
(0.16)0.04
(0.35)0.20
(1.17)0.47
(1.35)1381 Global Life Satisfaction (percent dissatisfied) 6 months 5.4*
(2.49)5.8*
(2.43)5.7**
(2.61)7.0
(1.83)0.13
(0.41)4022 12 months 2.2
(0.94)3.5
(1.22)5.0*
(2.07)7.1*
(1.97)0.24
(0.79)3441 18 months 1.2
(0.31)0.3
(0.08)2.6
(0.66)0.3
(0.05)0.24
(0.65)1325 NOTE: Tvalues are reported in parentheses. For the corrected estimates, (1) these are computed from standard errors which have been adjusted for heteroskedasticity using methods developed by Heckman (1979) and Greene (1981). For the corrected estimates (2), these are simply the unadjusted tstatistic for the treatment status coefficient and are likely to be close to those adjusted for heteroskedasticity.  Rho is the estimated correlation between the disturbance terms in the impact regression (u_{1}) and the attrition equation (u_{2}), obtained by dividing the estimated coefficient on the attrition correction term by the estimated standard error of the disturbance term in the outcome equation. The tvalue in this column is the tvalue of the coefficient on the correction term in the outcome equation.
* Statistically significant at the 5 percent level for a twotailed test.
** Statistically significant at the 1 percent level for a twotailed test.These differences are not compelling evidence of attrition bias. In addition to the fact that most of the estimated correlations were low and the estimated changes due to controlling for attrition were small, the two cases where significance levels did change were in different time periods and had estimated correlations of opposite signs. It seems unlikely that if attrition bias were present, it would be positive for one of these variables and negative for a related outcome, or positive in one period and negative in the next. These small changes suggest that bias in estimates of channelings nursing home impacts is unlikely. The conclusion that channeling had little impact on nursing home use in basic sites and none in financial control sites is unchanged when the potential effects of attrition are considered.
2. WellBeing Outcomes
Estimated impacts on wellbeing, contained in Table V.4, were also relatively unaffected by attrition. Although the estimate of rho in the ADL equations is positive and large in all 3 periods and statistically significant in one of them, the conclusion that channeling led to higher reported impairment on ADL in the financial control sites but not in basic sites is unchanged by the attrition correction. Estimated rhos for the unmet needs and life satisfaction outcomes are statistically insignificant in both models for all three time periods, and impact estimates exhibit only minor changes after the attrition correction term is added.
3. Formal and Informal Care Outcomes
Estimates of rho for these outcomes, given in Table V.5, again are statistically insignificant. The estimated impacts on formal care for the incommunity sample are very similar before and after controlling for attrition effects. Statistically significant estimates remain significant and are approximately the same sizes. Insignificant estimates remain insignificant. Thus, despite the difference observed in Chapter IV between the full and incommunity samples in estimated impacts on total reimbursements for Medicarecovered community services in the basic model at 6 months, we find no evidence of bias in overall use of formal care, for this time period and model or any other.
The results for informal care lead us to a similar conclusionthe estimated correlations between unobserved determinants of attrition and informal care outcomes are statistically insignificant. However, one substantive difference is observed in the estimated impacts on whether informal care was received from visiting caregivers. The estimate for the financial control model at 6 months is considerably smaller and statistically insignificant after correcting for attrition. Based on the unadjusted estimates, we had concluded (Christianson, forthcoming) that there was some evidence that channeling led to modest reductions in the percent of treatments receiving informal care. The attrition corrected estimates suggest that reductions may be even more modest than the unadjusted estimates show. However, for neither set of estimates are there significant reductions in the amount (hours or visits) of informal care received because of channeling. The lack of significant rhos and the lack of consistent findings across outcome measures or models that attrition corrected estimates differ markedly from uncorrected estimates on t his sample lead us to conclude that estimates of channeling impacts on informal care are not distorted by attrition.
TABLE V.5: Estimates of Channeling Impacts on Formal and Informal Care Use, With and Without Corrections for Attrition Bias: 6 and 12Month InCommunity Samples Basic Model Financial Control Model Rho^{a} Uncorrected
EstimateCorrected
EstimateUncorrected
EstimateCorrected
EstimateFORMAL CARE Whether Received inHome Care from Visiting Formal Caregiver During Reference Week (percent) 6 months after randomization 10.7**
(5.15)9.9**
(4.57)22.8**
(10.84)19.8**
(6.93)0.34
(1.51)12 months after randomization 10.0**
(4.20)11.3**
(4.24)20.1**
(8.48)22.1**
(7.36)0.25
(1.06)Total Hours of Visits by Visiting Formal Caregivers 6 months after randomization 0.82
(0.99)0.95
(1.11)7.40**
(8.91)7.84**
(6.92)0.13
(0.57)12 months after randomization 1.74
(1.77)1.94
(1.77)6.35**
(6.48)6.65**
(5.38)0.10
(0.41)Number of Visits by Visiting Formal Caregivers 6 months after randomization 0.48**
(3.10)0.52**
(3.22)2.15**
(13.75)2.28**
(10.68)0.20
(0.88)12 months after randomization 0.55**
(3.01)0.71**
(3.47)2.12**
(11.56)2.37**
(10.22)0.40
(1.74)INFORMAL CARE Whether Received inHome Care from Visiting Informal Caregiver During Reference Week 6 months after randomization 2.2
(0.90)1.7
(0.69)4.8*
(1.97)3.2
(0.96)0.16
(0.71)12 months after randomization 0.7
(0.27)1.4
(0.48)3.9
(1.46)0.5
(0.14)0.38
(1.67)Total Hours of Visits by Visiting Informal Caregivers 6 months after randomization 1.11
(1.04)1.36
(1.23)0.79
(0.75)1.65
(1.14)0.20
(0.87)12 months after randomization 0.19
(0.18)0.56
(0.47)0.11
(0.10)0.47
(0.35)0.17
(0.70)Number of Visits by Visiting Informal Caregivers 6 months after randomization 0.20
(0.63)0.05
(0.15)0.21
(0.65)0.31
(0.72)0.39
(1.76)12 months after randomization 0.15
(0.49)0.33
(0.98)0.47
(1.56)0.19
(0.49)0.28
(1.22)NOTE: See Table V.4 for notes.


C. A More General Model of Attrition Bias

The results above provide evidence that attrition did not lead to bias in estimates of channeling impacts. Nevertheless, this finding could be due to overly restrictive assumptions imposed by the statistical procedure used. Below we first describe the more general model, and then compare the results obtained to those presented above.
1. The Model
Two assumptions in the model used above that seem particularly strong and capable of influencing our findings are:

The relationship between observed screen characteristics and attrition is the same for treatments and controls and the same for basic and financial control models.

The relationship between unobserved factors affecting attrition and outcomes is the same across experimental groups and models.
The first assumption requires that the attrition model be the same for the four groups. The presence of binary site and treatment status variables (T_{B} and T_{F}) in the model ensures that the model reflects differences in the rates of response for the groups, but the use of a single equation does not take into account other possible differences between treatments and controls, such as the effect of ADL impairments on the probability of attrition. Thus, the attrition model may be poorly estimated if this assumption is false.
The second assumption implies that unobserved factors affecting attrition for treatments is the same as for controls. Suppose, for example, that treatment group members who do not respond at followup are those who are most impaired or in poorest health, given their screen characteristics. Suppose, on the other hand, that among controls with the same set of screen characteristics, those who drop out of the sample are those who are relatively healthy but refused the baseline interview because they were annoyed about being assigned to the control group. In this example, the relationship between unmeasured health status and attrition is positive for one group and negative for the other. Since unmeasured health status also affects outcomes (e.g., nursing home use) we have a positive relationship (rho) between disturbance terms in the two equations for one group and negative for the other group, contrary to the assumptions of the model. Since the model employed above does not take into account such possibilities, rho may be estimated as zero overall, implying no bias when the true bias could be substantial.
In this section, we relax these two assumptions and then reestimate channeling impacts. The first assumption is removed by estimating four separate probit modelsone for each experimental group/model combination. Using the expression given in Chapter III, an M term is constructed for each sample member using the appropriate attrition equation. To relax the second possibly restrictive assumption requires that four separate M terms be included in the regression equation to control for attrition, instead of just one. The need for this can be seen by noting that under the assumption that correlations are different for the four treatment/model groups, the expression for the expected value of an outcome, given that the sample member is included in the analysis sample, is:
(10) E(Y  included in the analysis sample) = Xβ + M_{i}_{i}, for members of group i, where i indicates which of the four treatment/model groups the individual belongs to, _{i} is the correlation between the disturbance terms in the attrition and outcome equations for members of group i, and a is the standard deviation of the disturbance term in the outcome equation. Since coefficients on X in the outcome equation are assumed to be the same for all groups, this can be written in a way that applies to all sample members:
(11) E(Y  included in the analysis sample) = Xβ + M_{1}_{1} + M_{2}_{2} + M_{3}_{3} + M_{4}_{4}, where M_{i} = the M term as defined in Chapter III for members of group i, created from the appropriate probit equation. For those not in group i, M_{i} = 0. Thus, each sample member now has 4 M terms, 3 of which are set to 0. Coefficients on the M_{i}'s reflect the possibly different correlations between attrition and outcomes.
2. Results from the More General Model of Attrition
To investigate whether the more general model discussed above changes our conclusions about the presence of bias, we use this model to obtain new estimates of rho and of channeling impacts. Controlling for possible effects of attrition, this analysis focuses on the three nursing home outcomes (because of the central importance of this outcome measure) and on the formal and informal care outcomes (because of the results from Chapter IV that showed some differences between the full and followup sample estimates of impacts on Medicarecovered services) . Hence, we estimate probit models, separately for each treatment/model group, for the probability of being in each of the following four samples:
 Nursing home sample, 6 and 12 months
 Incommunity sample, 6 and 12 months
These estimates are then used to form the appropriate 14 terms for inclusion in the outcome regressions.
TABLE V.6: Probit Coefficients for Models of Inclusion in the 6Month Nursing Home Sample, by Treatment Status and Model Screen Variable Basic Model Financial Model Full Sample Treatment Controls Treatment Controls Coefficient tvalue Coefficient t
valueCoefficient t
valueCoefficient t
valueCoefficient t
valueTREATMENT STATUS Basic Model 0.165 (3.35)** Financial Control Model 0.453 (8.88)** SITE Basic Model Baltimore 0.018 (0.14) 0.135 (1.00) 0.366 (3.60)** E. Kentucky 0.303 (2.16)* 0.174 (1.26) 0.073 (0.68) Middlesex County 0.112 (0.97) 0.546 (4.46)** 0.616 (6.31)** Houston 0.112 (0.75) 0.015 (0.09) 0.257 (2.36)* (S. Maine) 0.321 (3.14)** Financial Control Cleveland 0.051 (0.36) 0.554 (3.50)** 0.338 (3.41)** Greater Lynn 0.185 (1.27) 0.489 (3.48)** 0.342 (3.55)** Miami 0.365 (2.68)** 0.734 (5.23)** 0.584 (6.23)** Philadelphia 0.025 (0.19) 0.479 (3.25)** 0.251 (2.68)** (Rensselaer) IMPAIRMENT OF ABILITY TO PERFORM ACTIVITY OF DAILY LIVING (ADL)^{a} Extremely severe 0.192 (1.55) 0.042 (0.30) 0.275 (2.16)* 0.062 (0.43) 0.112 (1.71) Highly severe 0.127 (1.20) 0.021 (0.18) 0.116 (1.01) 0.035 (0.28) 0.073 (1.30) Moderately severe 0.209 (1.97)* 0.010 (0.08) 0.200 (1.71) 0.214 (1.67) 0.065 (1.15) (Mild or none) CONTINENCE^{a} Colostomy bag, device, need help 0.162 (1.24) 0.290 (2.11)* 0.264 (2.31)* 0.205 (1.56) 0.231 (3.68)** Incontinent 0.085 (1.19) 0.095 (1.16) 0.053 (0.68) 0.066 (0.77) 0.045 (1.16) (Continent) REFERRAL SOURCE Hospital or nursing home 0.095 (1.07) 0.246 (2.34)* 0.089 (0.92) 0.150 (1.37) 0.125 (2.59)** Home health agency 0.016 (0.15) 0.070 (0.56) 0.051 (0.53) 0.079 (0.74) 0.018 (0.35) (Other) ETHNICITY Black 0.025 (0.25) 0.291 (2.52)* 0.112 (1.20) 0.214 (1.83) 0.139 (2.69)** Hispanic 0.370 (1.31) 1.414 (3.04)** 0.866 (3.72)** 0.125 (0.58) 0.537 (4.32)** (White) MALE 0.238 (3.09)** 0.165 (1.85) 0.188 (2.39)* 0.121 (1.31) 0.171 (4.15)** AGE (in years) 0.007 (1.57) 0.001 (0.17) 0.001 (0.21) 0.000 (0.08) 0.003 (1.35) COGNITIVE IMPAIRMENT^{b} Severe 0.197 (1.85) 0.052 (0.43) 0.074 (0.69) 0.144 (1.16) 0.115 (2.06)* Moderate 0.192 (2.15) 0.018 (0.18) 0.057 (0.64) 0.084 (0.88) 0.056 (1.22) (Mild or none) INTERVIEWER ASSESSED UNMET NEEDS High 0.093 (1.00) 0.032 (0.32) 0.120 (1.26) 0.054 (0.50) 0.004 (0.09) Medium 0.146 (1.71) 0.062 (0.64) 0.071 (0.79) 0.059 (0.60) 0.021 (0.46) (Low) MEDICAID INSURANCE 0.585 (5.91)** 0.467 (4.30)** 0.430 (4.21)** 0.748 (6.49)** 0.535 (10.37)** PROXY USE OF SCREEN 0.243 (2.37)* 0.019 (0.16) 0.062 (0.62) 0.013 (0.11) 0.048 (0.91) REGULAR HELP RECEIVED WITH Meal preparation 0.050 (0.39) 0.054 (0.39) 0.036 (0.29) 0.103 (0.74) 0.075 (1.16) Housework, shopping 0.085 (0.65) 0.315 (2.15)* 0.265 (2.13)* 0.117 (0.79) 0.188 (2.83)** Taking medicine 0.046 (0.46) 0.098 (0.85) 0.223 (2.06)* 0.019 (0.16) 0.055 (1.04) Medical treatments at home 0.103 (1.21) 0.028 (0.29) 0.028 (0.30) 0.018 (0.17) 0.053 (1.16) Personal care 0.100 (0.85) 0.076 (0.61) 0.044 (0.37) 0.060 (0.43) 0.067 (1.10) INCOME <$500/month 0.226 (1.71) 0.039 (0.25) 0.114 (0.72) 0.058 (0.35) 0.022 (0.29) $500  $999/month 0.019 (0.15) 0.107 (0.71) 0.001 (0.00) 0.071 (0.47) 0.057 (0.82) (>$1,000/month) ON WAITING LIST/APPLIED FOR NURSING HOME 0.103 (0.94) 0.277 (2.08)* 0.043 (0.34) 0.082 (0.60) 0.016 (0.26) NUMBER OF CONTACTS TO OBTAIN SCREEN INTERVIEW 0.059 (1.82) 0.051 (1.44) 0.078 (2.40)* 0.049 (1.35) 0.058 (3.50)** NUMBER OF MISSING INTEMS ON SCREEN 0030 (1.29) 0.004 (0.18) 0.013 (0.79) 0.013 (0.73) 0.015 (1.57) EXPECTED TO NEED HELP TO COMPLETE BASELINE 0.137 (1.46) 0.005 (0.05) 0.103 (1.07) 0.003 (0.03) 0.041 (0.85) LIVING ARRANGEMENT^{b} With child 0.019 (0.18) 0.028 (0.23) 0.201 (1.79) 0.053 (0.42) 0.051 (0.89) With other (not spouse or child) 0.310 (2.32)* 0.016 (0.11) 0.183 (1.20) 0.256 (1.51) 0.093 (1.26) Alone 0.241 (2.38)* 0.117 (1.01) 0.135 (1.28) 0.134 (1.14) 0.091 (1.71) (With spouse, not with child) CONSTANT 1.677 (4.36)** 0.719 (1.62) 1.307 (3.02) 1.217 (2.64)** 1.333 (6.05)** NUMBER OF CASES 1,779 1,345 1,923 1,279 6,326 PERCENT IN NURSING HOME SAMPLE 72.01 67.14 80.50 67.32 72.6 R^{2} 0.087 0.105 0.063 0.090 0.056 CHISQUARE STATISTIC^{c} 164.3** 149.7** 120.8** 121.8** 540.1** DEGREES OF FREEDOM 38 38 38 38 45 NOTE: For categorical variables with more than two possible values (e.g., living arrangement) the names of the omitted reference categories are enclosed in parentheses.  Missing values for this variable were replaced by the mean.
 A binary variable indicating for which observations data on this variable were missing was included in the model to account for possible differences in response rates between the relatively small number of cases lacking data on this variable and others.
 The chisquare statistic is a likelihood ratio test of whether all coefficients except the constant term are equal to zero. The 0.01 significance level for this test with 38 degrees of freedom is about 61.0.
* Statistically significant at the 5 percent level for a twotailed test.
** Statistically significant at the 1 percent level for a twotailed test.TABLE V.7: Probit Coefficients for Models of Inclusion in the 12Month Nursing Home Sample, by Treatment Status and Model Screen Variable Basic Model Financial Model Full Sample Treatment Controls Treatment Controls Coefficient tvalue Coefficient t
valueCoefficient t
valueCoefficient t
valueCoefficient t
valueTREATMENT STATUS Basic Model 0.238 (4.76)** Financial Control Model 0.464 (9.04)** SITE Basic Model Baltimore 0.088 (0.70) 0.066 (0.49) 0.225 (2.21)* E. Kentucky 0.473 (3.19)** 0.148 (1.08) 0.151 (1.39) Middlesex County 0.150 (1.27) 0.467 (3.81)** 0.439 (4.52)** Houston 0.082 (0.54) 0.124 (0.75) 0.161 (1.48) (S. Maine) 0.167 (1.64) Financial Control Cleveland 0.037 (0.26) 0.412 (2.60)** 0.225 (2.27)* Greater Lynn 0.215 (1.44) 0.370 (2.64)** 0.093 (0.97) Miami 0.181 (1.33) 0.647 (4.65)** 0.432 (4.63)** Philadelphia 0.037 (0.28) 0.419 (2.86)** 0.244 (2.63)** (Rensselaer) IMPAIRMENT OF ABILITY TO PERFORM ACTIVITY OF DAILY LIVING (ADL)^{a} Extremely severe 0.142 (1.13) 0.069 (0.49) 0.049 (0.39) 0.086 (0.59) 0.037 (0.56) Highly severe 0.047 (0.44) 0.020 (0.17) 0.063 (0.56) 0.096 (0.76) 0.028 (0.49) Moderately severe 0.102 (0.95) 0.049 (0.41) 0.123 (1.09) 0.004 (0.03) 0.055 (0.97) (Mild or none) CONTINENCE^{a} Colostomy bag, device, need help 0.119 (0.87) 0.136 (0.98) 0.122 (1.00) 0.003 (0.02) 0.037 (0.57) Incontinent 0.052 (0.72) 0.073 (0.89) 0.218 (2.81)** 0.096 (1.12) 0.034 (0.087) (Continent) REFERRAL SOURCE Hospital or nursing home 0.007 (0.08) 0.040 (0.38) 0.140 (1.41) 0.072 (0.66) 0.060 (1.20) Home health agency 0.061 (0.55) 0.103 (0.83) 0.062 (0.64) 0.112 (1.06) 0.017 (0.32) (Other) ETHNICITY Black 0.058 (0.58) 0.378 (3.21)** 0.034 (0.37) 0.159 (1.36) 0.139 (2.67)** Hispanic 0.150 (0.57) 1.305 (2.81)** 0.543 (2.44)* 0.220 (1.00) 0.458 (3.71)** (White) MALE 0.177 (2.24) 0.075 (0.83) 0.104 (1.30) 0.048 (0.51) 0.098 (2.34)* AGE (in years) 0.003 (0.70) 0.006 (1.07) 0.009 (1.79) 0.003 (0.59) 0.004 (1.63) COGNITIVE IMPAIRMENT^{b} Severe 0.099 (0.91) 0.044 (0.36) 0.067 (0.60) 0.108 (0.86) 0.040 (0.69) Moderate 0.222 (2.44)* 0.006 (0.06) 0.083 (0.91) 0.116 (1.20) 0.069 (1.50) (Mild or none) INTERVIEWER ASSESSED UNMET NEEDS High 0.019 (0.20) 0.098 (0.97) 0.164 (1.72) 0.104 (0.98) 0.001 (0.03) Medium 0.107 (1.22) 0.184 (1.87) 0.071 (0.78) 0.071 (0.73) 0.051 (1.12) (Low) MEDICAID INSURANCE 0.458 (4.56)** 0.398 (3.64)** 0.342 (3.36)** 0.604 (5.29)** 0.434 (8.38)** PROXY USE OF SCREEN 0.057 (0.54) 0.045 (0.39) 0.069 (0.68) 0.061 (0.51) 0.010 (0.18) REGULAR HELP RECEIVED WITH Meal preparation 0.027 (0.21) 0.063 (0.46) 0.119 (0.99) 0.265 (1.87) 0.029 (0.45) Housework, shopping 0.011 (0.08) 0.164 (1.11) 0.044 (0.36) 0.187 (1.26) 0.056 (0.85) Taking medicine 0.043 (0.43) 0.104 (0.90) 0.156 (1.46) 0.170 (1.42) 0.078 (1.46) Medical treatments at home 0.035 (0.40) 0.082 (0.85) 0.055 (0.58) 0.140 (1.35) 0.069 (1.48) Personal care 0.035 (0.30) 0.154 (1.23) 0.033 (0.28) 0.051 (0.36) 0.071 (1.18) INCOME <$500/month 0.163 (1.21) 0.115 (0.72) 0.108 (0.67) 0.019 (0.12) 0.108 (1.43) $500  $999/month 0.114 (0.91) 0.062 (0.41) 0.074 (0.50) 0.055 (0.36) 0.021 (0.29) (>$1,000/month) ON WAITING LIST/APPLIED FOR NURSING HOME 0.169 (1.51) 0.134 (1.00) 0.052 (0.40) 0.038 (0.27) 0.009 (0.14) NUMBER OF CONTACTS TO OBTAIN SCREEN INTERVIEW 0.042 (1.26) 0.087 (2.47)* 0.030 (0.91) 0.102 (2.80)** 0.060 (3.60)** NUMBER OF MISSING INTEMS ON SCREEN 0.032 (1.42) 0.006 (0.28) 0.028 (1.59) 0.014 (0.80) 0.017 (1.75) EXPECTED TO NEED HELP TO COMPLETE BASELINE 0.039 (0.40) 0.056 (0.53) 0.039 (0.40) 0.121 (1.17) 0.027 (0.56) LIVING ARRANGEMENT^{b} With child 0.125 (1.15) 0.071 (0.58) 0.113 (0.99) 0.083 (0.65) 0.096 (1.66) With other (not spouse or child) 0.031 (0.22) 0.015 (0.10) 0.201 (1.22) 0.222 (1.32) 0.004 (0.06) Alone 0.038 (0.37) 0.118 (1.01) 0.039 (0.37) 0.144 (1.23) 0.078 (1.46) (With spouse, not with child) CONSTANT 1.035 (2.66)** 1.197 (2.69)** 1.632 (3.78)** 0.890 (1.93) 1.102 (4.98)** NUMBER OF CASES 1,779 1,345 1,923 1,279 6,326 PERCENT IN NURSING HOME SAMPLE 76.39 69.52 82.01 68.88 75.1 R^{2} 0.047 0.092 0.039 0.075 0.053 2 LOG LIKELIHOOD RATIO 95.9 129.1 79.1 101.5 394.0 DEGREES OF FREEDOM 38 38 38 38 45 NOTE: See notes to Table V.6. Estimates of the probit model of being in the nursing home sample, obtained on each of the four treatment/model groups separately, are presented in Table V.6 (6.month sample) and Table V.7 (12 month sample) along with the estimates from the previous single model of inclusion in the sample. Comparing across groups, we find consistent signs for the coefficients at six months, if not their significance levels. Eligibility for Medicaid significantly increases the probability that sample members are included in the sample, as was expected, given that those with Medicaid coverage throughout the analysis period were automatically included in the sample, provided that they completed a baseline. Other results indicate that more impaired individuals (those with at least moderately severe ADL impairment, those who were incontinent or needed help with devices related to incontinence, those referred to the program by a hospital or nursing home, and those with moderate or severe cognitive impairment), whites and males were all less likely to be included in the sixmonth nursing home sample. Increased age was also associated with attrition from the sample. The variables included solely in the model of analysis sample inclusion (number of contacts needed to obtain the screen interview, number of items missing from the screen, and whether the respondent was expected to need help completing the baseline interview) were rarely statistically significant, although a greater number of contacts to complete the screen was consistently associated with decreased likelihood of sample inclusion.
With the exception of Medicaid eligibility, which was statistically significant for all four treatment/model groups, specific variables tended to be significant for only one or two of these groups. This may reflect differing attrition patterns across the treatment status/model categories. However, the signs of the coefficient tended to be the same for the 4 groups when the estimated effect was statistically significant for one or more of the groups. Futhermore, if it were the case that attrition patterns were very different across groups, one would expect to see for a particular treatment status/model subgroup greater numbers of significant variables within broad groupings of similar variables. For instance, in the basic model treatment group, the variable for moderately severe ADL impairment is statistically significant, whereas the variables for highly and extremely severe impairment are not, nor are the continence and referral source variables. Thus, apart from consistency in the signs of the coefficients, one could not argue for a strong association between impairment and sample attrition among basic model treatments that did not exist in the other three groups. Extending this argument to other types of variables, it appears that patterns of attrition did not differ markedly across the four subgroups in spite of their differing rates of attrition.
The equation to predict sample selection met with varying degrees of overall success with respect to explanatory power as measured by the Chisquare statistics.^{27} All four test statistics were significant at the .01 level, indicating that the variables used did distinguish to some extent between sample members included in the analysis samples and those not included. The model was best able to predict the likelihood of sample inclusion at six months for basic model treatments and least able to predict for treatments and controls in the financial model. Furthermore, explanatory power dropped off markedly in the models of sample inclusion at twelve months for all subgroups, both according to the overall Chisquare statistic and the number of statistically significant variables. (Only Medicaid coverage remained a significant predictor of sample inclusion at twelve months for all four subgroups.) This decrease in power is not surprising, given the increase in the length of time between the screen and the followup.
Finally, we can compare the more general separate models of sample selection for each treatment/model subgroup to the more restrictive model estimated earlier with the four groups pooled in order to determine whether the lessening of restrictions increased our ability to predict sample inclusion. The similarity of coefficients across treatment/model subgroups would suggest that pooling the subgroups would not grossly alter the inferences and that is borne out by the comparison to the estimated coefficients in the pooled model, which are reported in the last columns of Table V.6 and Table V.7. Although there are exceptions, coefficients that are large and statistically significant in the pooled model are in most cases large and of the same sign in the four subgroups (though not always statistically significant, because of the much smaller sample sizes in the individual probits). The similarity of these coefficients and the fact that the R^{2} statistics for the individual probits are not much larger than the R^{2} for the pooled model suggest that the less restrictive approach of estimating separate models of sample inclusion for each treatment/model subgroup does not produce substantially improved predictions of inclusion in the nursing home sample.
Table V.8 and Table V.9 contain probit coefficients for models of selection into the samples of those living in the community at six and twelve months after random assignment, respectively. The incommunity sample was used to obtain an estimate of channeling's impact on sample members use of services during the time they were in the community. Since sample members who were never alive during the analysis period obviously spent no time in the community, only sample members alive at the start of the relevant sixmonth analysis period were included in the full sample upon which the probit models were estimated. Thus, the sixmonth probit used the full screen sample, since all sample members were alive at random assignment, but the twelvemonth probit used only those screen sample members who were alive on their sixmonth anniversaries.
Again, we find that the coefficients from the more general separate models do not differ in major ways across the four subgroups, nor from the previously estimated pooled model of sample attrition reported in the last columns of Table V.8 and Table V.9. Those who were more impaired, white, male, or older were more likely to be excluded from the analysis sample, as were those who were waitlisted for or who had applied to nursing homes at the screen or who required a greater number of contacts to complete the screen interview. The pooled estimates are statistically significant more frequently because of the much larger sample size obtained by pooling.
TABLE V.8: Probit Coefficients for Models of Inclusion in the Community Analysis Sample at 6 Months, by Treatment Status and Model Screen Variable Basic Model Financial Model Full Sample Treatment Controls Treatment Controls Coefficient tvalue Coefficient t
valueCoefficient t
valueCoefficient t
valueCoefficient t
valueTREATMENT STATUS Basic Model 0.098 (2.09)* Financial Control Model 0.355 (7.54)** SITE Basic Model Baltimore 0.157 (1.34) 0.150 (1.15) 0.087 (0.93) E. Kentucky 0.356 (2.78)** 0.300 (2.32)* 0.203 (2.09)* Middlesex County 0.014 (0.13) 0.350 (2.92)** 0.283 (3.12)** Houston 0.176 (1.26) 0.019 (0.12) 0.034 (0.34) (S. Maine) 0.155 (1.64) Financial Control Cleveland 0.035 (0.28) 0.139 (0.92) 0.087 (0.97) Greater Lynn 0.039 (0.31) 0.333 (2.54)* 0.172 (1.99)* Miami 0.057 (0.47) 0.405 (3.09)** 0.225 (2.65)** Philadelphia 0.128 (1.09) 0.243 (1.76) 0.049 (0.58) (Rensselaer) IMPAIRMENT OF ABILITY TO PERFORM ACTIVITY OF DAILY LIVING (ADL)^{a} Extremely severe 0.404 (3.49)** 0.026 (0.19) 0.025 (0.23) 0.061 (0.44) 0.125 (2.08)* Highly severe 0.226 (2.33)* 0.050 (0.45) 0.107 (1.10) 0.032 (0.27) 0.035 (0.68) Moderately severe 0.304 (3.12)** 0.013 (0.12) 0.098 (0.97) 0.241 (2.00)* 0.010 (0.19) (Mild or none) CONTINENCE^{a} Colostomy bag, device, need help 0.305 (2.37)** 0.432 (3.17)** 0.366 (3.51)** 0.216 (1.66) 0.324 (5.35)** Incontinent 0.018 (0.27) 0.189 (2.44)* 0.096 (1.42) 0.086 (1.06) 0.080 (2.26)* (Continent) REFERRAL SOURCE Hospital or nursing home 0.195 (2.34)* 0.296 (2.90)** 0.179 (2.10)* 0.168 (1.60) 0.193 (4.25)** Home health agency 0.000 (0.00) 0.041 (0.34) 0.051 (0.61) 0.069 (0.69) 0.022 (0.46) (Other) ETHNICITY Black 0.027 (0.29) 0.324 (2.96)** 0.151 (1.83) 0.094 (0.85) 0.115 (2.42)* Hispanic 0.616 (2.46)* 0.507 (1.70) 0.564 (3.39)** 0.540 (2.70)** 0.547 (5.28)** (White) MALE 0.287 (3.85)** 0.224 (2.58)* 0.176 (2.47)* 0.119 (1.33) 0.192 (4.90)** AGE (in years) 0.007 (1.59) 0.011 (2.17)* 0.000 (0.10) 0.007 (1.40) 0.006 (2.47)* COGNITIVE IMPAIRMENT^{b} Severe 0.348 (3.46)** 0.062 (0.54) 0.091 (0.94) 0.270 (2.23)* 0.192 (3.65)** Moderate 0.168 (2.00)* 0.058 (0.60) 0.055 (0.70) 0.173 (1.90) 0.077 (1.80) (Mild or none) INTERVIEWER ASSESSED UNMET NEEDS High 0.045 (0.53) 0.020 (0.21) 0.035 (0.42) 0.149 (1.47) 0.036 (0.81) Medium 0.066 (0.81) 0.035 (0.38) 0.024 (0.31) 0.081 (0.86) 0.020 (0.47) (Low) MEDICAID INSURANCE 0.080 (0.96) 0.085 (0.89) 0.093 (1.13) 0.246 (2.05)* 0.017 (0.39) PROXY USE OF SCREEN 0.081 (0.86) 0.125 (1.15) 0.132 (1.47) 0.086 (0.75) 0.066 (1.35) REGULAR HELP RECEIVED WITH Meal preparation 0.023 (0.19) 0.140 (1.08) 0.039 (0.37) 0.078 (0.60) 0.049 (0.84) Housework, shopping 0.015 (0.13) 0.321 (2.34)* 0.139 (1.27) 0.049 (0.35) 0.121 (2.00)* Taking medicine 0.185 (1.98)* 0.034 (0.31) 0.153 (1.65) 0.089 (0.79) 0.019 (0.38) Medical treatments at home 0.064 (0.81) 0.048 (0.52) 0.110 (1.34) 0.109 (1.11) 0.065 (1.51) Personal care 0.082 (0.76) 0.104 (0.90) 0.050 (0.50) 0.049 (0.37) 0.038 (0.68) INCOME <$500/month 0.199 (1.55) 0.120 (0.77) 0.014 (0.10) 0.115 (0.71) 0.042 (0.59) $500  $999/month 0.105 (0.87) 0.095 (0.64) 0.094 (0.71) 0.055 (0.37) 0.051 (0.76) (>$1,000/month) ON WAITING LIST/APPLIED FOR NURSING HOME 0.555 (5.14)** 0.327 (2.61)** 0.449 (4.01)** 0.616 (4.36)** 0.465 (7.92)** NUMBER OF CONTACTS TO OBTAIN SCREEN INTERVIEW 0.051 (1.63) 0.023 (0.68) 0.82 (2.91)** 0.046 (1.31) 0.056 (3.59)** NUMBER OF MISSING INTEMS ON SCREEN 0.002 (0.09) 0.012 (0.55) 0.022 (1.55) 0.009 (0.53) 0.013 (1.49) EXPECTED TO NEED HELP TO COMPLETE BASELINE 0.016 (0.19) 0.063 (0.63) 0.022 (0.26) 0.044 (0.44) 0.018 (0.40) LIVING ARRANGEMENT^{b} With child 0.044 (0.44) 0.070 (0.60) 0.013 (0.13) 0.045 (0.37) 0.015 (0.27) With other (not spouse or child) 0.213 (1.67) 0.074 (0.50) 0.034 (0.26) 0.089 (0.54) 0.078 (1.13) Alone 0.182 (1.90) 0.119 (1.07) 0.042 (0.44) 0.155 (1.35) 0.094 (1.86) (With spouse, not with child) CONSTANT 1.230 (3.44)** 1.111 (2.62)** 0.707 (1.87) 1.312 (2.98)** 1.277 (5.69)** NUMBER OF CASES 1,779 1,345 1,923 1,279 5,228 PERCENT IN NURSING HOME SAMPLE 54.75 51.45 62.30 48.87 55.18 2 LOG LIKELIHOOD RATIO 185.5 136.0 136.8 115.4 367.9 DEGREES OF FREEDOM 38 38 38 38 45 NOTE: See notes to Table V.6. TABLE V.9: Probit Coefficients for Models of Survivors at 6 Months Being in the Community Analysis Sample at 12 Months, by Treatment Status and Model Screen Variable Basic Model Financial Model Full Sample Treatment Controls Treatment Controls Coefficient tvalue Coefficient t
valueCoefficient t
valueCoefficient t
valueCoefficient t
valueTREATMENT STATUS Basic Model 0.163 (3.72)** Financial Control Model 0.318 (6.20)** SITE Basic Model Baltimore 0.046 (0.35) 0.339 (2.32)* 0.123 (1.19) E. Kentucky 0.305 (2.12)* 0.229 (1.60) 0.295 (2.77)** Middlesex County 0.202 (1.61) 0.445 (3.26)** 0.269 (2.67)** Houston 0.013 (0.08) 0.398 (2.26)* 0.068 (0.62) (S. Maine) 0.009 (0.08) Financial Control Cleveland 0.178 (1.28) 0.182 (1.10) 0.022 (0.22) Greater Lynn 0.212 (1.53) 0.407 (2.79)** 0.050 (0.52) Miami 0.052 (0.39) 0.418 (2.88)** 0.175 (1.88) Philadelphia 0.134 (1.02) 0.289 (1.90) 0.085 (0.92) (Rensselaer) IMPAIRMENT OF ABILITY TO PERFORM ACTIVITY OF DAILY LIVING (ADL)^{a} Extremely severe 0.371 (2.92)** 0.024 (0.16) 0.028 (0.24) 0.142 (0.94) 0.136 (2.06)* Highly severe 0.198 (1.93) 0.015 (0.12) 0.017 (0.16) 0.209 (1.62) 0.098 (1.77) Moderately severe 0.236 (2.29)* 0.034 (0.27) 0.053 (0.51) 0.122 (0.96) 0.110 (2.00) (Mild or none) CONTINENCE^{a} Colostomy bag, device, need help 0.005 (0.03) 0.321 (1.95) 0.273 (2.22)* 0.207 (1.36) 0.206 (2.91)** Incontinent 0.010 (0.14) 0.267 (3.13)** 0.194 (2.71)** 0.064 (0.73) 0.123 (3.19)** (Continent) REFERRAL SOURCE Hospital or nursing home 0.044 (0.47) 0.012 (0.10) 0.007 (0.07) 0.127 (1.09) 0.040 (0.77) Home health agency 0.186 (1.63) 0.097 (0.72) 0.040 (0.44) 0.053 (0.48) 0.080 (1.52) (Other) ETHNICITY Black 0.079 (0.78) 0.448 (3.67)** 0.140 (1.56) 0.164 (1.34) 0.190 (3.66)** Hispanic 0.258 (1.07) 0.862 (2.67)** 0.621 (3.38)** 0.216 (1.05) 0.504 (4.67)** (White) MALE 0.176 (2.13)* 0.195 (1.94) 0.037 (0.45) 0.042 (0.42) 0.087 (1.98)* AGE (in years) 0.008 (1.76) 0.020 (3.63)** (0.011) (2.44)* 0.003 (0.51) 0.010 (4.16)** COGNITIVE IMPAIRMENT^{b} Severe 0.291 (2.62)** 0.223 (1.66) 0.149 (1.39) 0.213 (1.60) 0.224 (3.82)** Moderate 0.208 (2.24) 0.014 (0.13) 0.045 (0.53) 0.069 (0.68) 0.092 (1.96)* (Mild or none) INTERVIEWER ASSESSED UNMET NEEDS High 0.047 (0.51) 0.060 (0.55) 0.049 (0.53) 0.272 (2.43)* 0.042 (0.86) Medium 0.078 (0.86) 0.138 (1.32) 0.148 (1.77) 0.092 (0.90) 0.031 (0.68) (Low) MEDICAID INSURANCE 0.259 (2.84)** 0.047 (0.44) 0.058 (0.64) 0.288 (2.57)* 0.048 (0.99) PROXY USE OF SCREEN 0.061 (0.59) 0.086 (0.72) 0.159 (1.62) 0.019 (0.15) 0.042 (0.78) REGULAR HELP RECEIVED WITH Meal preparation 0.094 (0.78) 0.042 (0.31) 0.059 (0.54) 0.094 (0.68) 0.054 (0.88) Housework, shopping 0.179 (1.49) 0.106 (0.73) 0.003 (0.02) 0.081 (0.55) 0.052 (0.82) Taking medicine 0.065 (0.64) 0.238 (1.94) 0.018 (0.18) 0.186 (1.54) 0.048 (0.90) Medical treatments at home 0.026 (0.29) 0.130 (1.24) 0.031 (0.35) 0.215 (2.04)* 0.056 (1.18) Personal care 0.113 (0.99) 0.002 (0.02) 0.050 (0.48) 0.118 (0.85) 0.056 (0.97) INCOME <$500/month 0.162 (1.15) 0.121 (0.68) 0.235 (1.51) 0.244 (1.38) 0.074 (0.94) $500  $999/month 0.236 (1.78) 0.036 (0.21) 0.254 (1.77) 0.103 (0.63) 0.107 (1.46) (>$1,000/month) ON WAITING LIST/APPLIED FOR NURSING HOME 0.635 (5.31)** 0.373 (2.60)** 0.606 (4.81)** 0.676 (4.17)** 0.554 (8.42)** NUMBER OF CONTACTS TO OBTAIN SCREEN INTERVIEW 0.056 (1.63) 0.032 (0.82) 0.029 (0.95) 0.109 (2.72)** 0.050 (2.88)** NUMBER OF MISSING INTEMS ON SCREEN 0.005 (0.22) 0.001 (0.03) 0.020 (1.30) 0.031 (1.67) 0.014 (1.59) EXPECTED TO NEED HELP TO COMPLETE BASELINE 0.123 (1.28) 0.084 (0.73) 0.015 (0.17) 0.047 (0.43) 0.037 (0.75) LIVING ARRANGEMENT^{b} With child 0.141 (1.26) 0.212 (1.60) 0.140 (1.28) 0.235 (1.71) 0.003 (0.05) With other (not spouse or child) 0.021 (0.15) 0.009 (0.05) 0.173 (1.22) 0.149 (0.85) 0.080 (1.05) Alone 0.037 (0.36) 0.124 (0.99) 0.055 (0.53) 0.094 (0.75) 0.038 (0.69) (With spouse, not with child) CONSTANT 1.412 (3.60)** 2.145 (4.46)** 1.170 (2.86)** 1.064 (2.17)* 1.026 (5.04)** NUMBER OF CASES 1,472 1,091 1,600 1,065 6,326 PERCENT IN NURSING HOME SAMPLE 56.93 50.60 60.88 48.92 55.15 2 LOG LIKELIHOOD RATIO 125.6 131.3 95.3 96.1 524.5 DEGREES OF FREEDOM 38 38 38 38 45 NOTE: See notes to Table V.6. It appears then that the relationships between screen characteristics and inclusion in the analysis samples are not markedly different across experimental groups or models. Comparison of R^{2} statistics, likelihood ratios, and distributions of predicted probabilities for the separate models of attrition to those for the pooled model indicates that separate models of attrition for the different groups do not lead to noticeably more accurate predictions of the probability of attrition. Again, it appears that attrition is not closely tied to sample members' characteristics.
This finding does not imply that the second assumption of the pooled approach is correct, howeveri.e., that the correlation between unobserved factors affecting attrition and outcomes is the same across models and treatment groups. Hence, we proceed to the second stage of this more general approach, including in the outcome regressions separate attrition correction terms for each of the four groups.
Table V.10 presents estimates of channeling's impact on nursing home use and expenditures before and after correction for attrition bias. There are two corrected estimates presented for comparison. Estimate 1 is based on the more restrictive model of sample selection described in Chapter III and presented earlier in this chapter (Table V.3). We concluded earlier that these estimates offered no evidence of attrition bias in channeling's impact on nursing home use and expenditures. Estimate 2 is based on the more general model of sample selection described by equation (11). Corresponding to each corrected impact estimate is an estimate of the correlation between unobserved factors that influence sample selection and unobserved factors that influence the outcome. These are designated as "'Rho 1" and "Rho 2," respectively. Note that there is a Rho 2 estimate of correlation for each treatment status/model subgroup since the corrected outcome equation contained a correction factor for each subgroup.
For the 1 to 6 month period, the rhos are all small and statistically insignificant. Thus, the large changes in some of these impact estimates after correction for attrition (e.g., nursing home expenditures in the basic model) should be ignored. However, the 7 to 12 month correlations are large (and negative) for the treatment groups in both models for all three nursing home outcomes, and statistically significant in 3 cases. These results suggest that treatment group members who were excluded from the 12 month sample were more likely to use nursing home services during this period, implying that the treatment group use of nursing homes is underestimated. This in turn would imply that the treatment/control differences is underestimated. This is reflected in the change in estimates at 12 months from negative (a reduction in nursing home use) before correction for attrition to positive, after the more general correction model is employed. However, none of the impact estimates for the 7 to 12 month period, either with or without correction for attrition bias, are significantly different from zero. Thus; there is no evidence that our inference about the lack of channeling impacts on nursing home use, based on the nursing home samples, is incorrect because of attrition.
TABLE V.10: Impacts of Channeling on Nursing Home Use and Expenditures, Estimated With and Without Corrections for Attrition Bias Basic Model Financial Model Rho 1^{a} Rho 2^{b} Sample
SizeUncorrected
EstimateCorrected
Estimate
1Corrected
Estimate
2Uncorrected
EstimateCorrected
Estimate
1Corrected
Estimate
2Basic
TreatmentsBasic
ControlsFinancial
TreatmentsFinancial
ControlsANY NURSING HOME ADMISSION LAST SIX MONTHS (percent) Months 1 to 6 0.52
(0.37)0.34
(0.23)4.05
(1.19)0.37
(0.27)0.08
(0.05)0.12
(0.03)0.07
(0.37)0.25
(1.38)0.08
(0.44)0.04
(0.55)0.06
(0.32)4,593 Months 7 to 12 2.23
(1.88)3.03*
(2.20)1.40
(0.43)0.29
(0.25)1.24
(0.70)0.97
(0.28)0.27
(1.17)0.41
(1.72)0.27
(1.38)0.03
(0.11)0.07
(0.35)4,752 NUMBER OF NURSING HOME DAYS LAST SIX MONTHS Months 1 to 6 2.36
(1.93)1.98
(1.54)2.24
(0.74)1.14
(0.94)0.17
(0.10)0.79
(0.25)0.18
(0.89)0.14
(0.78)0.21
(1.17)0.13
(0.58)0.06
(0.31)4,593 Months 7 to 12 1.19
(0.63)2.61
(1.19)5.84
(1.13)2.19
(1.15)4.94
(1.75)3.09
(0.57)0.31
(1.32)0.55*
(2.30)0.10
(0.52)0.59*
(2.15)0.11
(0.55)4,752 TOTAL NURSING HOME EXPENDITURES LAST SIX MONTHS Months 1 to 6 165*
(2.15)136
(1.67)34
(0.18)8
(0.11)68
(0.66)123
(0.63)0.22
(1.11)0.01
(0.05)0.24
(1.31)0.11
(0.49)0.08
(0.41)4,593 Months 7 to 12 58
(0.56)144
(1.20)124
(0.44)103
(0.99)270
(1.74)226
(0.76)0.34
(1.46)0.40
(1.68)0.16
(0.83)0.57*
(2.08)0.07
(0.33)4,752 NOTE: Tvalues are reported in parentheses. For corrected estimate 1, these are computed from standard errors which have been adjusted for heteroskedasticity using methods developed by Heckman (1979) and Greene (1981). For corrected estimate 2, these are simply the unadjusted tstatistic for the treatment status coefficient and are likely to be close to those adjusted for heteroskedasticity.  Rho is the estimated correlation between the disturbance terms in the impact regression (µ_{1}) and the attrition equation (µ_{2}), obtained by dividing the estimated coefficient on the attrition correction term by the estimated standard error of the disturbance term in the outcome equation. The tvalue in this column is the tvalue of the coefficient on the correction term in the outcome equation.
* Statistically significant at the 5 percent level for a twotailed test.
** Statistically significant at the 1 percent level for a twotailed test.TABLE V.11: Impacts of Channeling on Formal Care Use, Estimated With and Without Corrections for Attrition Bias Basic Model Financial Model Rho 1^{a} Rho 2^{b} Sample
SizeUncorrected
EstimateCorrected
Estimate
1Corrected
Estimate
2Uncorrected
EstimateCorrected
Estimate
1Corrected
Estimate
2Basic
TreatmentsBasic
ControlsFinancial
TreatmentsFinancial
ControlsWHETHER RECEIVED INHOME CARE FROM VISITING FORMAL CAREGIVER DURING REFRENCE WEEK (percent) 6 Months After Randomization 10.7**
(5.15)9.9**
(4.57)12.4
(1.85)22.8**
(10.84)19.8**
(6.93)24.1**
(3.34)0.34
(1.51)0.09
(0.49)0.03
(0.16)0.41*
(1.97)0.26
(1.27)3,351 12 Months After Randomization 10.0**
(4.20)11.3**
(4.24)10.3
(1.38)20.1**
(8.48)22.1**
(7.36)25.4**
(2.83)0.25
(1.06)0.39
(1.80)0.35
(1.74)0.14
(0.58)0.05
(0.23)2,786 TOTAL HOURS OF VISITS FROM VISITING FORMAL CAREGIVERS 6 Months After Randomization 0.82
(0.99)0.95
(1.11)8.33**
(3.15)7.40**
(8.91)7.84**
(6.92)6.81*
(2.38)0.13
(0.57)0.27
(1.40)0.40
(1.93)0.07
(0.34)0.01
(0.03)3,351 12 Months After Randomization 1.74
(1.77)1.94
(1.77)3.11
(1.01)6.35**
(6.48)6.65**
(5.38)5.89
(1.60)0.10
(0.41)0.17
(0.80)0.23
(0.92)0.22
(0.92)0.21
(0.97)2,786 NUMBER OF VISITS FROM VISITING FORMAL CAREGIVERS 6 Months After Randomization 0.48**
(3.10)0.52*
(3.22)0.73
(1.46)2.15**
(13.75)2.28**
(10.68)2.14**
(3.98)0.20
(0.88)0.09
(0.45)0.03
(0.15)0.13
(0.63)0.10
(0.46)3,351 12 Months After Randomization 0.55**
(3.01)0.71**
(3.47)0.33
(0.56)2.12**
(11.56)2.37**
(10.22)2.14**
(3.09)0.40
(1.74)0.19
(0.87)0.07
(0.34)0.08
(0.33)0.05
(0.26)2,786 NOTE: See notes to Table V.10. TABLE V.12: Impacts of Channeling on Informal Care Use, Estimated With and Without Corrections for Attrition Bias Basic Model Financial Model Rho 1^{a} Rho 2^{b} Sample
SizeUncorrected
EstimateCorrected
Estimate
1Corrected
Estimate
2Uncorrected
EstimateCorrected
Estimate
1Corrected
Estimate
2Basic
TreatmentsBasic
ControlsFinancial
TreatmentsFinancial
ControlsWHETHER RECEIVED INHOME CARE FROM VISITING INFORMAL CAREGIVER DURING REFERENCE WEEK (percent) 6 Months After Randomization 2.2
(0.90)1.7
(0.69)16.0
(2.08)4.8
(1.97)3.2
(0.96)0.4
(0.05)0.16
(0.71)0.33
(1.74)0.10
(0.50)0.25
(1.20)0.33
(1.60)3,351 12 Months After Randomization 0.7
(0.27)1.4
(0.48)19.3
(2.30)3.9
(1.46)0.5
(0.14)2.0
(0.20)0.38
(1.67)0.58**
(2.70)0.03
(0.17)0.13
(0.53)0.06
(0.28)2,786 TOTAL HOURS OF VISITS FROM VISITING INFORMAL CAREGIVERS 6 Months After Randomization 1.11
(1.04)1.36
(1.23)2.84
(0.84)0.79
(0.75)1.65
(1.14)3.20
(0.87)0.20
(0.87)0.19
(0.99)0.06
(0.280.22
(1.07)0.01
(0.06)3,351 12 Months After Randomization 0.19
(0.18)0.56
(0.47)0.55
(0.16)0.11
(0.10)0.47
(0.35)0.95
(0.23)0.17
(0.70)0.03
(0.16)0.00
(0.02)0.03
(0.11)0.05
(0.24)2,786 NUMBER OF VISITS FROM VISITING INFORMAL CAREGIVERS 6 Months After Randomization 0.20
(0.63)0.05
(0.15)2.19*
(2.17)0.21
(0.65)0.31
(0.72)0.53
(0.48)0.39
(1.76)0.53**
(2.81)0.04
(0.21)0.47*
(2.26)0.28
(1.36)3,351 12 Months After Randomization 0.15
(0.49)0.33
(0.98)1.22
(1.29)0.47
(1.56)0.19
(0.49)0.43
(0.38)0.28
(1.22)0.23
(1.09)0.15
(0.75)0.15
(0.65)0.11
(0.53)2,786 NOTE: See notes to Table V.10. Table V.11 presents estimates of channeling impacts on formal care for the incommunity sample, with and without the more general correction for attrition, and repeats the results from the simpler, more restrictive method of controlling for attrition for ease of comparison. Examining the estimated correlations ("Rho 2"), we find a few estimates that are substantial, but only one which is statistically significant. Furthermore, there appears to be no pattern to these correlations. For example, the one significant correlation coefficient is for whether received formal care for treatment group members in the financial control model at 12 months. However, the estimated correlations of the attrition disturbance with the disturbances in both the hours of care and number of visits equations are small and of the opposite sign. The correlations at 12 months for this group are also small for all 3 formal care variables. The same lack of pattern exists for other cases where the estimated rho is large.
There are a few other estimates in this table that warrant further discussion before turning to the informal care results for this sample. First, there are several instances where the estimate of channeling impacts controlling for attrition bias is not statistically significant, but the unadjusted estimate is significant. However, in each case the estimated impact is about the same size (very large) before and after controlling for the possible effects of attrition. The drop in statistical significance is due to the increased variance that results from adding the attrition correction terms to the regression equation. Given the conclusion that there is no evidence of attrition bias, the appropriate estimate is the unadjusted one, which is highly significant.
The other result to note in this table is the estimated impact on hours of care at month 6 in the basic model. The estimate, which is very near zero and insignificant before controlling for possible attrition bias, is very large and highly significant after attrition is controlled for. This results from the estimated rhos for this outcome for treatments and controls in the basic model at 6 months, which are both large but of opposite signs. The estimates imply that treatment group use of services was understated because of attrition, whereas control group use was overestimated (e.g., above average users of services may have dropped out of the sample if they were in the treatment group but remained in if in the control group). Given that identification of such different patterns of attrition for the two groups, if they existed, was precisely the reason for pursuing the more general model, the results are of particular interest. However, the fact that the estimated rhos for both groups change sign at 12 months, and the lack of a similar pattern of results for the other formal care outcomes suggest that the large change at 6 months in the basic model is a statistical fluke, due to chance, rather than real evidence of attrition bias. Furthermore, the pattern of attrition implied by these estimates differs totally from the potential pattern of attrition for this model and time period implied by Medicare comparisons of Chapter IV. Those comparisons suggested no bias in control group mean use at 6 months, but overestimation of use by the treatment group. This is in marked contrast to the results here. Hence, there is no pattern of results across procedures either.
Finally, in Table V.12, we examine the results for informal care. Here we find persistent evidence of a positive correlation between disturbances in the attrition and outcome equations for treatment group members in both models at 6 months, and no evidence of substantial correlations for the control group. This leads to large changes in impact estimates on whether received formal services and number of visits. Prior to correction for bias we find some evidence of small reductions in informal care due to channeling, although only the financial control model estimate for whether received visiting informal care at 6 months was statistically significant. After adding the terms to control for possible bias we find that in the basic model the estimates imply that channeling led to very large reductions in the percent of sample members receiving informal care, but had no impact in the financial control model. Thus, the new estimates imply that the reduction due to channeling on the percent receiving informal care was grossly understated in the basic model because of attrition but substantially overstated in the financial control model.
These results seem implausible, for several reasons:

The financial control model was the one with the large treatment/control differences in response rates, yet we find the biggest change in impacts for the basic model.

We find no evidence of bias for formal care outcomes for these same samples. If informal care impact estimates were biased by attrition to such a degree, we would expect formal care impact estimates to he biased as well (and probably other outcomes as well).

The opposite direction of the implied bias in the two models seems unlikely.

The correlations at 12 months not are consistent with those at 6 months (4 out of the 6 correlations for treatments are negative at 12 months, but all are positive at 6 months).

The attrition corrected estimates are too large to be plausible, especially those for whether receive informal care (the estimated reduction in informal care is larger than the estimated increases in formal care brought about by channeling).

There are only two instances where the estimated correlation of disturbances is statistically significant and the interpretation of the results changes when the new attrition corrected impact estimates are substituted for the unadjusted estimates.

If channelinginduced reductions in the percent receiving informal care were as large as estimated in the basic model, we would expect this to result in large reductions in the number of visits and hours. However, these estimates were not statistically significant in 3 of the 4 cases.

The implications of the adjusted estimates are that informal care was greatly reduced because of channeling in basic sites, but not at all in financial control sites. Yet, if reductions in informal care were due to substitution of formal for informal care, as was hypothesized, we would expect the substitution to be much greater in the financial control model, since that is where the largest increases in formal care are observed.
These arguments suggest that the large, significant estimates of rho and the substantial differences observed for the basic model at 6 months between estimated impacts on informal care before and after controlling for attrition effects are anomalous, and are not indicative of attrition bias but rather appear to be reflecting other relationships between screen characteristics and outcomes. The estimates obtained from the model without controlling for possible effects of attrition are much more plausible and consistent across outcome measures, time periods, and models.



D. Sensitivity Tests

In addition to the heuristic approach of comparing impacts on Medicarecovered outcomes for full and analysis samples and the statistical approach of determining whether attrition bias exists, we also conducted some sensitivity tests as a way of assessing the effects of attrition. These results, presented in Wooldridge and Schore (forthcoming, Appendix E), show how estimates of channeling impacts on nursing home use would have changed if the full sample were available for analysis, under alternative assumptions about use of nursing homes by sample members not included in the nursing home sample.^{28} Three different procedures for imputing nursing home use to dropouts from the nursing home sample were employed:

Overall mean usage levels for treatment and control groups were reestimated by forming a weighted average of mean use by sample members who survived the period (and had available data on nursing home use) and sample members who died within the period (but for whom data on use were available). The weights used were P and 1P, respectively, where P was the proportion of the full sample that survived the entire period. This new estimate was intended to adjust for the underrepresentation in the nursing home sample of those who died within the analysis period, since it was felt that use by this group could be quite different from use by survivors.

Estimates of mean use by nonrespondents were obtained that reflected observed differences between responders and nonresponders on screen characteristics.

Estimates of mean use by nonrespondents were obtained that also reflected differences between respondents and nonrespondents on hospital use and Medicarecovered nursing home use during the analysis period for which total nursing home use was unknown.
The results of this analysis are reported in Wooldridge and Schore (forthcoming) and are simply summarized here. The alternative estimates were only slightly different from the original estimates obtained on the nursing home sample. The reasons for this are that: (1) contrary to expectations, those who die within the period generally had slightly fewer nursing home days on average than those who survived the period, for all four treatment/model groups, and (2) the observed characteristics (including prerandomization characteristics and concurrent hospital and nursing home use recorded in Medicare claims) of those in the nursing home sample do not differ greatly from the observed characteristics of those who were not in this sample. The average number of nursing home days for those who die within a period and those who survive the period are displayed below for the first six month period for the nursing home sample.
Survivors Decedents Treatment Group: Basic Model 9.9 6.4 Financial Control Model 8.6 9.0 Control Group: Basic Model 12.3 9.6 Financial Control Model 10.1 5.3 The similarity of use for decedents and survivors for both treatment and control groups suggests that the substantial underrepresentation of decedents in the nursing home sample does not lead to bias in the estimate means or impacts. Thus, the first alternative estimate must yield means and impact estimates that are not substantially different from those obtained previously. The similarity of most screen characteristics for persons included in and excluded from the nursing home sample resulted in imputed means for nursing home use for those excluded from the nursing home sample that were quite similar to those observed for the nursing home sample; hence, the second alternative yielded no substantive changes in estimates over the first alternative. Finally, those included in and those excluded from the nursing home sample were quite similar in their use of hospital and nurisng home days derived from Medicare claims; hence, estimates under the third alternative were relatively unchanged from those found using the other two approaches.
These results suggest that attrition, and most importantly, the consequent underrepresentation of persons who die within the analysis period, does not greatly distort estimates of channeling impacts on nursing home use. However, it may be the case that persons that were not included in the nursing home sample have very different nursing home use, even from those persons in the sample with similar characteristics. Even though the observed use of hospital and nursing home days derived from Medicare claims was similar for those included in and those excluded from the nursing home samples, this is not a guarantee that unobserved nursing home use that was paid for out of pocket or by Medicaid (the major payors) would be similar for those included in and those excluded from the nursing home samples. However, since actual nursing home values are unobserved for a portion of the sample, the approach of looking for and exploiting known differences between persons included in and excluded from the analysis sample is the only way to project what the use of those not in the sample actually was. It seems unlikely that those not in the sample would be so similar to those included on so many observed characteristics, some of which are known to affect or be correlated with nursing home use, and yet so different on unobserved characteristics that the results are seriously biased by the omission of these observations.


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