Final Report on the Effects of Sample Attrition on Estimates of Channeling's Impacts. C. A More General Model of Attrition Bias

01/13/1986

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 (TB and TF) 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 models--one 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 + Mii,

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 + M11 + M22 + M33
+ M44,

where Mi = 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, Mi = 0. Thus, each sample member now has 4 M terms, 3 of which are set to 0. Coefficients on the Mi'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 Medicare-covered 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
  • In-community 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 6-Month Nursing Home Sample, by Treatment Status and Model
Screen Variable Basic Model Financial Model Full Sample
  Treatment     Controls     Treatment     Controls     Coefficient     t-value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
TREATMENT 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)                    
CONTINENCEa
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 IMPAIRMENTb
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 ARRANGEMENTb
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
R2 0.087 0.105 0.063 0.090 0.056
CHI-SQUARE STATISTICc 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.
  1. Missing values for this variable were replaced by the mean.
  2. 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.
  3. The chi-square 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 two-tailed test.
** Statistically significant at the 1 percent level for a two-tailed test.


TABLE V.7: Probit Coefficients for Models of Inclusion in the 12-Month Nursing Home Sample, by Treatment Status and Model
Screen Variable Basic Model Financial Model Full Sample
  Treatment     Controls     Treatment     Controls     Coefficient     t-value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
TREATMENT 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)                    
CONTINENCEa
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 IMPAIRMENTb
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 ARRANGEMENTb
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
R2 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 six-month 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 Chi-square 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 Chi-square 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 R2 statistics for the individual probits are not much larger than the R2 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 in-community 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 six-month analysis period were included in the full sample upon which the probit models were estimated. Thus, the six-month probit used the full screen sample, since all sample members were alive at random assignment, but the twelve-month probit used only those screen sample members who were alive on their six-month 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     t-value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
TREATMENT 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)                    
CONTINENCEa
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 IMPAIRMENTb
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 ARRANGEMENTb
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     t-value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
  Coefficient   t-
  value  
TREATMENT 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)                    
CONTINENCEa
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 IMPAIRMENTb
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 ARRANGEMENTb
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 R2 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, however--i.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 1a   Rho 2b   Sample  
Size
  Uncorrected  
Estimate
  Corrected  
Estimate
1
  Corrected  
Estimate
2
  Uncorrected  
Estimate
  Corrected  
Estimate
1
  Corrected  
Estimate
2
Basic
  Treatments  
Basic
  Controls  
  Financial  
Treatments
  Financial  
Controls
ANY 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: T-values 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 t-statistic for the treatment status coefficient and are likely to be close to those adjusted for heteroskedasticity.
  1. Rho is the estimated correlation between the disturbance terms in the impact regression (µ1) and the attrition equation (µ2), 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 t-value in this column is the t-value of the coefficient on the correction term in the outcome equation.

* Statistically significant at the 5 percent level for a two-tailed test.
** Statistically significant at the 1 percent level for a two-tailed test.


TABLE V.11: Impacts of Channeling on Formal Care Use, Estimated With and Without Corrections for Attrition Bias
  Basic Model Financial Model   Rho 1a   Rho 2b   Sample  
Size
  Uncorrected  
Estimate
  Corrected  
Estimate
1
  Corrected  
Estimate
2
  Uncorrected  
Estimate
  Corrected  
Estimate
1
  Corrected  
Estimate
2
Basic
  Treatments  
Basic
  Controls  
  Financial  
Treatments
  Financial  
Controls
WHETHER RECEIVED IN-HOME 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 1a   Rho 2b   Sample  
Size
  Uncorrected  
Estimate
  Corrected  
Estimate
1
  Corrected  
Estimate
2
  Uncorrected  
Estimate
  Corrected  
Estimate
1
  Corrected  
Estimate
2
Basic
  Treatments  
Basic
  Controls  
  Financial  
Treatments
  Financial  
Controls
WHETHER RECEIVED IN-HOME 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
(0.28
0.22
(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 in-community 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 channeling-induced 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.

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