To adjust expected community long term care costs for hospital use, the expected proportion of time outside of a nursing home that an individual can be expected to spend in a hospital, equivalent to the probability of being in hospital conditional on not being in a nursing home, was estimated. Because most observed values for days spent in hospital over the 12-month study period are zeros, a tobit model was used to obtain predicted values. Only survivors over the entire 12 months with a complete nursing home indicator time series were used in the estimation because the level of hospital use by those near death so skewed the distribution that the tobit estimation was unacceptably unstable.
For each of the individuals that remained, two variables were created, total community (i.e., non-nursing home) days and total community days spent in the hospital. To estimate total community days, we multiplied 30.4 times the number of months in which the individual spent no time in a nursing home. To determine total community days spent in the hospital we counted the number of hospital days in months in which the individual spent no time in a nursing home. Observations were dropped if (1) total community days was missing; (2) total community days spent in the hospital was missing; or (3) total community days did not exceed total community days spent in the hospital (indicating a coding error).
For the 2,654 observations that remained, the ratio of total community days spent in a hospital to total community days was formed. Using the tobit procedure available in SAS, the ratio was regressed on: a constant term, the treatment group binary, age, marital status, a binary variable for living alone, informal care hours, number of visits to a physician over the previous two months, self-perceived health, indicators for nursing home application and being on a nursing home waiting list, life satisfaction, cognitive and functional impairment indicators, an unmet needs indicator, and nine of the ten site indicators. A predicted value for the ratio was calculated for each of the 3,446 individuals in the main data set using the coefficients from this regression. The maximum value of the predicted ratio (proportion of community time spent in hospital) was 0.18, the minimum value was zero, and the mean value was 0.02. Hence the estimated, probability of being in the community (and not in hospital) conditional on not being in nursing home care was on average .98, ranging from .82 to 1.0. Call this probability g. Then by the joint probability law, the probability of a surviving individual being outside a nursing home but also not in the hospital is given by g (1-). It is this latter term which is used to weight community care costs in expressions (5) and (8) in the text for the empirical simulations.