The analysis is straightforward. For each outcome we estimate the bivariate association between each indicator of caregiving arrangements (indicating one of the analytic hypotheses) and the outcome. Our estimate of association is the odds ratio:
|OR = P(O) / X = CARE
P(O) / X = NO CARE
|where|| X = an indicator of caregiving
0 = an outcome
In a simple logistic regression of outcome on the caregiving indicator, the estimated regression coefficient will be the logarithm of the odds ratio 1n(OR). The odds ratio is obtained through a simple transformation. The significance test of 1n(OR), a z-test based on the ratio 1n(OR) over its standard error, is equivalent to the significance test of OR.
We then employ a multivariate analysis to determine whether any of the set of confounders appreciably alters the estimated association between caregiving arrangements and outcome. In the case of multivariate logistic regression the 1n(OR) and OR associated with caregiving is a net value adjusted for the other variables in the equation.
Because there were many potential confounders, we undertook several analytic steps to trim their number. First we regressed the outcome on the set of health variables. We eliminated variables that were not significantly related to the outcome. We tested to assure that the deletion of the predictors did not significantly diminish the model chi-square. We repeated these steps for the social and demographic variables. We then combined the trimmed social and health models and trimmed this model. This was done for both mortality and institutionalization with differing results.