Estimating Mediated Effects with Survival Data

Summary

Mediation analyses help identify variables in the causal sequence relating predictor variables to outcome variables. In many studies, outcomes are time until an event occurs and survival analyses are applied. This study examines the point and interval estimates of the mediated effect using two methods of survival analyses: the log-survival time and log-hazard time models. The results show that, under the condition of no censored data, the assumption that mediated effects calculated by the product of coefficients method (αß) and those calculated by the difference in coefficients method (τ − τ’) are identical does apply to log-survival time survival analyses but not to log-hazard time survival analyses. The standard error of the mediated effect can be calculated with the delta formula, the second order Taylor series formula, and the unbiased formula. Consistent with ordinary least squares regression, the three formulas yield similar results. Although the log-survival time model and the log-hazard time model utilize different estimation methods, the results of the significant tests, using the ratio of αß to se_αß, were comparable between the two methods. However, the significance tests based on the empirical standard error appear to be more conservative than those from the three analytical standard errors.