Survival Analysis Using Auxiliary Variables Via Multiple Imputation, with Application to AIDS Clinical Trial Data

Abstract

We develop an approach, based on multiple imputation, to using auxiliary variables to recover information from censored observations in survival analysis. We apply the approach to data from an AIDS clinical trial comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable. To facilitate imputation, a joint model is developed for the data, which includes a hierarchical change-point model for CD4 counts and a time-dependent proportional hazards model for the time to AIDS. Markov chain Monte Carlo methods are used to multiply impute event times for censored cases. The augmented data are then analyzed and the results combined using standard multiple-imputation techniques. A comparison of our multiple-imputation approach to simply analyzing the observed data indicates that multiple imputation leads to a small change in the estimated effect of ZDV and smaller estimated standard errors. A sensitivity analysis suggests that the qualitative findings are reproducible under a variety of imputation models. A simulation study indicates that improved efficiency over standard analyses and partial corrections for dependent censoring can result. An issue that arises with our approach, however, is whether the analysis of primary interest and the imputation model are compatible.

Survival analysis using auxiliary variables via non‐parametric multiple imputation

“…For both the treatment and placebo groups, the imputation analyses produce very similar estimated survival to the PO method. This agrees with the conclusion in Reference [14].…”

“…We apply the non-parametric multiple imputation schemes and the IPCW method to AIDS data from the ACTG-019 clinical trial [14,27]. There are 1337 subjects, with 428 subjects in the placebo arm and 909 subjects in the treated arm, where this latter arm is a combination of two doses of ZDV.…”

“…For example, Schenker and Taylor [13] employed three auxiliary variables to determine the distribution of residual times from which to impute a time of AIDS. Faucett et al [14] used a parametric joint longitudinal-survival model to impute event times in an AIDS clinical trial. In this research, we propose using the auxiliary variables to deÿne a nearest neighbourhood of similar observations for each censored case, and then generate imputes from this set of neighbours.…”

Basic Concepts and Methods for Joint Models of Longitudinal and Survival Data

“…These articles include DeGruttola and Tu, 1 Tsiatis et al, 2 Faucett and Thomas, 3 Faucett et al, 4 LaValley and DeGruttola, 5 Wulfsohn and Tsiatis, 6 Pawitan and Self, 7 Taylor et al, 8 Brown et al, 9 Wang and Taylor, 10 and Chi and Ibrahim. 11 Other approaches considering a multivariate longitudinal measure include Henderson et al, 12 Xu and Zeger, 13,14 and Song et al…”

Bayesian Estimator of a Change Point in the Hazard Function

“…Therefore, obtaining a correct estimate of the change point plays an important role in medical and biological researches. Some recent studies in these fields are given as Gupta et al [1], Tabnak et al [2], Faucett et al [3], Gijbels and Gurler [4], Lin [5], Daniel and Nader [6], Karasoy and Kadilar [7], etc.…”