Survival analysis via nonparametric multiple imputation.

In survival analysis, censored observations can be regarded as missing event time data. For analysis of censored survival data, we propose a direct approach, multiple imputation, of the event times followed by analysis of the completed data. This approach can handle both interval-censored and right-censored data. For right censored data, we propose two nonparametric multiple imputation schemes, risk set imputation and Kaplan-Meier imputation, which both share common ideas with the redistribute to the right algorithm. In one sample situations, we show that with a large number of imputes the imputation methods will reproduce the Kaplan-Meier estimates. In interval-censored data situations, we propose a nonparametric multiple imputation scheme, NPMLE imputation. The imputation methods convert interval-censored data problems to completed data problems, which enables estimates of measures of uncertainty to be more easily obtained. Besides the primary endpoint of interest, in many medical studies there are other auxiliary variables, e.g. biomarkers, obtained about subjects which are often associated with the event time. For the goal of estimating the marginal survival distribution; these biomarkers may provide some additional information on primary endpoint occurrence times for censored observations. We extend the imputation methods to incorporate information from the auxiliary variables to achieve this goal. To conduct the imputation, we use two working proportional hazards models to choose a set of nearest neighbors for each censored observation. These sets of neighbors are called the imputing risk sets. The imputation schemes are then conducted on the imputing risk sets. This approach can handle complex structures of auxiliary variables. We show that multiple imputation-based methods have a double robustness property and with a large number of imputes will reproduce weighted Kaplan-Meier estimates in a situation with a categorical auxiliary variable. In addition, in simulation studies we show that the use of multiple imputation methods can improve the efficiency of estimators and reduce bias due to dependent censoring. These findings of improved efficiency and reduced bias can be seen in both interval-censored and right-censored data. The methods are applied to AIDS data sets.Ph.D.Pure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123864/2/3106083.pd