Multiple imputation for interval censored data with auxiliary variables

We propose a non-parametric multiple imputation scheme, NPMLE imputation, for the analysis of interval censored survival data. Features of the method are that it converts interval-censored data problems to complete data or right censored data problems to which many standard approaches can be used, and that measures of uncertainty are easily obtained. In addition to the event time of primary interest, there are frequently other auxiliary variables that are associated with the event time. For the goal of estimating the marginal survival distribution, these auxiliary variables may provide some additional information about the event time for the interval censored observations. We extend the imputation methods to incorporate information from auxiliary variables with potentially complex structures. To conduct the imputation, we use a working failure-time proportional hazards model to define an imputing risk set for each censored observation. The imputation schemes consist of using the data in the imputing risk sets to create an exact event time for each interval censored observation. In simulation studies we show that the use of multiple imputation methods can improve the efficiency of estimators and reduce the effect of missing visits when compared to simpler approaches. We apply the approach to cytomegalovirus shedding data from an AIDS clinical trial, in which CD4 count is the auxiliary variable. Copyright © 2006 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/55943/1/2581_ftp.pd

Survival Analysis Using Auxiliary Variables via Nonparametric Multiple Imputation

We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variables to recover information for censored observations. To conduct the imputation, we use two working survival models to de fine a nearest neighbour imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, two non-parametric multiple imputation methods are considered: risk set imputation, and Kaplan–Meier imputation. For both methods a future event or censoring time is imputed for each censored observation. With a categorical auxiliary variable, we show that with a large number of imputes the estimates from the Kaplan–Meier imputation method correspond to the weighted Kaplan–Meier estimator. We also show that the Kaplan–Meier imputation method is robust to mis-speci cation of either one of the two working models. In a simulation study with time independent and time-dependent auxiliary variables, we compare the multiple imputation approaches with an inverse probability of censoring weighted method. We show that all approaches can reduce bias due to dependent censoring and improve the e ciency. We apply the approaches to AIDS clinical trial data comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable. Copyright 2005 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91939/1/Hsu Stat in Med paper 2006.pd

Nonparametric comparison of two survival functions with dependent censoring via nonparametric multiple imputation

When the event time of interest depends on the censoring time, conventional two-sample test methods, such as the log-rank and Wilcoxon tests, can produce an invalid test result. We extend our previous work on estimation using auxiliary variables to adjust for dependent censoring via multiple imputation, to the comparison of two survival distributions. To conduct the imputation, we use two working models to define a set of similar observations called the imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, a nonparametric multiple imputation method, Kaplan–Meier imputation, is used to impute a future event or censoring time for each censored observation. After imputation, the conventional nonparametric two-sample tests can be easily implemented on the augmented data sets. Simulation studies show that the sizes of the log-rank and Wilcoxon tests constructed on the imputed data sets are comparable to the nominal level and the powers are much higher compared with the tests based on the unimputed data in the presence of dependent censoring if either one of the two working models is correctly specified. The method is illustrated using AIDS clinical trial data comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable. Copyright © 2008 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/61537/1/3480_ftp.pd

Extrapolation before imputation reduces bias when imputing censored covariates

Modeling symptom progression to identify informative subjects for a new Huntington's disease clinical trial is problematic since time to diagnosis, a key covariate, can be heavily censored. Imputation is an appealing strategy where censored covariates are replaced with their conditional means, but existing methods saw over 200% bias under heavy censoring. Calculating these conditional means well requires estimating and then integrating over the survival function of the censored covariate from the censored value to infinity. To estimate the survival function flexibly, existing methods use the semiparametric Cox model with Breslow's estimator, leaving the integrand for the conditional means (the estimated survival function) undefined beyond the observed data. The integral is then estimated up to the largest observed covariate value, and this approximation can cut off the tail of the survival function and lead to severe bias, particularly under heavy censoring. We propose a hybrid approach that splices together the semiparametric survival estimator with a parametric extension, making it possible to approximate the integral up to infinity. In simulation studies, our proposed approach of extrapolation then imputation substantially reduces the bias seen with existing imputation methods, even when the parametric extension was misspecified. We further demonstrate how imputing with corrected conditional means helps to prioritize patients for future clinical trials.Comment: 16 pages main text (incl. 2 tables and 3 figures); Supplemental Materials, R code, and R package available on GitHub (linked in main text

A Predictive Approach to Bayesian Nonparametric Survival Analysis

Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is conjugate with respect to right-censored data. Eliciting these priors, particularly in the presence of covariates, can be challenging and inference typically relies on computationally intensive Markov chain Monte Carlo schemes. In this paper, we build on recent work that recasts Bayesian inference as assigning a predictive distribution on the unseen values of a population conditional on the observed samples, thus avoiding the need to specify a complex prior. We describe a copula-based predictive update which admits a scalable sequential importance sampling algorithm to perform inference that properly accounts for right-censoring. We provide theoretical justification through an extension of Doob’s consistency theorem and illustrate the method on a number of simulated and real data sets, including an example with covariates. Our approach enables analysts to perform Bayesian nonparametric inference through only the specification of a predictive distribution