PubMed · 13324962
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W M BORTHWICK. 1956. Genito-urinary tuberculosis.. https://doi.org/10.1016/s0041-3879(56)80121-9
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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 define 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-specification 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 efficiency. We apply the approaches to AIDS clinical trial data comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable.
The Cox proportional hazards model is the most common method to analyse survival data. However, the proportional hazards assumption might not hold. The natural extension of the Cox model is to introduce time-varying effects of the covariates. For some covariates such as (surgical)treatment non-proportionality could be expected beforehand. For some other covariates the non-proportionality only becomes apparent if the follow-up is long enough. It is often observed that all covariates show similar decaying effects over time. Such behaviour could be explained by the popular (gamma-) frailty model. However, the (marginal) effects of covariates in frailty models are not easy to interpret. In this paper we propose the reduced-rank model for time-varying effects of covariates. Starting point is a Cox model with p covariates and time-varying effects modelled by q time functions (constant included), leading to a pxq structure matrix that contains the regression coefficients for all covariate by time function interactions. By reducing the rank of this structure matrix a whole range of models is introduced, from the very flexible full-rank model (identical to a Cox model with time-varying effects) to the very rigid rank one model that mimics the structure of a gamma-frailty model, but is easier to interpret. We illustrate these models with an application to ovarian cancer patients.
In this paper, we considered a missing outcome problem in causal inferences for a randomized encouragement design study. We proposed both moment and maximum likelihood estimators for the marginal distributions of potential outcomes and the local complier average causal effect (CACE) parameter. We illustrated our methods in a randomized encouragement design study on the effectiveness of flu shots.