Multiple imputation of partially observed covariates in discrete-time survival analysis

Abstract

Many phenomena in the social or the medical sciences can be described as events, meaning that a qualitative change occurs at some particular point in time. Typical research questions focus on whether, when, and under which circumstances events occur. In the social sciences, discrete-time-to-event models are popular (Discrete-Time Survival Analysis Model, DTSAM). Data analyzed through DTSAMs is in the so-called person-period format. The model is a logistic regression model with the event indicator as the dependent variable. However, like many other statistical applications, the practical analysis of discrete-time survival data is challenged by missing data in one or more covariates. Negative consequences of such missing data range from efficiency losses to bias. A popular approach to circumvent these unwanted effects of missing data is multiple imputation (MI). With multiple imputation, it is crucial to include outcome information in the model for imputing partially observed covariates. Unfortunately, this is not straightforward in case of DTSAM, since we (a) usually have a partly observed (left- or right-censored) outcome, (b) do not have only one outcome variable, but two: the event indicator and the time-to-event and (c) have to decide whether to impute while the data set is still in person format or after transformation in person-period format, especially if we look at time-invariant information. Since there is little guidance on how to incorporate the observed outcome information in the imputation model of missing covariates in discrete-time survival analysis, we explore different approaches using fully conditional specification (FCS) (van Buuren 2006) and the newer substantial model compatible (SMC-) FCS MI (Bartlett et al., 2014). These approaches vary in their complexity with which we incorporate the outcome into the imputation model, the FCS algorithm used, and the data format used during the imputation. We compare the methods using Monte Carlo simulations and provide a practical example using data from the German Family Panel pairfam.We confirm the results by White and Royston (2009) and Beesley et al. (2016) that imputing conditional on the (partly imputed) uncensored time-to-event yields high bias. A compatible imputation model for SMC-FCS MI with data in person-period format proves to be the key to imputations with good performance results under different simulation conditions.

The Re-Evaluation of a New Weight from Nicomedia

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