Missing data

I’m pleased to announce the release of an R package, smcfcs, which implements multiple imputation of missing covariates using substantive model compatible fully conditional specification. As described in a previous post, this is a modified version of the popular fully conditional specification, or chained equations, approach to multiple imputation (e.g. as implemented in the excellent MICE package).

smcfcs is an attractive approach when the outcome or substantive model includes interactions or non-linear covariate effects, or is itself a non-linear model, such as Cox’s proportional hazards model. In these case, it can be difficult, or sometimes impossible, to directly specify an imputation model for partially observed covariates that is compatible with the outcome/substantive model. Such incompatibility can lead to biased estimates, due to mis-specification of the imputation model. smcfcs resolves this potential problem by ensuring that each partially observed covariate is imputed from an imputation model which is compatible with a user specified outcome/substantive model.

smcfcs is available on CRAN in R. It supports linear and logistic regression outcome models, as well as Cox proportional hazards models for censored time to event outcomes. Competing risks outcomes can also be accommodated through specification of Cox models for each cause specific hazard function. A Stata version is all available, and can be installed from within Stata from the SSC archive using: ssc install smcfcs

It’s sometimes thought that when data are missing, complete case analysis or complete records analysis, where those with missing values on the variables involved in the analysis are dropped, is biased unless data are missing completely at random (MCAR). In a previous post I explored the fact that complete case/records analysis can in fact be unbiased so long as missingness is unrelated to the outcome variable, conditional on the covariates. Depending on which variable(s) suffer from missingness, this can correspond to data being missing at random (MAR) or even missing not at random (MNAR).

Yesterday I gave a seminar at LSHTM discussing some recent work which brings together earlier results which have perhaps been somewhat neglected, looking at the specific case of logistic regression models. It turns out that because of the special symmetry property of the odds ratio measure which lies at the heart of logistic regression, a logistic regression complete case/records analysis can be unbiased for the association of a variable of interest (e.g. exposure) adjusted for a number of other covariates (e.g. confounders) in a perhaps surprising range of situations. The slides can be downloaded here, and an audio recording version is available here.

As described in the slides, missingness can depend on the outcome and confounders, or exposure and confounders, and the complete records estimate of the exposure association is unbiased. Depending on which variables have missing values, these conditions sometimes correspond to the MAR assumption and other times to an MNAR assumption. In general if missingness depends jointly on exposure and outcome, estimates of the exposure association are biased. However, as described in the slides, there are even special cases here where estimates for the exposure association remain unbiased.

October 2015: This work has now been published in the American Journal of Epidemiology, and is available open-access here.