Speaker
Description
Multiple imputation (MI) continues to be a popular approach to deal with missing at-random covariate data. For MI to perform well, it is advisable to ensure that the imputation model for a given covariate does not make conflicting assumptions with substantive/analysis model. In the case of substantive models that assume proportional hazards (e.g., the standard Cox model for a single time-to-event outcome), it is not straightforward to correctly specify an imputation model: even with simple time-constant log-linear effects, the conditional distribution of a partially observed covariate given the remaining covariates and outcomes will usually have non-linear expectation, and non-constant variance. This means that default approaches, such as for example the use of MI using chained equations (MICE) with predictive mean matching, are prone to bias when estimating quantities such as hazard ratios or survival probabilities.
In order to draw imputed values from a conditional distribution that is instead consistent with the assumptions made by the specified substantive model, a variant of MICE called substantive-model-compatible fully conditional specification (SMC-FCS) was developed [Bartlett et al., 2015, SMMR]. Over the past decade, this methodology has been adapted to accommodate different kinds of proportional hazards models, such as cause-specific Cox models, the Fine–Gray model, flexible parametric excess hazard models, and more. The relevant simulation studies, which tend to compare SMC-FCS with complete-case analysis (CCA) and the competing MICE approach, all point in the same direction: both MI approaches outperform CCA in terms of efficiency gains, but SMC-FCS is preferable to MICE in terms of bias. In contrast, the results of the applied data examples from these publications paint a more neutral picture: the differences between SMC-FCS and MICE are often negligible.
In this work, we take a critical look at the reasons behind the disconnect between these simulation studies and their associated real data examples, and reflect on neutral or ‘honest’ ways in which we could more efficiently build up empirical evidence in this setting. Due to the vast parameter space in methodological research about missing data, simulation studies are often restricted to relatively narrow and unrealistic settings. Producing more generalisable evidence may instead require enriching data examples using thorough performance benchmarking (e.g., applying SMC-FCS and competing methods for a range of increasingly complex substantive models, in addition to the original ‘illustrative’ one), or using these datasets as a basis for plasmode simulations (i.e., resampling covariate data, and controlling the outcome-generating process).
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