Bayesian correction for covariate measurement error: a frequentist evaluation and comparison with regression calibration

Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration (RC), arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to RC, and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next we describe the closely related maximum likelihood and multiple imputation approaches, and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of RC and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey

Missing covariates in competing risks analysis.

Studies often follow individuals until they fail from one of a number of competing failure types. One approach to analyzing such competing risks data involves modeling the cause-specific hazards as functions of baseline covariates. A common issue that arises in this context is missing values in covariates. In this setting, we first establish conditions under which complete case analysis (CCA) is valid. We then consider application of multiple imputation to handle missing covariate values, and extend the recently proposed substantive model compatible version of fully conditional specification (SMC-FCS) imputation to the competing risks setting. Through simulations and an illustrative data analysis, we compare CCA, SMC-FCS, and a recent proposal for imputing missing covariates in the competing risks setting

Bootstrap Inference for Multiple Imputation under Uncongeniality and Misspecification

Multiple imputation has become one of the most popular approaches for handling missing data in statistical analyses. Part of this success is due to Rubin's simple combination rules. These give frequentist valid inferences when the imputation and analysis procedures are so called congenial and the complete data analysis is valid, but otherwise may not. Roughly speaking, congeniality corresponds to whether the imputation and analysis models make different assumptions about the data. In practice imputation and analysis procedures are often not congenial, such that tests may not have the correct size and confidence interval coverage deviates from the advertised level. We examine a number of recent proposals which combine bootstrapping with multiple imputation, and determine which are valid under uncongeniality and model misspecification. Imputation followed by bootstrapping generally does not result in valid variance estimates under uncongeniality or misspecification, whereas bootstrapping followed by imputation does. We recommend a particular computationally efficient variant of bootstrapping followed by imputation.Comment: Updated (fixed) reference based simulation results. Now included tables which were previously not included as they were in supplementary information document. Swapped order of the two simulation studies. Added acknowledgement and funding statement

The value of hippocampal and temporal horn volumes and rates of change in predicting future conversion to AD.

Hippocampal pathology occurs early in Alzheimer disease (AD), and atrophy, measured by volumes and volume changes, may predict which subjects will develop AD. Measures of the temporal horn (TH), which is situated adjacent to the hippocampus, may also indicate early changes in AD. Previous studies suggest that these metrics can predict conversion from amnestic mild cognitive impairment (MCI) to AD with conversion and volume change measured concurrently. However, the ability of these metrics to predict future conversion has not been investigated. We compared the abilities of hippocampal, TH, and global measures to predict future conversion from MCI to AD. TH, hippocampi, whole brain, and ventricles were measured using baseline and 12-month scans. Boundary shift integral was used to measure the rate of change. We investigated the prediction of conversion between 12 and 24 months in subjects classified as MCI from baseline to 12 months. All measures were predictive of future conversion. Local and global rates of change were similarly predictive of conversion. There was evidence that the TH expansion rate is more predictive than the hippocampal atrophy rate (P=0.023) and that the TH expansion rate is more predictive than the TH volume (P=0.036). Prodromal atrophy rates may be useful predictors of future conversion to sporadic AD from amnestic MCI