Marginal regression models with a time to event outcome and discrete multiple source predictors

Abstract

Information from multiple informants is frequently used to assess psychopathology. We consider marginal regression models with multiple informants as discrete predictors and a time to event outcome. We fit these models to data from the Stirling County Study; specifically, the models predict mortality from self report of psychiatric disorders and also predict mortality from physician report of psychiatric disorders. Previously, Horton et al. found little relationship between self and physician reports of psychopathology, but that the relationship of self report of psychopathology with mortality was similar to that of physician report of psychopathology with mortality. Generalized estimating equations (GEE) have been used to fit marginal models with multiple informant covariates; here we develop a maximum likelihood (ML) approach and show how it relates to the GEE approach. In a simple setting using a saturated model, the ML approach can be constructed to provide estimates that match those found using GEE. We extend the ML technique to consider multiple informant predictors with missingness and compare the method to using inverse probability weighted (IPW) GEE. Our simulation study illustrates that IPW GEE loses little efficiency compared with ML in the presence of monotone missingness. Our example data has non-monotone missingness; in this case, ML offers a modest decrease in variance compared with IPW GEE, particularly for estimating covariates in the marginal models. In more general settings, e.g. categorical predictors and piecewise exponential models, the likelihood parameters from the ML technique do not have the same interpretation as the GEE. Thus, the GEE is recommended to fit marginal models for its flexibility, ease of interpretation and comparable efficiency to ML in the presence of missing data.

The impact of correlated exposures and missing data on multiple informant models used to identify critical exposure windows

“…There have been several studies on multiple informant models using GEE or ML theory (Table 1), 4,[20][21][22][23][24][25]29,33,45 but only a few focused on the impact of missing data or more than two informants. 4,21,22,24,25 While some simulation studies have been conducted to evaluate the performance of MIMs, 24,25,29,33,45 none have explored the impact of correlated exposures on the operating characteristics of this approach, especially MIM GEE.…”

“…There have been several studies on multiple informant models using GEE or ML theory (Table 1), 4,[20][21][22][23][24][25]29,33,45 but only a few focused on the impact of missing data or more than two informants. 4,21,22,24,25 While some simulation studies have been conducted to evaluate the performance of MIMs, 24,25,29,33,45 none have explored the impact of correlated exposures on the operating characteristics of this approach, especially MIM GEE. One of the seminal MIM studies applied MIM GEE to identify childhood predictors of obesity, analyzing information measured on different family members that were assumed to follow a MCAR structure when data measurements were missing.…”

“…22 Fitting IPW models for each period is equivalent to repeating the Xie and Paik approach for each exposure window, which has been implemented in previous multiple informant model literature. 22,24 To be consistent with this literature, we fit IPW models for the simulated and example data that were based only on the observed outcome and confounder. Although this is a specific setting of missing data, we also acknowledge the work of Sun and Tchetgen Tchetgen, 36 who developed a method for handling more general cases of nonmonotonic missingness.…”

“…Because the coefficients are statistically dependent, nonoverlapping confidence intervals cannot be used to demonstrate that associations differ 4 . Second, each model may generate associations based on different subsamples of the data 24‐26 . The repeated measuring of individuals over time is a fundamental feature of cohort studies, but may lead to missing data if participants do not attend all scheduled visits 27 .…”

“…4 Second, each model may generate associations based on different subsamples of the data. [24][25][26] The repeated measuring of individuals over time is a fundamental feature of cohort studies, but may lead to missing data if participants do not attend all scheduled visits. 27 The associations may be biased if the determination of the analytical sample depends on the availability of observed exposure and outcome measures and no correction is made (eg, inverse probability-weighting (IPW)).…”