Estimation of marginal regression models with multiple source predictors

In estimating regression models, researchers are often faced with choosing between different measures of the predictors of interest. We consider settings where possible predictors are obtained from different individuals or sources to measure one construct. A common application is diagnostic testing where the goal is to determine which test of several possible best predicts disease. We review a generalized estimating equations (GEE) approach for fitting regression models using continuous multiple informants with a continuous outcome and introduce a new maximum likelihood (ML) approach. ML and GEE yield the same regression coefficient estimates in many situations. With the ML technique, likelihood ratio tests can be formed to easily compare regression models and a broader array of models can be fit. Using asymptotic relative efficiency, we show that a constrained model assuming equal variance is more efficient than an unconstrained model. We apply the methods to a study investigating the effect of vigorous exercise on body mass index with exercise measurements collected on two informants: children and their mothers. Frequently, studies with multiple informants have incomplete observations; we extend the marginal models to include data with missingness. Simulation results illustrate that ML offers potentially large efficiency gains compared with GEE; the example described above confirms these results.; We also consider marginal regression models with multiple informants as discrete predictors and a time to event outcome. We fit the models using a GEE technique and a new ML approach to data addressing the relationship between mortality and diagnosis of depression; specifically, we consider whether physician diagnosis and self diagnosis give comparable results. We identify those cases where the GEE and ML approaches yield the same estimates. 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 does not lose much 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.