The Effect of Misspecified Response Probabilities on Parameter Estimates from Weighted Estimating Equations

Abstract

Inference for the marginal mean using longitudinal data with monotone drop-outs in the response can be drawn with the weighted estimating equations (WEE; Robins, Rotnitzky&Zhao, 1995). Estimation proceeds in two steps. In the first step, a generalised linear model is usually applied to estimate response probabilities. In the second step, parameters of the mean structure are estimated by weighting a response inversely proportional to its estimated observation probability. The parameter estimates of the WEE are asymptotically normal and semiparametric efficient under suitable regularity conditions that include the correct specification of the model for the response probabilities. In this paper, we investigate the effect of misspecifying a) the parameters used to estimate the response probabilities and b) the link function for the response probabilities in a simulation study. We demonstrate that a slightly misspecified model for the response probabilities has an unimportant effect on the parameter estimates of the marginal mean from the WEE. We furthermore show that the choice of the link function has a negligible effect on the estimates of the marginal mean from the WEE. Our results are in line with classical findings for generalised linear models and for generalised estimating equations. Theoretical work should be added to our simulations that allow a quantification of the bias introduced by a misspecification of the model for the response probabilities.