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

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.