Adjusting for nonignorable drop-out using semiparametric nonresponse models

Consider a study whose design calls for the study subjects to be followed f rom enrollment (time t = 0) to time t = T, at which point a primary endpoin t of interest Y is to be measured. The design of the study also calls for m easurements on a vector V(t) of covariates to be made at one or more times t during the interval (0,T). We are interested in making inferences about t he marginal mean mu(0) of Y when some subjects drop out of the study at ran dom times Q prior to the common fixed end of follow-up rime T. The purpose of this article is to show how to make inferences about mu(0) when the cont inuous drop-out time Q is modeled semiparametrically and no restrictions ar e placed on the joint distribution of the outcome and other measured variab les. In particular, we consider two models for the conditional hazard of dr op-our given ((V) over bar(T), Y), where (V) over bar(t) denotes the histor y of the process V(t) through time t, t is an element of (0,T). In the firs t model, we assume that lambda(Q)(t\(V) over bar(T), Y) = lambda(0)(t\(V) o ver bar(t)) exp(alpha(0)Y), where alpha(0) is a scalar parameter and lambda (0)(t\(V) over bar(t)) is an unrestricted positive function of t and the pr ocess (V) over bar(t). When the process (V) over bar(t) is high dimensional , estimation in this model is not feasible with moderate sample sizes, due to the curse of dimensionality. For such situations, we consider a second m odel that imposes the additional restriction that lambda(0)(t\(V) over bar( t)) = lambda(0)(t) exp(gamma(0)'W(t)), where lambda(0)(t) is an unspecified baseline hazard function, W(t) = w(t, (V) over bar(t)), w(.,.) is a known function that maps (t, (V) over bar(t)) to R-q, and gamma(0)' is a q x 1 un known parameter vector. When alpha(0) not equal 0, then drop-out is nonigno rable. On account of identifiability problems, joint estimation of the mean mu(0) Of Y and the selection bias parameter ao may be difficult or impossi ble. Therefore, we propose regarding the selection bias parameter alpha(0) as known, rather than estimating it from the data. We then perform a sensit ivity analysis to see how inference about mu(0) changes as we vary alpha(0) over a plausible range of values. We apply our approach to the analysis of ACTG 175, an AIDS clinical trial.