Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models

Consider a study whose design calls for the study subjects to be followed from enrollment (time t = 0) to time t = T, at which point a primary endpoint of interest Y is to be measured. The design of the study also calls for measurements on a vector Vt) of covariates to be made at one or more times t during the interval [0, T). We are interested in making inferences about the marginal mean μ₀ of Y when some subjects drop out of the study at random times Q prior to the common fixed end of follow-up time T. The purpose of this article is to show how to make inferences about μ₀ when the continuous drop-out time Q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables. In particular, we consider two models for the conditional hazard of drop-out given (V(T), Y), where V(t) denotes the history of the process Vt) through time t, t ∈ [0, T). In the first model, we assume that λ_Q(t|V(T), Y) exp(α₀Y), where α₀ is a scalar parameter and λ₀(t|V(t)) is an unrestricted positive function of t and the process V(t). When the process Vt) 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 model that imposes the additional restriction that λ₀(t|V(t)) = λ₀(t) exp(γ′₀(t)), where λ⁰t) is an unspecified baseline hazard function, W(t) = w(t, V(t)), w(·,·) is a known function that maps (t, V(t)) to R^q, and γ₀ is a q × 1 unknown parameter vector. When α₀ ≠ 0, then drop-out is nonignorable. On account of identifiability problems, joint estimation of the mean μ₀ of Y and the selection bias parameter α₀ may be difficult or impossible. Therefore, we propose regarding the selection bias parameter α₀ as known, rather than estimating it from the data. We then perform a sensitivity analysis to see how inference about α₀ changes as we vary α₀ over a plausible range of values. We apply our approach to the analysis of ACTG 175, an AIDS clinical trial.