DOUBLY ROBUST ESTIMATION OF OPTIMAL TREATMENT REGIMES FOR SURVIVAL DATA-WITH APPLICATION TO AN HIV/AIDS STUDY

Abstract

In many biomedical settings, assigning every patient the same treatment may not be optimal due to patient heterogeneity. Individualized treatment regimes have the potential to dramatically improve clinical outcomes. When the primary outcome is censored survival time, a main interest is to find optimal treatment regimes that maximize the survival probability of patients. Since the survival curve is a function of time, it is important to balance short-term and long-term benefit when assigning treatments. In this paper, we propose a doubly robust approach to estimate optimal treatment regimes that optimize a user specified function of the survival curve, including the restricted mean survival time and the median survival time. The empirical and asymptotic properties of the proposed method are investigated. The proposed method is applied to a data set from an ongoing HIV/AIDS clinical observational study conducted by the University of North Carolina (UNC) Center of AIDS Research (CFAR), and shows the proposed methods significantly improve the restricted mean time of the initial treatment duration. Finally, the proposed methods are extended to multi-stage studies.

Keywords: Doubly robust estimation; median survival time; optimal treatment regimen; restricted mean survival time.

Fig. 1

Simulation results for maximizing the RMST. The left column is for extreme value distributed error, while the right column is for logistic distributed error. The first row displays box plots for $R\left({\widehat{\eta }}^{\mathrm{opt}}\right)$, with the horizontal lines indicating the upper bound R(η^opt). The second row displays box plots for MR, with the horizontal lines indicating zero. The third row displays box plots for $\widehat{R}\left({\widehat{\eta }}^{\mathrm{opt}}\right)$, with the horizontal lines indicating the true value R(η^opt). The fourth row presents the empirical coverage probability of the confidence interval of ${\widehat{R}}_K\left({\widehat{\eta }}^{\mathrm{opt}}\right)$, with the horizontal lines indicating the nominal level of 95%. Within each panel, the left half of the plot is for correctly specified logistic regression, while right half of the plot is for misspecified logistic regression.

Fig. 2

Simulation results for maximizing the median survival time. See Figure 1 for detailed descriptions of the plots.

Fig. 3

Survival function estimates if all the patients followed $g(x;{\widehat{\eta }}_{\mathit{SA}}^{\mathrm{opt}})$ (solid line), the observed treatment (dashed line), received treatment 1 (dotted line) or received treatment 0 (dotted dashed line).

Fig. 4

Comparison of treatment allocation percentages stratified on each categorical covariates. The left panel is for the observed assignment while the right panel is for the estimated optimal treatment regime (denoted by gSA).

Fig. 5

Comparison of treatment allocation percentages stratified on each continuous covariates (based on quartiles). The left panel is for the observed assignment while the right panel is for the estimated optimal treatment regime (denoted by gSA).