Improving the efficiency of estimation in randomized trials of adaptive treatment strategies

Background Given the history of treatments to date, and the responses of the patient, what is the best treatment to try next? An ensemble of sequential, multistage rules guiding such adaptive decision making can be described as an 'adaptive treatment strategy (ATS)'. Robins' G-computation can be used for estimation of the mean outcome of an ATS from a 'sequential multiple assignment randomized (SMAR)' trial. Purpose To develop a variance estimate for the G-computation formula, based on a sequential analysis of the states and treatments observed in the trial, and compare its properties with those of the 'marginal mean' method described by Murphy, which is based on an estimating equation. Methods We use both mathematical calculation and simulation studies to demonstrate the properties of the G-computation and its sequential variance estimate, including finite-sample bias and coverage. Results The sequential method is unbiased and more efficient when the variation in intervening states contributes substantially to the variation in final outcome, and when the study can be designed to guarantee full observation of the ATS under study. The method extends to the comparison of two or more ATS. Limitations If full observation cannot be guaranteed, the method may have poor finite-sample properties. Conclusions When the states used to adapt treatment contribute substantially to the outcome, and good design technique can be applied, the sequential method provides more efficient estimation.