Harvard School of Public Health - Department of Biostatistics
Using observational data, we estimate the effects of treatment regimes that start treatment once a covariate, X, drops below a certain level, x. This type of analysis is difficult to carry out using experimental data, because the number of possible values of x may be large. In addition, we estimate the optimal value of x, which maximizes the expected value of the outcome of interest within the class of treatment regimes studied in this paper. Our identifying assumption is that there are no unmeasured confounders.
We illustrate our methods using the French Hospital Database on HIV. The best moment to start Highly Active AntiRetroviral Therapy (HAART) in HIV positive patients is unknown. It may be the case that withholding HAART in the beginning is beneficial, because it postpones the time patients develop drug resistance, and hence might improve the patients' long term prognosis. However, it is unknown how long initiation of HAART can safely be postponed.