Optimal precision of coarse structural nested mean models to estimate the effect of initiating ART in early and acute HIV infection

Time-dependent coarse structural nested mean models (coarse SNMMs) were developed to estimate treatment effects from longitudinal observational data. Coarse SNMMs estimate the combined effect of multiple treatment dosages and are thus useful to estimate the effect of treatments that are initiated and then never stopped. Coarse SNMMs lead to a large class of estimators, with widely varying estimates and standard errors. To optimize precision, we derive an explicit solution for the optimal coarse SNMM estimator. We apply our methods by estimating how the effect on immune reconstitution of initiating 1 year of ART depends on the time between HIV infection and ART initiation, in the early stages of HIV infection. The CDC and the WHO are encouraging HIV testing, leading to earlier HIV diagnoses. Thus, more treatment decisions need to be made in early and acute infection. However, evidence is lacking about the clinical benefits of initiating ART in early and acute HIV infection, with guidelines developed mostly from analyzing patients with chronic infection. In the simulations and our motivating HIV application, naive coarse SNMM estimators render useless inference, whereas our new fitting methods render informative analyses. We thus hope that this article leads to broader applicability of SNMMs.