  Evidence supporting the current World Health Organization recommendations of
early antiretroviral therapy (ART) initiation for adolescents is inconclusive.
We leverage a large observational data and compare, in terms of mortality and
CD4 cell count, the dynamic treatment initiation rules for HIV-infected
adolescents. Our approaches extend the marginal structural model for estimating
outcome distributions under dynamic treatment regimes (DTR), developed in
Robins et al. (2008), to allow the causal comparisons of both specific regimes
and regimes along a continuum. Furthermore, we propose strategies to address
three challenges posed by the complex data set: continuous-time measurement of
the treatment initiation process; sparse measurement of longitudinal outcomes
of interest, leading to incomplete data; and censoring due to dropout and
death. We derive a weighting strategy for continuous time treatment initiation;
use imputation to deal with missingness caused by sparse measurements and
dropout; and define a composite outcome that incorporates both death and CD4
count as a basis for comparing treatment regimes. Our analysis suggests that
immediate ART initiation leads to lower mortality and higher median values of
the composite outcome, relative to other initiation rules.
