# Modeling the Causal Effect of Treatment Initiation Time on Survival: Application to HIV/TB Co-infection

## TL;DR

This paper develops a flexible statistical model to analyze how the timing of ART initiation affects survival in HIV/TB co-infected patients, providing detailed insights into optimal treatment timing based on patient characteristics.

## Contribution

It introduces a novel proportional hazards model that accounts for censored treatment times and outcomes, enabling continuous analysis of ART initiation effects on survival.

## Key findings

- Identifies optimal ART initiation times for different CD4 count groups.
- Provides detailed survival curves for various treatment timings.
- Reveals differential effects of ART timing within patient subgroups.

## Abstract

The timing of antiretroviral therapy (ART) initiation for HIV and tuberculosis (TB) co-infected patients needs to be considered carefully. CD4 cell count can be used to guide decision making about when to initiate ART. Evidence from recent randomized trials and observational studies generally supports early initiation but does not provide information about effects of initiation time on a continuous scale. In this paper, we develop and apply a highly flexible structural proportional hazards model for characterizing the effect of treatment initiation time on a survival distribution. The model can be fitted using a weighted partial likelihood score function. Construction of both the score function and the weights must accommodate censoring of the treatment initiation time, the outcome, or both. The methods are applied to data on 4903 individuals with HIV/TB co-infection, derived from electronic health records in a large HIV care program in Kenya. We use a model formulation that flexibly captures the joint effects of ART initiation time and ART duration using natural cubic splines. The model is used to generate survival curves corresponding to specific treatment initiation times; and to identify optimal times for ART initiation for subgroups defined by CD4 count at time of TB diagnosis. Our findings potentially provide "higher resolution" information about the relationship between ART timing and mortality, and about the differential effect of ART timing within CD4 subgroups.