Dynamic models for estimating the effect of HAART on CD4 in observational studies: application to the Aquitaine Cohort study and the Swiss HIV Cohort Study

TL;DR

This paper compares dynamic models, including discrete and continuous time approaches, for estimating HAART's effect on CD4 counts in observational HIV studies, highlighting their advantages and challenges.

Contribution

It introduces and compares three discrete-time linear increment models and continuous-time ODE models for causal inference in observational data, incorporating biological knowledge.

Findings

ODE-NLME models effectively incorporate biological mechanisms.

LIMs offer a balance between simplicity and accuracy.

Models applied successfully to HIV cohort data.

Abstract

Highly active antiretroviral therapy (HAART) has proved efficient in increasing CD4 counts in many randomized clinical trials. Because randomized trials have some limitations (e.g., short duration, highly selected subjects), it is interesting to assess it using observational studies. This is challenging because treatment is started preferentially in subjects with severe conditions, in particular in subjects with low CD4 counts. This general problem had been treated using Marginal Structural Models (MSM) relying on the counterfactual formulation. Another approach to causality is based on dynamical models. First, we present three discrete-time dynamic models based on linear increments (LIM): the simplest model is described by one difference equation for CD4 counts; the second has an equilibrium point; the third model is based on a system of two difference equations which allows jointly modeling CD4 counts and viral load. Then we consider continuous time models based on ordinary differential equations with random effects (ODE-NLME). These mechanistic models allow incorporating biological knowledge when available, which leads to increased power for detecting treatment effect. Inference in ODE-NLME models, however, is challenging from a numerical point of view, and requires specific methods and softwares. LIMs are a valuable intermediary option in terms of consistency, precision and complexity. The different approaches are compared in simulation and applied to HIV cohorts (the ANRS CO3 Aquitaine Cohort and the Swiss HIV Cohort Study).