History-adjusted marginal structural models for estimating time-varying effect modification

Abstract

Much of epidemiology and clinical medicine is focused on estimating the effects of treatments or interventions administered over time. In such settings of longitudinal treatment, time-dependent confounding is often an important source of bias. Marginal structural models (MSMs) are a powerful tool for estimating the causal effect of a treatment using observational data, particularly when time-dependent confounding is present. In recent statistical work, van der Laan et al. presented a generalized form of MSMs called "history-adjusted" MSMs (Int J Biostat 2005;1:article 4). Unlike standard MSMs, history-adjusted MSMs can be used to estimate modification of treatment effects by time-varying covariates. Estimation of time-dependent causal effect modification is frequently of great practical relevance. For example, clinical researchers are often interested in how the prognostic significance of a biomarker for treatment response can change over time. This article provides a practical introduction to the implementation and interpretation of history-adjusted MSMs. The method is illustrated using a clinical question drawn from the treatment of human immunodeficiency virus infection. Observational cohort data from San Francisco, California, collected between 2000 and 2004, are used to estimate the effect of time until switching antiretroviral therapy regimens among patients receiving a non suppressive regimen and how this effect differs depending on CD4-positive T-lymphocyte count.

FIGURE 1

Estimated weights for standard and history-adjusted marginal structural models, the latter assuming a common model across time points, among human immunodeficiency virus-infected subjects with virologic failure sampled from a cohort in San Francisco, California, 2000–2004. For marginal structural models, estimated weights are plotted separately for each distinct episode of virologic failure, represented numerically on the x-axis as an index; for history-adjusted marginal structural models, estimated weights are plotted separately for each distinct episode of virologic failure and each time point at which subjects remain on their nonsuppressive therapy, represented numerically on the x-axis as an index.

FIGURE 2

Separate history-adjusted marginal structural model fitted for each of 9 months beginning at the time of virologic failure, showing the estimated effect of each additional month until switching therapy on CD4 T-cell count 8 months later, given current CD4 T-cell count (CD4(j)) and elapsed months since failure occurred (j), among human immunodeficiency virus-infected subjects with virologic failure sampled from a cohort in San Francisco, California, 2000–2004. Results were estimated among persons who had not yet switched therapy and had not resuppressed the virus.

FIGURE 3

Common history-adjusted marginal structural model fitted for the 9 months beginning at the time of virologic failure, showing the estimated effect of each additional month until switching therapy on CD4 T-cell count 8 months later, given current CD4 T-cell count (CD4(j)) and elapsed months since failure occurred (j), among human immunodeficiency virus-infected subjects with virologic failure sampled from a cohort in San Francisco, California, 2000–2004. Results were estimated among persons who had not yet switched therapy and had not resuppressed the virus.