Marginal structural models for repeated measures where intercept and slope are correlated: An application exploring the benefit of nutritional supplements on weight gain in HIV-infected children initiating antiretroviral therapy

Background: The impact of nutritional supplements on weight gain in HIV-infected children on antiretroviral treatment (ART) remains uncertain. Starting supplements depends upon current weight-for-age or other acute malnutrition indicators, producing time-dependent confounding. However, weight-for-age at ART initiation may affect subsequent weight gain, independent of supplement use. Implications for marginal structural models (MSMs) with inverse probability of treatment weights (IPTW) are unclear. Methods: In the ARROW trial, non-randomised supplement use and weight-for-age were recorded monthly from ART initiation. The effect of supplements on weight-for-age over the first year was estimated using generalised estimating equation MSMs with IPTW, both with and without interaction terms between baseline weight-for-age and time. Separately, data were simulated assuming no supplement effect, with use depending on current weight-for-age, and weight-for-age trajectory depending on baseline weight-for-age to investigate potential bias associated with different MSM specifications. Results: In simulations, despite correctly specifying IPTW, omitting an interaction in the MSM between baseline weight-for-age and time produced increasingly biased estimates as associations between baseline weight-for-age and subsequent weight trajectory increased. Estimates were unbiased when the interaction between baseline weight-for-age and time was included, even if the data were simulated with no such interaction. In ARROW, without an interaction the estimated effect was +0.09 (95%CI +0.02,+0.16) greater weight-for-age gain per month’s supplement use; this reduced to +0.03 (-0.04,+0.10) including the interaction. Discussion: This study highlights a specific situation in which MSM model misspecification can occur and impact the resulting estimate. Since an interaction in the MSM (outcome) model does not bias the estimate of effect if the interaction does not exist, it may be advisable to include such a term when fitting MSMs for repeated measures.