Derivation of a multivariate longitudinal causal effects model

This paper presents a causal inference estimation method for longitudinal observational studies with multiple outcomes. The method uses marginal structural models with inverse probability treatment weights (MSM-IPTWs). In developing the proposed method, we re-define the weights as a product of inverse weights at each time point, accounting for time-varying confounders and treatment exposures and possible correlation between and within (serial) the multiple outcomes. The proposed method is evaluated by simulation studies and with an application to estimate the effect of HIV positivity awareness on condom use and multiple sexual partners using the Malawi Longitudinal Study of Families and Health (MLSFH) data. The simulation study shows that the joint MSM-IPTW performs well with coverage within the expected 95% level for a large sample size (n = 1000) and moderate to strong between and within outcome correlation strength ( $ \rho _j=0.3 $ ρj=0.3, 0.75, $ \rho _k=0.4 $ ρk=0.4, 0.8) when the effects are similar. The joint MSM-IPTW performed relatively the same as the adjusted standard joint model when the treatment effect estimate was the same for the outcomes. In the application, HIV positivity awareness increased the usage of condoms and did not affect the number of sexual partners. We recommend using the proposed MSM-IPTWs to correctly control for time-varying treatment and confounders when estimating causal effects for longitudinal observational studies with multiple outcomes.