Comparative Effectiveness of Dynamic Treatment Regimes: An Application of the Parametric G-Formula

Abstract

Ideally, randomized trials would be used to compare the long-term effectiveness of dynamic treatment regimes on clinically relevant outcomes. However, because randomized trials are not always feasible or timely, we often must rely on observational data to compare dynamic treatment regimes. An example of a dynamic treatment regime is “start combined antiretroviral therapy (cART) within 6 months of CD4 cell count first dropping below x cells/mm3 or diagnosis of an AIDS-defining illness, whichever happens first” where x can take values between 200 and 500. Recently, Cain et al (2011) used inverse probability (IP) weighting of dynamic marginal structural models to find the x that minimizes 5-year mortality risk under similar dynamic regimes using observational data. Unlike standard methods, IP weighting can appropriately adjust for measured time-varying confounders (e.g., CD4 cell count, viral load) that are affected by prior treatment. Here we describe an alternative method to IP weighting for comparing the effectiveness of dynamic cART regimes: the parametric g-formula. The parametric g-formula naturally handles dynamic regimes and, like IP weighting, can appropriately adjust for measured time-varying confounders. However, estimators based on the parametric g-formula are more efficient than IP weighted estimators. This is often at the expense of more parametric assumptions. Here we describe how to use the parametric g-formula to estimate risk by the end of a user-specified follow-up period under dynamic treatment regimes. We describe an application of this method to answer the “when to start” question using data from the HIV-CAUSAL Collaboration.

Smoking cessation and long-term weight gain in the Framingham Heart Study: an application of the parametric g-formula for a continuous outcome

“…The parametric g-formula is a generalized version of standardization that provides unbiased estimates under the assumptions of no unmeasured confounding, no measurement error, and no model misspecification [26,27]. An outline of the parametric g-formula algorithm is as follows:…”

“…Our estimates of 20-year weight under each strategy implicitly include an intervention to remove censoring due to loss to follow-up or death [27]. If censoring is non-informative, the observed distribution of outcome and covariates should equal that estimated by the parametric g-formula under no intervention on smoking (i.e., the natural course) when a parametric model for smoking is added to step A.…”

Optimal timing of antiretroviral treatment initiation in HIV-positive children and adolescents: a multiregional analysis from Southern Africa, West Africa and Europe

“…In addition, we assumed that treatment is started at one visit after reaching eligibility; see Supplementary Textbox 1 and other work for implementation details. 16,34,35 To explore whether our implicit assumptions of correct model specification and non-informative censoring were likely met or not, we compared the estimates of the g-formula under no treatment strategy ('natural course scenario') with the observed data. All results are presented with 95% nonparametric bootstrap confidence intervals (CI).…”

Assessing the Causal Effect of Policies: An Example Using Stochastic Interventions

“…The regimes they discuss are of the type "initiate treatment within m months after the recorded CD4 cell count first falls below x." They are interested in an atomic intervention in the CD4 cell count X, and a discrete uniform f0; mg post-intervention distribution for the number of months before treatment M. Such intervention is discussed in more detail by Young et al [19].…”