Methods for dealing with time‐dependent confounding

Abstract

Longitudinal studies, where data are repeatedly collected on subjects over a period, are common in medical research. When estimating the effect of a time-varying treatment or exposure on an outcome of interest measured at a later time, standard methods fail to give consistent estimators in the presence of time-varying confounders if those confounders are themselves affected by the treatment. Robins and colleagues have proposed several alternative methods that, provided certain assumptions hold, avoid the problems associated with standard approaches. They include the g-computation formula, inverse probability weighted estimation of marginal structural models and g-estimation of structural nested models. In this tutorial, we give a description of each of these methods, exploring the links and differences between them and the reasons for choosing one over the others in different settings.

Estimating long‐term treatment effects in observational data: A comparison of the performance of different methods under real‐world uncertainty

“…Finally, no unmeasured confounding means that conditional on the past observed variables the treatment received at visit t is independent of the counterfactual outcome, $Y_t^{{\overline{x}}_t}⫫X_{t}false|{\overline{X}}_{t-1},{\overline{Y}}_{t-1},{\overline{\mathbf{C}}}_t,\mathrm{boldB}$. 1 …”

“…The inverse of the estimated probabilities can be used directly as the weights, but it is usually preferable to use so‐called stabilised weights1 where the numerator of the weights is the probability of receiving treatment based on previous treatment history and baseline covariates only, $S{W}_t=\frac{\mathrm{normalP}\left({\overline{X}}_{t}false|{\overline{X}}_{t-1},\mathrm{boldB}\right)}{\mathrm{normalP}\left({\overline{X}}_{t}false|{\overline{X}}_{t-1},{\overline{Y}}_{t-1},{\overline{\mathbf{C}}}_t,\mathrm{boldB}\right)}=true\prod _{i=1}^t\frac{\mathrm{normalP}\left(X_{i}false|{\overline{X}}_{i-1},\mathrm{boldB}\right)}{\mathrm{normalP}\left(X_{i}false|{\overline{X}}_{i-1},{\overline{Y}}_{i-1},{\overline{\mathbf{C}}}_i,\mathrm{boldB}\right)}.$ …”

Promises and pitfalls of electronic health record analysis

“…For example, if we wish to examine the effect of CKD stage on mortality in individuals with diabetes, then HbA 1c may be a time-varying confounder of the association but CKD stage may also influence future HbA 1c . Methodological approaches to dealing with time-varying confounders affected by prior treatment include inverse probability weighting of marginal structural models, g-computation and g-estimation [38]. In theory, these methods correctly adjust for the time-varying confounding without losing any effect of exposure that acts via future values of the confounder, subject to certain assumptions [38].…”

“…Methodological approaches to dealing with time-varying confounders affected by prior treatment include inverse probability weighting of marginal structural models, g-computation and g-estimation [38]. In theory, these methods correctly adjust for the time-varying confounding without losing any effect of exposure that acts via future values of the confounder, subject to certain assumptions [38]. If such methodologies are not feasible, simpler study designs in which exposures are assumed to remain fixed from study entry (analogous to intention to treat analyses) may still be used to examine exposure/outcome associations but such designs can only answer more limited questions that ignore the reality of individuals changing treatments over time.…”

Use of Causal Diagrams to Inform the Design and Interpretation of Observational Studies: An Example from the Study of Heart and Renal Protection (SHARP)

“…(Note that the analysis of data with time-varying treatments or exposures may require specialist statistical methods to be used, such as marginal structural models [4,5]. )…”