Estimating parsimonious models of longitudinal causal effects using regressions on propensity scores

Abstract

Parsimony is important for the interpretation of causal effect estimates of longitudinal treatments on subsequent outcomes. One method for parsimonious estimates fits marginal structural models by using inverse propensity scores as weights. This method leads to generally large variability that is uncommon in more likelihood-based approaches. A more recent method fits these models by using simulations from a fitted g-computation, but requires the modeling of high-dimensional longitudinal relations that are highly susceptible to misspecification. We propose a new method that, first, uses longitudinal propensity scores as regressors to reduce the dimension of the problem and then uses the approximate likelihood for the first estimates to fit parsimonious models. We demonstrate the methods by estimating the effect of anticoagulant therapy on survival for cancer and non-cancer patients who have inferior vena cava filters.

Keywords: causal inference; causal models; propensity scores; survival analysis.

Figure 1

Kaplan–Meier estimates of survival observed in each of the treatment by cancer groups. Tick marks show censoring times that are not also failure times.

Figure 2

Estimates of survival in each of the treatment by cancer groups calculated by the propensity score-based g-computation formula. Dashed lines indicate pointwise 95% confidence intervals.

Figure 3

Comparison of the log odds ratio for death comparing AC with no AC therapy for cancer and non-cancer patients. Using thin lines, the nonparametrically estimated log odds ratios are shown. On the right, the thick solid black and gray lines indicate the fitted parsimonious model for a common log odds ratio between 50 and 90 days. Thick dashed lines indicate 95% confidence intervals.