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.