The Rhythm of Treatment: Modeling Causal Effects Over Time With Marginal Structural Models and ODEs

Treatment in everyday care is reactive: doses change because patients change, creating time-varying confounding. Purely predictive models can fit well, yet encode the wrong causal story(e.g. appearing to show that insulin raises glucose simply because insulin is given when glucose is high). At the population level, we identify marginal effects using stabilized generalized propensity score weights and then learn a sparse ODE with SINDy to produce interpretable, deconfounded short-horizon glucose predictions from free-living CGM, insulin, and meal data. Stabilized generalized propensity scores reweight observations so treatment is as-if randomized given history; on this adjusted signal, we learn a sparse ODE whose terms clinicians can inspect. Using the public HUPA–UCM Type 1 diabetes dataset (5-minute CGM, insulin, carbohydrates), we compare the equations learned directly with those learned after MSM adjustment. After weighting, signs are physiologically coherent—boluses reduce glucose and meals increase it while the unweighted fit shows indication bias and achieves lower short-horizon RMSE and MAE than the unadjusted baseline, which reflects confounding by indication. In summary, the learned equations yield interpretable and deconfounded glucose trajectory predictions at the population level.