Causal Identification Conditions for the Effect of Treatment in the Treated: Illustration Using the Northwest Germany...

A set of conditions sufficient to identify the average treatment effect (ATE) in observational data includes no measurement error, causal consistency, and conditional mean exchangeability with positivity. The average treatment effect in the treated (ATT) is identified under a subset of these conditions, specifically relaxing the symmetry of conditional exchangeability with positivity.

We reanalyzed data from the Northwest Germany Stroke Registry (2020-2021) to estimate the effect of tissue-type plasminogen activator (tPA) on inhospital mortality. We used inverse probability of treatment weighting for the ATE and standardized mortality ratio (SMR) weighting for the ATT. We also conducted 5000 simulations of 6000 patients, varying the prevalence of treatment indication. We generated homogeneous and heterogeneous treatment effects under two scenarios: (1) positivity holds for treated and untreated groups and (2) positivity only holds for the treated.

Among 6000 patients, 20% received tPA, and 5% died. The inverse probability of treatment weighting risk ratio (ATE) was 1.70 (95% CI: 0.80, 3.64), while the SMR-weighted risk ratio (ATT) was 0.82 (95% CI: 0.59, 1.14). In simulations, ATT estimates of the risk ratio remained unbiased when we violated positivity for the untreated. However, ATE estimates showed increasing log-scale bias with increased nonpositivity, ranging from 0.2 to 1.1 for homogeneous effects and 0.2 to 0.9 for heterogeneous effects.

While ATE estimates suggested harm from tPA, ATT estimates suggest a protective effect. Simulations show that when one-sided positivity violations exist, epidemiologists can leverage weaker identification conditions to consistently estimate the ATT, even when estimates of the ATE are biased.