An Unbiased Method to Approximate a Principal Estimand

The causality between treatments and outcomes in a principal stratification is a focus of clinical research. The principal stratification of patients depends on the occurrence of potential outcomes of intercurrent events. However, the related occurrence of intercurrent events of patients could be observed only in the situation where they actually received the treatments. Therefore, the belonging of principal stratification for patients would not be known only based on the observed data, which is a challenge when using the principal stratification strategy to deal with intercurrent events. To solve this problem, a new, understandable, and operatable method is proposed in this study. For the generalizability of this approach, we describe it in the context of observational studies rather than randomized controlled trials, and the target trial helps here. There are two stages for the application of this approach: the first stage determines variables that have a significant impact on the occurrence of intercurrent events and outcomes (i.e., features) based only on the information of patients in the control group; the second stage uses the information of features from the first stage to identify patients in the treatment group who are the “similar” as those in the control group. The “similar” here means that the values of the features of the patients in the treatment group are the same as or close to the values of these features of those in the control group. These patients are the principal stratification of interest, and causal methods related to risk differences are used to estimate the effects. This method requires one assumption about the relationship between features and intercurrent events and outcomes, that is, it needs to be verified that the features can fully explain the occurrence of intercurrent events and outcomes statistically. In the simulation part, we set different scenarios to compare the performance of this method with existing methods (depending on covariates, the representative one is the principal score method). In addition, simulations were also conducted to compare the predictive performance of features and covariates. In our simulations, the two-stage unbiased method (TUM) has the following advantages over the existing method (the principal score method, PSM): first, the features-based model is sufficient to explain the occurrence of intercurrent events and outcomes (both AIC and BIC are smaller than PSM); second, the predictive performance of TUM is better (MAE, MSE, 0.9QAD, and AUC are smaller); so this method does not require any unverifiable additional assumptions about covariates; third, TUM can estimate the treatment effect more accurately in large samples (the values of the principal estimand are larger than those of PSM) and can ensure that the bias is small (SE is smaller). In addition, the performance of this study is improved, in terms of the prediction of variables, with its calibration curve, decision curve analysis, and clinical impact curve all outperforming PSM. This further demonstrates that TUM is more reasonable as well as its practicability. The method in this study is more recommended compared to methods based on covariates (or all variables) in situations with larger samples and fewer features. Overall, features have a better interpretation because they were selected by rigorous and commonly used mathematical and statistical methods. Furthermore, there is a traceable way to discuss the robustness of the results rather than depend on some assumptions that could not be verifiable.