TABLE 2.

Justification of the identification assumptions in the context of the CALGB 9633 trial and the NCDB sample

Assumptions	Justifications
1 Consistency	The extracted OS samples are stage IB NSCLC patients who had surgery and then received either adjuvant chemotherapy or on observation (i.e., no chemotherapy) and with age greater than 20. Like CALGB 9633 patients, they did not receive any of the neoadjuvant chemotherapy, radiation therapy, induction therapy, immunotherapy, hormone therapy, transplant/endocrine procedures, or systemic treatment before their surgery. Thus, the same treatment or comparison conditions were given in the same setting in both studies.
2 Treatment ignorability and positivity	The CALGB 9633 trial implemented treatment randomization and had good patient compliance (Strauss et al., 2008).
3 Sampling ignorability and positivity	The four covariates, gender, age, histology, and tumor size, have been considered strong prognostic factors or disease recurrence after surgical resection for early NSCLC. The positivity condition holds because the OS data for NSCLC stage IB patients were extracted from NCDB with the same eligibility criteria as CALGB 9633.
7 Generalizability of the outcome mean functions from the RCT sample to the OS sample	The likelihood ratio test of a reduced model (i.e., a single logistic regression with the sieve basis for the combined sample) against a full model (that is, two separate logistic regressions with the sieve basis for the two samples) has a p-value of 0.09. If a conservative investigator uses 0.1 to determine the critical value, the investigator can choose estimators using only trial data, for example, ACW-t(S) and ACW-t(SO). On the other hand, if the investigator uses 0.05 to determine the critical value, one can choose estimators using both data sources, that is, ACW-b(S) and ACW-b(SO).