Instrumental variable approach for estimating a causal hazard ratio: Application to the effect of postmastectomy radiotherapy on breast cancer patients

The use of postmastectomy radiotherapy (PMRT) on women with AJCC (American Joint Committee on Cancer) pT1-2pN1 breast cancer is controversial in practice. Huo et al. (2015) found that PMRT was associated with longer survival among a high-risk subgroup of AJCC pT1-2pN1 patients using a Cox model on data from the National Cancer Database. To address unmeasured confounding in this observational study, we consider the variation among facilities in the use of PMRT as an instrumental variable (IV). Recently, there has been widespread use of the two-stage residual inclusion (2SRI) method offered by Terza et al. (2008) for nonlinear models, and 2SRI has been the method of choice for analyzing proportional hazards model using IV in clinical studies. However, the causal parameter using 2SRI is only identified under a homogeneity assumption that goes beyond the standard assumptions of IV, and Wan et al. (2015) demonstrated that under standard IV assumptions, 2SRI could fail to consistently estimate the causal hazard ratio for compliers. In this paper, following Yu et al. (2015), we apply a model-based IV approach (Imbens and Rubin, 1997; Hirano et al., 2000) which allows consistent estimation of the causal hazard ratio for survival outcomes with a proportional hazards model specification under standard IV assumptions while flexibly incorporating the restrictions imposed by IV assumptions. Simulation studies show that when there is unmeasured confounding, both 2SRI and the standard Cox regression could provide biased estimates of the causal hazard ratio among compliers, while this model-based IV approach provides consistent estimates. We apply this IV method to the breast cancer study and our IV analysis did not find strong evidence to support the benefit of PMRT on survival among the targeted patients. In addition, we develop sensitivity analysis approaches to assess the sensitivity of causal conclusions to violations of the exclusion restrictions assumption for IV.