Bias in estimating the causal hazard ratio when using two-stage instrumental variable methods.

Area of Science:

• Biostatistics
• Epidemiology
• Health Services Research

Background:

• Two-stage instrumental variable methods are crucial for estimating causal effects of treatments on survival, especially with confounding.
• Two-stage residual inclusion (2SRI) is often preferred over two-stage predictor substitution (2SPS) in clinical settings.
• Direct comparisons of bias between 2SRI and 2SPS in causal hazard ratio estimation are limited.

Purpose of the Study:

• To directly compare the bias of causal hazard ratios estimated by 2SRI and 2SPS methods.
• To analyze the performance of these methods under varying degrees of unmeasured confounding.

Main Methods:

• Derivation of closed-form solutions for asymptotic bias under a principal stratification framework.
• Analysis assumes Weibull distribution for survival time with random censoring.
• Extensive simulation studies and application to prostate cancer treatment data (SEER-Medicare).

Main Results:

• When no unmeasured confounding exists, 2SRI is generally asymptotically unbiased, while 2SPS is not.
• In scenarios with substantial unmeasured confounding, 2SPS demonstrates lower bias than 2SRI.
• Analytic findings are corroborated by simulation studies and real-world data analysis.

Conclusions:

• The choice between 2SRI and 2SPS depends on the presence and extent of unmeasured confounding.
• 2SRI offers unbiased estimation without unmeasured confounding, whereas 2SPS may be preferable when unmeasured confounding is significant.
• These findings inform the selection of appropriate causal inference methods in survival analysis.