Time dependent hazard ratio estimation using instrumental variables without conditioning on an omitted covariate

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Instrumental variables (IV) estimation is established for linear models but less so for time-to-event analysis.
• Existing IV methods for Cox regression hazard ratios (HR) have limitations.
• Confounding bias can be reduced by using IVs derived from natural experiments or randomization.

Purpose of the Study:

• To extend IV-based estimation for Cox's model beyond proportional hazards.
• To estimate marginal time-dependent hazard ratios, unlike conditional approaches.
• To develop robust IV estimators for log-linear and piecewise constant hazard ratios.

Main Methods:

• Developed novel estimating equations based on Martingale representations.
• Estimated marginal time-dependent hazard ratios, not conditional ones.
• Used simulations with copulas to model time-to-event data with unmeasured confounding.

Main Results:

• The proposed method performed well in simulations for stepwise time-dependent hazard ratios.
• Some bias was observed as the hazard ratio deviated from unity.
• The approach showed strong performance for log-linear hazard ratios where no other IV methods exist.
• It compared favorably to other IV-based methods for stepwise constant hazard ratios.

Conclusions:

• The proposed IV-based estimating equations effectively estimate time-dependent hazard ratios.
• This procedure is recommended for time-dependent hazard ratio estimation when unmeasured confounding is present and a suitable IV is available.
• The method offers a valuable tool for survival data analysis in the presence of unmeasured confounding.