Asymptotically robust variance estimation for person-time incidence rates

Area of Science:

• Biostatistics
• Epidemiology
• Medical Research

Background:

• Person-time incidence rates are crucial in medical research.
• Standard estimation relies on the assumption of a constant hazard function over time.
• This constant hazard assumption is often unrealistic in practical applications.

Purpose of the Study:

• To define an average rate parameter as the ratio of expected event count to expected time at risk.
• To propose an asymptotically robust variance estimator for the log of this average rate parameter.
• To evaluate the performance of the proposed estimator against standard methods.

Main Methods:

• Analytical derivation of statistical properties for the proposed estimator.
• Simulation studies to compare estimator performance under various conditions.
• Application to five oncology study datasets.

Main Results:

• The proposed robust variance estimator is consistent under arbitrary independent and identically distributed (iid) event times.
• The estimator is also consistent or asymptotically conservative for independent but nonidentically distributed event times.
• The standard maximum-likelihood estimator can be anticonservative under nonconstant hazard, leading to inadequate confidence interval coverage.

Conclusions:

• The proposed robust variance estimator provides more reliable inference for person-time incidence rates when hazard functions are not constant.
• This method addresses limitations of standard estimators, particularly in complex medical research scenarios.
• The findings are supported by analytical results, simulations, and real-world oncology data.