Cohort size and maximum likelihood estimation of mortality parameters

Area of Science:

• Demography
• Biostatistics
• Gerontology

Background:

• Detecting leveling off of mortality rates at older ages often requires large cohorts.
• The impact of smaller cohort sizes on the statistical properties of mortality parameter estimates is less understood.
• Frailty mortality models are frequently used to analyze survival data.

Purpose of the Study:

• To investigate the effects of cohort size on maximum likelihood estimates of mortality parameters.
• To evaluate the performance of small cohorts (150-300 individuals) in mortality studies.
• To compare empirical and asymptotic standard errors for hypothesis testing in small cohort scenarios.

Main Methods:

• Simulated deaths using the frailty mortality model.
• Employed two parameter sets with over twofold differences in mean lifespan.
• Focused on the evaluation of small cohort sizes (approximately 150-300 individuals).

Main Results:

• Small cohorts produced parameter estimates with generally good statistical properties but relatively large standard errors.
• Empirical standard errors, derived from multiple cohorts, demonstrated superior performance over asymptotic standard errors from single cohorts for hypothesis testing.
• Empirical standard errors provided reliable Type I error rates in hypothesis tests.

Conclusions:

• While small cohorts can provide statistically sound estimates, their standard errors are larger.
• For robust hypothesis testing in mortality studies, especially when comparing populations or treatments, utilizing empirical standard errors from multiple cohorts is recommended.
• The use of empirical standard errors ensures more reliable statistical inference, particularly concerning Type I error rates.