Estimating mean time to reach a milestone, using retrospective data.

Area of Science:

• Biostatistics
• Epidemiology
• Demography

Background:

• Estimating the mean age at menarche is crucial for population health studies.
• Traditional methods face challenges with different data types (status quo vs. retrospective) and distribution assumptions (normal vs. non-normal).

Purpose of the Study:

• To develop and evaluate statistical estimators for the mean age at menarche using retrospective data under non-normal distribution assumptions.
• To compare the performance of these new estimators against existing methods.

Main Methods:

• Development of estimators for retrospective data with non-normal age at menarche distributions.
• Analysis of asymptotic distributions and optimal sampling allocations.
• Comparative evaluation through numerical examples.

Main Results:

• New estimators are derived for retrospective data and non-normal distributions.
• These estimators demonstrate superior performance in examples compared to estimators based on other assumptions.
• The study highlights the importance of utilizing retrospective data when available and reliable.

Conclusions:

• Retrospective data provides more accurate estimates for the mean age at menarche, particularly when the distribution is not normal.
• The developed estimators offer a robust approach for analyzing such data.
• Reliable retrospective data collection is recommended for future epidemiological and demographic surveys.