Inference on overlap index: with an application to cancer data

Area of Science:

• Ecology
• Biostatistics
• Genetics

Background:

• Quantifying overlap between distributions is crucial in biology, medicine, genetics, and ecology.
• Niche overlap analysis is essential for understanding species interactions and population dynamics.

Purpose of the Study:

• To introduce and analyze new overlap and containment indices for quantifying niche overlap between two species or populations.
• To study the estimation of these indices for exponential distributions with different scale parameters.
• To develop and compare the performance of various estimators and confidence intervals.

Main Methods:

• Development of new overlap and containment indices.
• Estimation of indices for exponential distributions.
• Asymptotic normality proof for maximum likelihood estimators.
• Construction and comparison of confidence intervals using three different approaches.

Main Results:

• New properties of the overlap and containment indices are established.
• Several estimators are proposed and their performance is compared using different loss functions.
• Asymptotic normality of maximum likelihood estimators is proven under specific conditions.
• Confidence intervals are obtained and their lengths and coverage probabilities are compared.

Conclusions:

• The proposed point and confidence interval procedures are effective for analyzing similarity in biological and medical data.
• The methods were successfully applied to breast cancer data to compare survival and relapse-free times between surgical groups.