Interval estimation for a proportion using a double-sampling scheme with two fallible classifiers.

Area of Science:

• Statistics
• Biostatistics
• Statistical Inference

Background:

• Double-sampling schemes reduce classification errors when gold-standard classifiers are impractical.
• Existing inference procedures often assume an infallible classifier for validation.
• This study addresses scenarios with two fallible classifiers.

Purpose of the Study:

• To propose and evaluate confidence interval procedures for proportions under double-sampling with two fallible classifiers.
• To compare performance under two distinct models based on classifier ascertainment assumptions.

Main Methods:

• Development and simulation of confidence interval procedures for proportions.
• Evaluation of modified Wald, Score-based, Bayesian credible, and Bootstrap percentile intervals.
• Comparison of methods under conditional independence and alternative models.

Main Results:

• Modified Wald, Score-based, Bayesian, and Bootstrap intervals performed well under the conditional independent assumption, even with small proportions/samples.
• Wald test, likelihood ratio, Score-based, and Bootstrap intervals were satisfactory without the conditional independence assumption.
• Log- and logit-transformed intervals showed good performance for larger proportions and validated samples.

Conclusions:

• Several confidence interval procedures are effective for estimating proportions in double-sampling with two fallible classifiers.
• Method performance varies depending on the underlying model assumptions and data characteristics.
• The study provides practical guidance for selecting appropriate methods in real-world applications.