Diagnostic Accuracy · LR-CI

Sample Size for Estimation of LR+ / LR-

Plan sample size for estimating a diagnostic test's positive or negative likelihood ratio with a prespecified clinically acceptable confidence bound.

1. Planning setup

Likelihood-ratio endpoint

LR+ (rule-in)LR- (rule-out)

Planned sampling approach

Balanced reference-standard groupsRecruit equal numbers of reference-standard-positive and reference-standard-negative participants (1:1).Consecutive / cross-sectional samplingRecruit from the target population; anticipated prevalence is required.

2. Information obtained from previous study/literature

Anticipated sensitivity (%)

Anticipated specificity (%)

Anticipated LR+: 4.000; Anticipated LR-: 0.250

3. Information decided by the researcher

Minimum acceptable lower confidence bound for LR+

The lower bound of the confidence interval should exceed this value.

Confidence level (%)

Anticipated dropout/non-response (%)

4. Results

Enter the likelihood-ratio estimation assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A study evaluates a rapid influenza test and wants to estimate its positive likelihood ratio with adequate precision using anticipated sensitivity, specificity, and prevalence.

Formula and methodological note

Scope and limitations: Use this calculator only for the diagnostic design named on this page and its stated independent or paired sampling assumptions. It does not cover clustering, repeated lesions, multiple-reader designs, prediction-model development, or non-inferiority/equivalence unless explicitly stated. The implemented normal or binormal approximation may be unsuitable near parameter boundaries or with sparse reference-standard groups. Where prevalence is used, it supports recruitment planning and does not necessarily form part of the core precision or hypothesis-test calculation.

This calculator estimates log-transformed confidence intervals for LR+ or LR-. Natural logarithms are used.

LR+ = Sensitivity / (1 - Specificity)

LR- = (1 - Sensitivity) / Specificity

z = Phi^-1(1 - alpha / 2)

LR+ balanced: n = ceiling(z^2 x [(1 - Se) / Se + Sp / (1 - Sp)] / [log(LR+) - log(lower bound)]^2)

LR+ consecutive: N = ceiling(z^2 x [(1 - Se) / (prevalence x Se) + Sp / ((1 - prevalence) x (1 - Sp))] / [log(LR+) - log(lower bound)]^2)

LR- balanced: n = ceiling(z^2 x [Se / (1 - Se) + (1 - Sp) / Sp] / [log(upper bound) - log(LR-)]^2)

LR- consecutive: N = ceiling(z^2 x [Se / (prevalence x (1 - Se)) + (1 - Sp) / ((1 - prevalence) x Sp)] / [log(upper bound) - log(LR-)]^2)

Methodological note: This calculator is intended for estimation of a single diagnostic test's positive or negative likelihood ratio at a fixed diagnostic threshold. It does not cover comparison of likelihood ratios between tests, paired tests, predictive values, clustering, repeated lesions, or multiple-reader studies.

Method references

Hajian-Tilaki K. Sample size estimation in diagnostic test studies of biomedical informatics. Journal of Biomedical Informatics. 2014;48:193-204. Section 6.4.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Estimation of a Likelihood Ratio (LR-CI).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/diagnostic-accuracy/likelihood-ratio/.