Related Experiment Video
Updated: May 17, 2026
An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
Comparison of approaches to estimate confidence intervals of post-test probabilities of diagnostic test results in a
Bas van Zaane1, Yvonne Vergouwe, A Rogier T Donders
1Julius Center for Health Sciences and Primary Care And Division of Anesthesiology, Intensive Care Care and Emergency Medicine, University Medical Center Utrecht, PO box 85500, 3508 GA Utrecht, The Netherlands. b.vanzaane@umcutrecht.nl
Background:
Nested case-control studies become increasingly popular as they can be very efficient for quantifying the diagnostic accuracy of costly or invasive tests or (bio)markers. However, they do not allow for direct estimation of the test's predictive values or post-test probabilities, let alone for their confidence intervals (CIs). Correct estimates of the predictive values itself can easily be obtained using a simple correction by the (inverse) sampling fractions of the cases and controls. But using this correction to estimate the corresponding standard error (SE), falsely increases the number of patients that are actually studied, yielding too small CIs. We compared different approaches for estimating the SE and thus CI of predictive values or post-test probabilities of diagnostic test results in a nested case-control study.
Methods:
We created datasets based on a large, previously published diagnostic study on 2 different tests (D-dimer test and calf difference test) with a nested case-control design. We compared six different approaches; the approaches were: 1. the standard formula for the SE of a proportion, 2. adaptation of the standard formula with the sampling fraction, 3. A bootstrap procedure, 4. A approach, which uses the sensitivity, the specificity and the prevalence, 5. Weighted logistic regression, and 6. Approach 4 on the log odds scale. The approaches were compared with respect to coverage of the CI and CI-width.
Results:
The bootstrap procedure (approach 3) showed good coverage and relatively small CI widths. Approaches 4 and 6 showed some undercoverage, particularly for the D-dimer test with frequent positive results (positive results around 70%). Approaches 1, 2 and 5 showed clear overcoverage at low prevalences of 0.05 and 0.1 in the cohorts for all case-control ratios.
Conclusion:
The results from our study suggest that a bootstrap procedure is necessary to assess the confidence interval for the predictive values or post-test probabilities of diagnostic tests results in studies using a nested case-control design.
Related Concept Videos
01:21Confidence Intervals
A confidence...
01:20Comparing the Survival Analysis of Two or More Groups
01:19Interpretation of Confidence Intervals
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
01:23Types of Biopharmaceutical Studies: Controlled and Non-Controlled Approaches
Non-controlled studies, commonly employed for initial exploration, lack a control group, rendering them susceptible to biases and external influences. In contrast, controlled...
01:24Testing a Claim about Population Proportion
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
01:14Decision Making: Traditional Method
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...