Efficiency of Case-Control Studies with Multiple Controls Per Case: Continuous or Dichotomous Data
Abstract
The statistical efficiency of a study design which matches each case with k controls is compared with that of the standard matched-pairs setup. For the situation in which the distribution of measurements on the factor under investigation is continuous, the comparison criterion used is the reciprocal of the variance ratio of the corresponding case-control difference estimators; for dichotomous observations, the Pitman efficiency of Miettinen's test [1969] or of Pike and Morrow's test [1970] relative to McNemar's test is used. When the variances for continuously distributed case and control measurements are equal to the same result, 2k/(k + 1), is obtained for both situations and, more generally, the efficiency of k1 controls relative to k2 controls is given by k1(k2 + 1)/k2(k1 + 1). The Pitman efficiency is compared with the "practical efficiency" for large-sample dichotomous situations.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Selecting multiple controls per case increases the statistical power of an investigation by increasing the sample size, and precision may improve with up to about three or four controls per case.
“This method increases the “statistical power” of the investigation by increasing the sample size. The precision of the findings may improve by having up to about three or four controls per case.21-23”
From Observational studies: Cohort and case-control studies (2010) · cites this paper as [21]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Statistical Aspects of the Analysis of Data From Retrospective Studies of Disease
(1959) · JNCI: Journal of the National Cancer Institute · doi:10.1093/jnci/22.4.719 · Cited by 14,689 · see citing works
Note on the Sampling Error of the Difference Between Correlated Proportions or Percentages
McNemar, Q. (1947) · Psychometrika · doi:10.1007/bf02295996 · Cited by 4,754 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Observational studies: Cohort and case-control studies
Song, J. W., & Chung, K. C. (2010) · Plastic and Reconstructive Surgery · doi:10.1097/prs.0b013e3181f44abc · Cited by 948 · see citing works
Perioperative Pulmonary Outcomes in Patients with Sleep Apnea After Noncardiac Surgery
Memtsoudis, S., Liu, S. S., Ma, Y., Chiu, Y. L., Walz, J. M., Gaber-Baylis, L. K., & Mazumdar, M. (2011) · Anesthesia & Analgesia · doi:10.1213/ane.0b013e3182009abf · Cited by 311 · see citing works
The nested case-control study in cardiology
Essebag, V., Genest, J., Suissa, S., & Pilote, L. (2003) · American Heart Journal · doi:10.1016/s0002-8703(03)00512-x · Cited by 173 · see citing works
Sutton, A. J., Muir, K. R., Mockett, S., & Fentem, P. (2001) · Annals of the Rheumatic Diseases · doi:10.1136/ard.60.8.756 · Cited by 101 · see citing works
- Authors
- Ury, H. K.
- Corresponding author
- Ury, Hans K.
- Venue
- Biometrics
- Publisher
- JSTOR
- Published
- 1975-09
- Volume
- 31
- Issue
- 3
- Pages
- 643
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W2080716821
- Cited by
- 249
- References
- 2
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 7 · 2023: 6 · 2022: 8 · 2021: 7 · 2020: 9 · 2019: 6 · 2018: 8 · 2017: 8 · 2016: 8 · 2015: 15 · 2014: 23 · 2013: 8 · 2012: 7
- FWCI
- 0.66
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrics (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Institutes of Health
- National Cancer Institute
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Keywords
- case-control study, paired design, statistical efficiency, Pitman efficiency, McNemar test, continuous data, dichotomous data, variance ratio, matched case-control studies
- MeSH terms
- Clinical Trials as Topic, Humans, Mathematics, Research Design, Sampling Studies, Statistics as Topic
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
