Introduction to sample size determination and power analysis for clinical trials
Abstract
The importance of sample size evaluation in clinical trials is reviewed and a general method is presented from which specific equations are derived for sample size determination or the analysis of power for a wide variety os statistical procedures. The method is discussed and illustrated in relation to the t test, tests for proportions, tests of survival time, and tests for correlations as they commonly occur in clinical trials. Most of the specific equations reduce to a simple general form for which tables are presented.
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Using formulas to calculate power for a test of two independent proportions, 75 CSOs per group will achieve 80% power (α=0.05) if the treatment entry rate in the CBT-CSO group is 35%.
“Thus, using formulas to calculate power for a test of two independent proportions,65 it is estimated that 75 CSOs per group will achieve 80% power (α=0.05) if the treatment entry rate in the CBT-CSO group is 35%.”
Cites
Biometry: The Principles and Practice of Statistics in Biological Research
Sokal, R. R., & Rohlf, F. J. (1969) · Cited by 20,963 · see citing works
Snedecor, G. W., Cochran, W. G., & STOUT, B. B. (1939) · Soil Science · doi:10.1097/00010694-193902000-00006 · Cited by 19,423 · see citing works
Statistical Methods for Rates and Proportions
Fleiss, J. L., Levin, B., & Paik, M. C. (2003) · Wiley Series in Probability and Statistics · doi:10.1002/0471445428 · Cited by 18,646 · see citing works
Peto, R., Pike, M. C., Armitage, P., Breslow, N. E., Cox, D. R., Howard, S. V., Mantel, N., McPherson, K., Peto, J., & Smith, P. G. (1977) · British Journal of Cancer · doi:10.1038/bjc.1977.1 · Cited by 8,285 · see citing works
Snedecor, G. W., & Cochran, W. G. (1967) · Cited by 6,573 · see citing works
Maximum utilization of the life table method in analyzing survival
Cutler, S. J., & Ederer, F. (1958) · Journal of Chronic Diseases · doi:10.1016/0021-9681(58)90126-7 · Cited by 2,870 · see citing works
Freiman, J. A., Chalmers, T. C., Smith, H., & Kuebler, R. R. (1978) · New England Journal of Medicine · doi:10.1056/nejm197809282991304 · Cited by 1,628 · see citing works
Distributions in Statistics: Continuous Multivariate Distributions.
Fisk, P. R., Johnson, N. L., & Kotz, S. (1973) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2344756 · Cited by 1,552 · see citing works
Statistical Methods for Rates and Proportions.
D., F. N., & Fleiss, J. L. (1973) · Biometrics · doi:10.2307/2529186 · Cited by 1,394 · see citing works
Distributions in Statistics: Continuous Univariate Distributions
Buckland, W. R., Johnson, N. L., & Kotz, S. (1971) · Revue de l Institut International de Statistique / Review of the International Statistical Institute · doi:10.2307/1402281 · Cited by 1,020 · see citing works
Analysis of Survival Data under the Proportional Hazards Model
Breslow, N. E. (1975) · International Statistical Review · doi:10.2307/1402659 · Cited by 596 · see citing works
Survival Distributions: Reliability Applications in the Biomedical Sciences
(1978) · Food and Cosmetics Toxicology · doi:10.1016/s0015-6264(78)80019-4 · Cited by 523 · see citing works
Statistical Methods for Rates and Proportions
Conover, W. J. (1974) · Technometrics · doi:10.1080/00401706.1974.10489195 · Cited by 521 · see citing works
Survival Distributions: Reliability Applications in the Biomedical Sciences
Heil, P. F., Gross, A. J., & Clark, V. A. (1976) · Technometrics · doi:10.2307/1268667 · Cited by 417 · see citing works
Planning the size and duration of a clinical trial studying the time to some critical event
George, S. L., & Desu, M. M. (1974) · Journal of Chronic Diseases · doi:10.1016/0021-9681(74)90004-6 · Cited by 279 · see citing works
Correlation Coefficients Measured on the Same Individuals
Dunn, O. J., & Clark, V. A. (1969) · Journal of the American Statistical Association · doi:10.2307/2283746 · Cited by 263 · see citing works
Sample sizes for medical trials with special reference to long-term therapy
Halperin, M., Rogot, E., Gurian, J. M., & Ederer, F. (1968) · Journal of Chronic Diseases · doi:10.1016/0021-9681(68)90082-9 · Cited by 135 · see citing works
The Matched Pairs Design in the Case of All-or-None Responses
Miettinen, O. S. (1968) · Biometrics · doi:10.2307/2528039 · Cited by 133 · see citing works
The Randomized Clinical Trial and Therapeutic Decisions.
McPherson, K., Tygstrup, N., Lachin, J. M., & Juhl, E. (1983) · Biometrics · doi:10.2307/2531034 · Cited by 70 · see citing works
Self-citationSample Size Determinations for r x c Comparative Trials
Lachin, J. M. (1977) · Biometrics · doi:10.2307/2529781 · Cited by 63 · see citing works
Self-citationSample size determinants for r X c comparative trials.
Lachin, J. M. (1977) · PubMed · Cited by 59 · see citing works
Self-citationGuidelines for detection of hepatotoxicity due to drugs and chemicals
Seeff, L. B. (1980) · Gastroenterology · doi:10.1016/0016-5085(80)90400-x · Cited by 58 · see citing works
Lachin, J. M., Marks, J. W., Schoenfield, L. J., Tyor, M. P., Bennett, P. H., Grundy, S. M., Hardison, W. G. M., Shaw, L., Thistle, J. L., Vlahcevic, Z. R., et al. (1981) · Controlled Clinical Trials · doi:10.1016/0197-2456(81)90012-x · Cited by 56 · see citing works
Self-citationSchork, M. A., & Remington, R. D. (1967) · Journal of Chronic Diseases · doi:10.1016/0021-9681(67)90005-7 · Cited by 53 · see citing works
Planning the duration of long-term survival time studies designed for accrual by cohorts
Pasternack, B. S., & Gilbert, H. S. (1971) · Journal of Chronic Diseases · doi:10.1016/0021-9681(71)90094-4 · Cited by 47 · see citing works
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Cited by
Sorted by citations
Sample size estimation and power analysis for clinical research studies
Suresh, K., & Chandrashekara, S. (2012) · Journal of Human Reproductive Sciences · doi:10.4103/0974-1208.97779 · Cited by 1,024 · see citing works
RetractedBayesian approaches to randomized trials
Spiegelhalter, D. J., Freedman, L. S., & Parmar, M. K. B. (1994) · Journal of the Royal Statistical Society. Series A (Statistics in Society) · doi:10.2307/2983527 · Cited by 720 · see citing works
Statistical Considerations in the Intent-to-Treat Principle
Lachin, J. M. (2000) · Controlled Clinical Trials · doi:10.1016/s0197-2456(00)00046-5 · Cited by 652 · see citing works
Self-citationRubenstein, L. Z., Stuck, A. E., Siu, A. L., & Wieland, D. (1991) · Journal of the American Geriatrics Society · doi:10.1111/j.1532-5415.1991.tb05927.x · Cited by 597 · see citing works
Svendsen, K. B., Jensen, T. S., & Bach, F. W. (2004) · BMJ · doi:10.1136/bmj.38149.566979.ae · Cited by 500 · see citing works
Palmer, J. P., Fleming, G. A., Greenbaum, C. J., Herold, K. C., Jansa, L. D., Kolb, H., Lachin, J. M., Polonsky, K. S., Pozzilli, P., Skyler, J. S., et al. (2004) · Diabetes · doi:10.2337/diabetes.53.1.250 · Cited by 491 · see citing works
Self-citationUsing mHealth Technology to Enhance Self-Monitoring for Weight Loss
Burke, L. E., Styn, M. A., Sereika, S. M., Conroy, M. B., Ye, L., Glanz, K., Sevick, M. A., & Ewing, L. J. (2012) · American Journal of Preventive Medicine · doi:10.1016/j.amepre.2012.03.016 · Cited by 295 · see citing works
Sample-size calculations for Cohen's kappa.
Cantor, A. B. (1996) · Psychological Methods · doi:10.1037/1082-989x.1.2.150 · Cited by 240 · see citing works
Study of the Atopic March: Development of Atopic Comorbidities
Schneider, L., Hanifin, J., Boguniewicz, M., Eichenfield, L. F., Spergel, J. M., Dakovic, R., & Paller, A. S. (2016) · Pediatric Dermatology · doi:10.1111/pde.12867 · Cited by 148 · see citing works
Imprint of assortative mating on the human genome
Yengo, L., Robinson, M. R., Keller, M. C., Kemper, K. E., Yang, Y., Trzaskowski, M., Gratten, J., Turley, P., Cesarini, D., Benjamin, D. J., et al. (2018) · Nature Human Behaviour · doi:10.1038/s41562-018-0476-3 · Cited by 148 · see citing works
Larson, E. L., Lin, S. X., Gomez-Pichardo, C., & Della-Latta, P. (2004) · Annals of Internal Medicine · doi:10.7326/0003-4819-140-5-200403020-00007 · Cited by 111 · see citing works
Mason, A. E., Jhaveri, K., Cohn, M., & Brewer, J. A. (2018) · Journal of Behavioral Medicine · doi:10.1007/s10865-017-9884-5 · Cited by 106 · see citing works
First-Episode Major Depression: Few Sex Differences in Course
Simpson, H. B. (1997) · Archives of General Psychiatry · doi:10.1001/archpsyc.1997.01830190059006 · Cited by 104 · see citing works
Mehnert, A., Koranyi, S., Philipp, R., Scheffold, K., Kriston, L., Lehmann‐Laue, A., Engelmann, D., Vehling, S., Eisenecker, C., Oechsle, K., et al. (2020) · Psycho-Oncology · doi:10.1002/pon.5521 · Cited by 47 · see citing works
Setaro, L., Santos-Silva, P. R., Nakano, E. Y., Sales, C. H., Nunes, N., Greve, J. M., & Colli, C. (2014) · Journal of Sports Sciences · doi:10.1080/02640414.2013.828847 · Cited by 45 · see citing works
Brooker, S., Bethony, J. M., Rodrigues, L. C., Alexander, N., Geiger, S. M., & Hotez, P. J. (2005) · Expert Review of Vaccines · doi:10.1586/14760584.4.1.35 · Cited by 40 · see citing works
Santina, T., Beaulieu, D., Gagné, C., & Guillaumie, L. (2021) · International Journal of Sport and Exercise Psychology · doi:10.1080/1612197x.2020.1735257 · Cited by 20 · see citing works
Magnusson, K., Nilsson, A., Hellner Gumpert, C., Andersson, G., & Carlbring, P. (2015) · BMJ Open · doi:10.1136/bmjopen-2015-008724 · Cited by 18 · see citing works
Garyga, V., Pochelu, F., Thivichon-Prince, B., Aouini, W., Santamaria, J., Lambert, F., Maucort-Boulch, D., Gueyffier, F., Gritsch, K., & Grosgogeat, B. (2019) · Trials · doi:10.1186/s13063-019-3738-0 · Cited by 14 · see citing works
Lachin, J. M., & Bautista, O. M. (1995) · Cancer Treatment and Research · doi:10.1007/978-1-4615-2009-2_10 · Cited by 12 · see citing works
Self-citation
- Authors
- Lachin, J. M.
- Affiliations
- George Washington University (US)
- Corresponding author
- Lachin, John M.
- ORCID
- Lachin, John M.
- Venue
- Controlled Clinical Trials
- Publisher
- Elsevier BV
- Published
- 1981-06
- Volume
- 2
- Issue
- 2
- Pages
- 93-113
- ISSN
- 0197-2456 (ISSN-L)
- OpenAlex
- W1997182468
- Cited by
- 1,012
- References
- 25
- Citations by year
- 2026: 13 · 2025: 27 · 2024: 37 · 2023: 21 · 2022: 24 · 2021: 32 · 2020: 23 · 2019: 33 · 2018: 25 · 2017: 30 · 2016: 30 · 2015: 38 · 2014: 35 · 2013: 27 · 2012: 23
- FWCI
- 13.44
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Controlled Clinical Trials (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- sample size determination, statistical power, clinical trials, t-test, survival analysis, correlation test, statistical tables
- MeSH terms
- Clinical Trials as Topic, Research Design, Sampling Studies, Statistics as Topic
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