Minimum sample size for developing a multivariable prediction model: Part I – Continuous outcomes

Statistics in Medicine

Volumn 38, Issue 7, 2019, Pages 1262-1275

  Riley, Richard D ^a   Snell, Kym I E ^a   Ensor, Joie ^a   Burke, Danielle L ^a   Harrell, Frank E ^b   Moons, Karel G M ^c   Collins, Gary S ^d  

^a KEELE UNIVERSITY   (United Kingdom)

^b VANDERBILT UNIVERSITY SCHOOL OF MEDICINE   (United States)

^c UNIVERSITY MEDICAL CENTER UTRECHT   (Netherlands)

^d UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

continuous outcome; linear regression; minimum sample size; multivariable prediction model; R squared

Indexed keywords

ADULT; AFRICAN AMERICAN; ARTICLE; CONTROLLED STUDY; FEMALE; HUMAN; HUMAN EXPERIMENT; LINEAR REGRESSION ANALYSIS; LUNG FUNCTION; MAJOR CLINICAL STUDY; MEDICAL LITERATURE; OPTIMISM; PREDICTION; PREVALENCE; SAMPLE SIZE; COMPUTER SIMULATION; LUNG FUNCTION TEST; MULTIVARIATE ANALYSIS;

AFRICAN AMERICANS; COMPUTER SIMULATION; FEMALE; HUMANS; MULTIVARIATE ANALYSIS; RESPIRATORY FUNCTION TESTS; SAMPLE SIZE;

EID: 85055265422     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.7993     Document Type: Article

References (37)

1. PROGRESS Group. Prognosis research strategy (PROGRESS) 3: prognostic model research. PLoS Med. 2013;10(2):e1001381.
2. Steyerberg EW. Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating. New York, NY: Springer; 2009.
3. Harrell FE. Ordinal Logistic Regression. In: Regression Modeling Strategies. 2nd Edition. Cham, Switzerland: Springer; 2015:311-325. Springer Series in Statistics (SSS).
4. Riley RD, Hayden JA, Steyerberg EW, et al. Prognosis research strategy (PROGRESS) 2: prognostic factor research. PLoS Med. 2013;10(2):e1001380.
5. Moons KG, Altman DG, Reitsma JB, et al. Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): explanation and elaboration. Ann Intern Med. 2015;162(1):W1-W73.
6. Harrell FE Jr, Lee KL, Mark DB. Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statist Med. 1996;15(4):361-387.
7. Riley RD, Snell KIE, Ensor J, et al. Minimum sample size for developing a multivariable prediction model: PART II - binary and time-to-event outcomes. Statist Med. 2018. https://doi.org/10.1002/sim.7992
8. Van Houwelingen JC. Shrinkage and penalized likelihood as methods to improve predictive accuracy. Stat Neerlandica. 2001;55:17-34.
9. Van Houwelingen JC, Le Cessie S. Predictive value of statistical models. Statist Med. 1990;9(11):1303-1325.
10. Copas JB. Regression, prediction, and shrinkage. J Royal Statist Soc B. 1983;45(3):311-354.
11. Tibshirani R. Regression shrinkage and selection via the lasso. J Royal Statist Soc B. 1996;58:267-288.
12. Pavlou M, Ambler G, Seaman SR, et al. How to develop a more accurate risk prediction model when there are few events. BMJ. 2015;351:h3868.
13. Efron B. Bootstrap Methods: Another Look at the Jackknife. In: Kotz S, Johnson NL. (eds) Breakthroughs in Statistics. New York, NY: Springer; 1992:569-593. Springer Series in Statistics (SSS).
14. Copas JB. Using regression models for prediction: shrinkage and regression to the mean. Stat Methods Med Res. 1997;6(2):167-183.
15. Riley RD, Kauser I, Bland M, et al. Meta-analysis of randomised trials with a continuous outcome according to baseline imbalance and availability of individual participant data. Statist Med. 2013;32(16):2747-2766.
16. Steyerberg EW, Harrell FEJ, Borsboom GJ, Eijkemans MJC, Vergouwe Y, Habbema JDF. Internal validation of predictive models: efficiency of some procedures for logistic regression analysis. J Clin Epidemiol. 2001;54:774-781.
17. 2 measures based on Wald and likelihood ratio joint significance tests. Am Stat. 1990;44(3):250-253.
18. Hendry DF, Nielsen B. Econometric Modeling: A Likelihood Approach. Princeton, NJ: Princeton University Press; 2012.
19. Goldberger AS. Econometric Theory. New York, NY: Wiley; 1964.
20. Debray TP, Damen JA, Snell KI, et al. A guide to systematic review and meta-analysis of prediction model performance. BMJ. 2017;356:i6460.
21. Wessler BS, Paulus J, Lundquist CM, et al. Tufts PACE clinical predictive model registry: update 1990 through 2015. Diagn Progn Res. 2017;1(1):20.
22. Kumar R, Seibold MA, Aldrich MC, et al. Genetic ancestry in lung-function predictions. N Engl J Med. 2010;363(4):321-330.
23. Austin PC, Steyerberg EW. The number of subjects per variable required in linear regression analyses. J Clin Epidemiol. 2015;68(6):627-636.
24. Algina J, Olejnik S. Determining sample size for accurate estimation of the squared multiple correlation coefficient. Multivar Behav Res. 2000;35(1):119-137.
25. Tan L. Confidence Intervals for Comparison of the Squared Multiple Correlation Coefficients of non-Nested Models [dissertation]. Ontario, Canada: School of Graduate and Postdoctoral Studies, The University of Western Ontario; 2012.
26. Lee YS. Tables of the upper percentage points of the multiple correlation. Biometrika. 1972;59:175-189.
27. Zou GY. Toward using confidence intervals to compare correlations. Psychol Methods. 2007;12(4):399-413.
28. Kelley K. Confidence intervals for standardized effect sizes: theory, application, and implementation. J Stat Softw. 2007;20(8):1-24.
29. Kelley K. Methods for the Behavioral, educational, and social sciences: an R package. Behav Res Methods. 2007;39(4):979-984.
30. Kelley K. MBESS (Version 4.0.0 and higher) [computer software and manual]. 2018. https://CRAN.R-project.org/package=MBESS
31. McClelland GH. Increasing statistical power without increasing sample size. Am Psychol. 2000;55(8):963-964.
32. Hsieh FY, Bloch DA, Larsen MD. A simple method of sample size calculation for linear and logistic regression. Statist Med. 1998;17(14):1623-1634.
33. Kelley K, Maxwell SE. Sample size for multiple regression: obtaining regression coefficients that are accurate, not simply significant. Psychol Methods. 2003;8(3):305-321.
34. Kelley K. Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach. Behav Res Methods. 2007;39(4):755-766.
35. Maxwell SE, Kelley K, Rausch JR. Sample size planning for statistical power and accuracy in parameter estimation. Annu Rev Psychol. 2008;59:537-563.
36. Ogundimu EO, Altman DG, Collins GS. Adequate sample size for developing prediction models is not simply related to events per variable. J Clin Epidemiol. 2016;76:175-182.
37. Knofczynski GT, Mundfrom D. Sample sizes when using multiple linear regression for prediction. Educ Psychol Meas. 2008;68(3):431-442.