Correction to: Minimum sample size for developing a multivariable prediction model: PART II - binary and time-to-event outcomes (Statistics in Medicine, (2019), 38, 7, (1276-1296), 10.1002/sim.7992);Minimum sample size for developing a multivariable prediction model: PART II - binary and time-to-event outcomes

Statistics in Medicine

Volumn 38, Issue 7, 2019, Pages 1276-1296

  Riley, Richard D ^a   Snell, Kym IE ^a   Ensor, Joie ^a   Burke, Danielle L ^a   Harrell, Frank E ^b   Moons, Karel GM ^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

binary and time to event outcomes; logistic and Cox regression; multivariable prediction model; pseudo R squared; sample size; shrinkage

Indexed keywords

ARTICLE; CHAGAS DISEASE; CRITERION VARIABLE; HUMAN; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PREDICTION; PREDICTIVE VALUE; PREDICTOR VARIABLE; PROGNOSIS; RISK ASSESSMENT; SAMPLE SIZE; STATISTICAL MODEL; VENOUS THROMBOEMBOLISM; COMPUTER SIMULATION; MULTIVARIATE ANALYSIS; REGRESSION ANALYSIS; TIME;

COMPUTER SIMULATION; HUMANS; MULTIVARIATE ANALYSIS; REGRESSION ANALYSIS; SAMPLE SIZE; TIME;

EID: 85055292302     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.8409     Document Type: Erratum

References (60)

1. Steyerberg EW. Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating. New York, NY: Springer Science+Business Media; 2009.
2. Royston P, Moons KG, Altman DG, Vergouwe Y. Prognosis and prognostic research: developing a prognostic model. Br Med J. 2009;338:1373-1377.https://doi.org/10.1136/bmj.b604
3. Steyerberg EW, Moons KG, van der Windt DA, et al. Prognosis research strategy (PROGRESS) 3: prognostic model research. PLoS Med. 2013;10(2):e1001381.
4. Wells PS, Anderson DR, Rodger M, et al. Derivation of a simple clinical model to categorize patients probability of pulmonary embolism: increasing the models utility with the SimpliRED D-dimer. Thromb Haemost. 2000;83(3):416-420.
5. Wells PS, Anderson DR, Bormanis J, et al. Value of assessment of pretest probability of deep-vein thrombosis in clinical management. Lancet. 1997;350(9094):1795-1798.
6. Anderson KM, Odell PM, Wilson PW, Kannel WB. Cardiovascular disease risk profiles. Am Heart J. 1991;121(1 Pt 2):293-298.
7. Hippisley-Cox J, Coupland C, Vinogradova Y, et al. Predicting cardiovascular risk in England and Wales: prospective derivation and validation of QRISK2. BMJ. 2008;336(7659):1475-1482.
8. Haybittle JL, Blamey RW, Elston CW, et al. A prognostic index in primary breast cancer. Br J Cancer. 1982;45(3):361-366.
9. Galea MH, Blamey RW, Elston CE, Ellis IO. The Nottingham prognostic index in primary breast cancer. Breast Cancer Res Treat. 1992;22(3):207-219.
10. Riley RD, Snell KIE, Ensor J, et al. Minimum sample size for developing a multivariable prediction model: PART I - continuous outcomes. Statist Med. 2018. https://doi.org/10.1002/sim.7993
11. Peduzzi P, Concato J, Feinstein AR, Holford TR. Importance of events per independent variable in proportional hazards regression analysis II. Accuracy and precision of regression estimates. J Clin Epidemiol. 1995;48(12):1503-1510.
12. Peduzzi P, Concato J, Kemper E, Holford TR, Feinstein AR. A simulation study of the number of events per variable in logistic regression analysis. J Clin Epidemiol. 1996;49(12):1373-1379.
13. Concato J, Peduzzi P, Holford TR, Feinstein AR. Importance of events per independent variable in proportional hazards analysis I. Background, goals, and general strategy. J Clin Epidemiol. 1995;48(12):1495-1501.
14. Vittinghoff E, McCulloch CE. Relaxing the rule of ten events per variable in logistic and Cox regression. Am J Epidemiol. 2007;165(6):710-718.
15. Harrell Jr FE. Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis. Second ed. Cham, Switzerland: Springer International Publishing; 2015.
16. 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.
17. Austin PC, Steyerberg EW. Events per variable (EPV) and the relative performance of different strategies for estimating the out-of-sample validity of logistic regression models. Stat Methods Med Res. 2017;26(2):796-808.
18. Wynants L, Bouwmeester W, Moons KG, et al. A simulation study of sample size demonstrated the importance of the number of events per variable to develop prediction models in clustered data. J Clin Epidemiol. 2015;68(12):1406-1414.
19. van der Ploeg T, Austin PC, Steyerberg EW. Modern modelling techniques are data hungry: a simulation study for predicting dichotomous endpoints. BMC Med Res Methodol. 2014;14(1):137.
20. Courvoisier DS, Combescure C, Agoritsas T, Gayet-Ageron A, Perneger TV. Performance of logistic regression modeling: beyond the number of events per variable, the role of data structure. J Clin Epidemiol. 2011;64(9):993-1000.
21. Cox DR, Snell EJ. The Analysis of Binary Data. Second ed. Boca Raton, FL: Chapman and Hall; 1989.
22. Van Houwelingen JC. Shrinkage and penalized likelihood as methods to improve predictive accuracy. Stat Neerlandica. 2001;55(1):17-34.
23. Van Houwelingen JC, Le Cessie S. Predictive value of statistical models. Statist Med. 1990;9(11):1303-1325.
24. Copas JB. Regression, prediction and shrinkage. J Royal Stat Soc Ser B Methodol. 1983;45(3):311-354.
25. Tibshirani R. Regression shrinkage and selection via the lasso. J Royal Stat Soc Ser B Methodol. 1996;58(1):267-288.
26. 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.
27. Moons KG, Donders AR, Steyerberg EW, Harrell FE. Penalized maximum likelihood estimation to directly adjust diagnostic and prognostic prediction models for overoptimism: a clinical example. J Clin Epidemiol. 2004;57(12):1262-1270.
28. Efron B. Bootstrap methods: another look at the jackknife. Ann Stat. 1979;7(1):1-26.
29. van Diepen M, Schroijen MA, Dekkers OM, et al. Predicting mortality in patients with diabetes starting dialysis. PLoS One. 2014;9(3):e89744.
30. Copas JB. Using regression models for prediction: shrinkage and regression to the mean. Stat Methods Med Res. 1997;6(2):167-183.
31. 2 measures based on wald and likelihood ratio joint significance tests. Am Stat. 1990;44(3):250-253.
32. Hendry DF, Nielsen B. Econometric Modeling: A Likelihood Approach. Princeton, NJ. Princeton University Press; 2012.
33. Mittlboeck M, Heinzl H. Pseudo R-squared measures of generalized linear models. In: Proceedings of the 1st European Workshop on the Assessment of Diagnostic Performance; 2004; Milan, Italy.
34. Nagelkerke N. A note on a general definition of the coefficient of determination. Biometrika. 1991;78:691-692.
35. Debray TP, Damen JA, Snell KI, et al. A guide to systematic review and meta-analysis of prediction model performance. BMJ. 2017;356:i6460.
36. 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.
37. McFadden D. Conditional logit analysis of qualitative choice behavior. In: Zarembka P, ed. Frontiers in Econometrics. Cambridge, MA: Academic Press; 1974:104-142.
38. O'Quigley J, Xu R, Stare J. Explained randomness in proportional hazards models. Statist Med. 2005;24(3):479-489.
39. Royston P. Explained variation for survival models. Stata J. 2006;6(1):83-96.
40. Royston P, Sauerbrei W. A new measure of prognostic separation in survival data. Statist Med. 2004;23(5):723-748.
41. Jinks RC, Royston P, Parmar MK. Discrimination-based sample size calculations for multivariable prognostic models for time-to-event data. BMC Med Res Methodol. 2015;15(1):82.
42. Poppe KK, Doughty RN, Wells S, et al. Developing and validating a cardiovascular risk score for patients in the community with prior cardiovascular disease. Heart. 2017;103(12):891-892.
43. Hippisley-Cox J, Coupland C. Development and validation of QDiabetes-2018 risk prediction algorithm to estimate future risk of type 2 diabetes: cohort study. BMJ. 2017;359:j5019.
44. Sultan AA, West J, Grainge MJ, et al. Development and validation of risk prediction model for venous thromboembolism in postpartum women: multinational cohort study. BMJ. 2016;355:i6253.
45. Dvoretzky A, Kiefer J, Wolfowitz J. Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Ann Math Stat. 1956;27(3):642-669.
46. Brasil PE, Xavier SS, Holanda MT, et al. Does my patient have chronic Chagas disease? Development and temporal validation of a diagnostic risk score. Rev Soc Bras Med Trop. 2016;49(3):329-340.
47. Ensor J, Riley RD, Jowett S, et al. Prediction of risk of recurrence of venous thromboembolism following treatment for a first unprovoked venous thromboembolism: systematic review, prognostic model and clinical decision rule, and economic evaluation. Health Technol Assess. 2016;20(12):1-190.
48. Royston P, Parmar MKB. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statist Med. 2002;21(15):2175-2197.
49. Royston P, Lambert PC. Flexible Parametric Survival Analysis Using Stata: Beyond the Cox Model. Boca Raton, Fl: CRC Press; 2011.
50. Maxwell SE, Kelley K, Rausch JR. Sample size planning for statistical power and accuracy in parameter estimation. Annu Rev Psychol. 2008;59:537-563.
51. Hsieh FY, Lavori PW, Cohen HJ, Feussner JR. An overview of variance inflation factors for sample-size calculation. Eval Health Prof. 2003;26(3):239-257.
52. Hsieh FY, Lavori PW. Sample-size calculations for the Cox proportional hazards regression model with nonbinary covariates. Control Clin Trials. 2000;21(6):552-560.
53. Schmoor C, Sauerbrei W, Schumacher M. Sample size considerations for the evaluation of prognostic factors in survival analysis. Stat Med. 2000;19(4):441-452.
54. Borenstein M. Planning for precision in survival studies. J Clin Epidemiol. 1994;47(11):1277-1285.
55. Feiveson AH. Power by simulation. Stata J. 2002;2(2):107-124.
56. 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.
57. van Smeden M, de Groot JA, Moons KG, et al. No rationale for 1 variable per 10 events criterion for binary logistic regression analysis. BMC Med Res Methodol. 2016;16(1):163.
58. Riley RD, Hayden JA, Steyerberg EW, et al. Prognosis research strategy (PROGRESS) 2: prognostic factor research. PLoS Med. 2013;10(2):e1001380.
59. 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.
60. van Smeden M, Moons KG, de Groot JA, et al. Sample size for binary logistic prediction models: beyond events per variable criteria. Stat Methods Med Res. 2018. In press.