In statistics, the one in ten rule is a rule of thumb for how many predictor parameters can be estimated from data when doing regression analysis (in particular proportional hazards models in survival analysis and logistic regression) while keeping the risk of overfitting and finding spurious correlations low. The rule states that one predictive variable can be studied for every ten events.[1][2][3][4] For logistic regression the number of events is given by the size of the smallest of the outcome categories, and for survival analysis it is given by the number of uncensored events.[3]
For example, if a sample of 200 patients is studied and 20 patients die during the study (so that 180 patients survive), the one in ten rule implies that two pre-specified predictors can reliably be fitted to the total data. Similarly, if 100 patients die during the study (so that 100 patients survive), ten pre-specified predictors can be fitted reliably. If more are fitted, the rule implies that overfitting is likely and the results will not predict well outside the training data. It is not uncommon to see the 1:10 rule violated in fields with many variables (e.g. gene expression studies in cancer), decreasing the confidence in reported findings.[5]
^Harrell, F. E. Jr.; Lee, K. L.; Califf, R. M.; Pryor, D. B.; Rosati, R. A. (1984). "Regression modelling strategies for improved prognostic prediction". Stat Med. 3 (2): 143–52. doi:10.1002/sim.4780030207. PMID 6463451.
^Harrell, F. E. Jr.; Lee, K. L.; Mark, D. B. (1996). "Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors" (PDF). Stat Med. 15 (4): 361–87. doi:10.1002/(sici)1097-0258(19960229)15:4<361::aid-sim168>3.0.co;2-4. PMID 8668867.
^ abPeduzzi, Peter; Concato, John; Kemper, Elizabeth; Holford, Theodore R.; Feinstein, Alvan R. (1996). "A simulation study of the number of events per variable in logistic regression analysis". Journal of Clinical Epidemiology. 49 (12): 1373–1379. doi:10.1016/s0895-4356(96)00236-3. PMID 8970487.
^"Chapter 8: Statistical Models for Prognostication: Problems with Regression Models". Archived from the original on October 31, 2004. Retrieved 2013-10-11.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
^Ernest S. Shtatland, Ken Kleinman, Emily M. Cain. Model building in Proc PHREG with automatic variable selection and information criteria. Paper 206–30 in SUGI 30 Proceedings, Philadelphia, Pennsylvania April 10–13, 2005. http://www2.sas.com/proceedings/sugi30/206-30.pdf
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