Review and evaluation of penalised regression methods for risk prediction in low-dimensional data with few events

Statistics in Medicine

Volumn 35, Issue 7, 2016, Pages 1159-1177

  Pavlou, Menelaos ^a   Ambler, Gareth ^a   Seaman, Shaun ^b   De iorio, Maria ^a   Omar, Rumana Z ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b MRC BIOSTATISTICS UNIT   (United Kingdom)

Author keywords

Bayesian regularisation; Overfitting; Rare events; Shrinkage

Indexed keywords

ELASTIC TISSUE; MAXIMUM LIKELIHOOD METHOD; MODEL; NOISE; PREDICTION; STATISTICAL MODEL; BAYES THEOREM; BIOSTATISTICS; COMPUTER SIMULATION; HUMAN; MALE; MORTALITY; PENIS TUMOR; PROGNOSIS; REGRESSION ANALYSIS; RISK FACTOR; STATISTICAL ANALYSIS; STATISTICAL BIAS;

BAYES THEOREM; BIAS (EPIDEMIOLOGY); BIOSTATISTICS; COMPUTER SIMULATION; DATA INTERPRETATION, STATISTICAL; HUMANS; LIKELIHOOD FUNCTIONS; LOGISTIC MODELS; MALE; MODELS, STATISTICAL; PENILE NEOPLASMS; PROGNOSIS; REGRESSION ANALYSIS; RISK FACTORS;

EID: 84959490685     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6782     Document Type: Article

References (49)

1. Moons KGM, Royston P, Vergouwe Y, Grobbee DE, Altman G. Prognosis and prognostic research: what, why, and how? British Medical Journal 2009; 338.
2. Moons KGM, Altman DG, Vergouwe Y, Royston P. Prognosis and prognostic research: application and impact of prognostic models in clinical practice. British Medical Journal 2009; 338.
3. Moons KGM, Kengne AP, Woodward M, Royston P, Vergouwe Y, Altman DG, Grobbee DE. Risk prediction models: I. Development, internal validation, and assessing the incremental value of a new (bio)marker. HEART 2012; 98(9):683-690.
4. Hippisley-Cox J, Coupland C, Vinogradova Y, Robson J, Minhas R, Sheikh A, Brindle P. Predicting cardiovascular risk in England and Wales: prospective derivation and validation of qrisk2. BMJ 2008; 336(7659):1475-1482.
5. D'Agostino RB, Vasan MJ RS and Pencina, Wolf PA, Cobain M, Massaro JM, Kannel WB. General cardiovascular risk profile for use in primary care: the Framingham Heart Study. Circulation; 117(1):743-53.
6. O' Mahony C, Jichi F, Pavlou M, Monserrat L, Anastasakis A, Rapezzi C, Biagini E, Gimeno R, Limongelli G, McKenna W, Omar R, Elliott P. A novel clinical risk prediction model for sudden cardiac death in hypertrophic cardiomyopathy. European Heart Journal 2013; 33(1):364.
7. Kayes O, Loddo M, Ambler G, Stoeber K, Williams GH, Ralph DJ, Minhas S. DNA replication licensing factors and aneuploidy are linked to tumour cell cycle states and clinical outcome in penile carcinoma. European Urology Supplements 2009; 8(4):368.
8. Harrell FE. Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival AnalysisSpringer (ed.). Springer: New York, 2001.
9. Peduzzi P, Concato J, Kemper E, Holford TR, Feinstein AR. A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology 1996; 49(12):1373-1379.
10. Vittinghoff E, McCulloch CE. Relaxing the rule of ten events per variable in logistic and Cox regression. American Journal of Epidemiology 2007; 165(6):710-718.
11. Bouwmeester W, Zuithoff NPA, Mallett S, Geerlings MI, Vergouwe Y, Steyerberg EW, Altman DG, Moons KGM. Reporting and methods in clinical prediction research: a systematic review. PLOS Medicine 2012; 9(5).
12. Steyerberg EW, Eijkemans MJC, Harrell FE, Habbema JDF. Prognostic modelling with logistic regression analysis: a comparison of selection and estimation methods in small data sets. Statistics in Medicine 2000; 19(8):1059-1079.
13. Ambler G, Seaman S, Omar RZ. An evaluation of penalised survival methods for developing prognostic models with rare events. Statistics in Medicine 2011; 31(11-12, SI):1150-1161.
14. Porzelius C, Schumacher M, Binder H. Sparse regression techniques in low-dimensional survival data settings. Statistics and Computing 2010; 20(2):151-163.
15. Sortari S. Penalized regression: bootstrap confidence intervals and variable selection for high-dimensional data sets. Ph.D. Thesis, Universita degli Studi di Milano, 2011.
16. Kyung M, Gill J, Ghosh M, Casella G. Penalized regression, standard errors, and Bayesian lassos. Bayesian Analysis 2010; 5(2):369-411.
17. Efron B. Frequentist accuracy of Bayesian estimates. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 2015; 77(3):617-646.
18. Rockova V, Lesaffre E, Luime J, Lowenberg B. Hierarchical Bayesian formulations for selecting variables in regression models. Statistics in Medicine 2012; 31(11-12, SI):1221-1237.
19. Verweij PJM, Van Houwelingen HC. Cross-validation in survival analysis. Statistics in Medicine 1993; 12(24):2305-2314.
20. Cessie SL, Houwelingen JCV. Ridge estimators in logistic regression. Journal of the Royal Statistical Society. Series C (Applied Statistics) 1992; 41(1):191-201.
21. Feig DG. Ridge regression - when biased estimation is better. Social Science Quarterly 1978; 58(4):708-716.
22. Tibshirani Robert. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 1996; 58: 267-288.
23. Zou H, Hastie T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 2005; 67(2):301-320.
24. B hlmann P, van de Geer S. Statistics for High-dimensional Data: Methods, Theory and Applications, 1. Springer Publishing Company, Incorporated: Berlin, 2011.
25. Zou H. The adaptive lasso and its oracle properties. Journal of the American Statistical Association 2006; 101(476):1418-1429.
26. Benner A, Zucknick M, Hielscher T, Ittrich C, Mansmann U. High-dimensional Cox models: the choice of penalty as part of the model building process. Biometrical Journal 2010; 52(1, SI):50-69.
27. Breheny P, Huang J. Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Annals of Applied Statistics 2011; 5(1):232-253.
28. Fan JQ, Li RZ. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 2001; 96(456):1348-1360.
29. Gelman A. Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine 2008; 27(15):2865-2873.
30. Goeman JJ. L1 and l2 penalized regression models, Technical Document, 2012.
31. Chatterjee A, Lahiri SN. Bootstrapping lasso estimators. Journal of the American Statistical Association 2011; 106(494):608-625.
32. Oehlert GW. A note on the delta method. The American Statistician 1992; 46(1):27-29.
33. Park T, Casella G. The Bayesian lasso. Journal of the American Statistical Association 2008; 103(482):681-686.
34. Fahrmeir L, Kneib T, Konrath S. Bayesian regularisation in structured additive regression: aăunifying perspective on shrinkage, smoothing and predictor selection. Statistics and Computing 2010; 20(2):203-219.
35. Kneib T, Konrath S, Fahrmeir L. High dimensional structured additive regression models: Bayesian regularization, smoothing and predictive performance. Journal of the Royal Statistical Society: Series C (Applied Statistics) 2011; 60(1):51-70.
36. George EI, McCulloch RE. Variable selection via Gibbs sampling. Journal of the American Statistical Association 1993; 88(423):881-889.
37. Ishwaran H, Rao JS. Spike and slab variable selection: frequentist and Bayesian strategies. Annals of Statistics 2005; 33(2):730-773.
38. O'Hara RB, Sillanpaa MJ. A review of Bayesian variable selection methods: what, how and which. Bayesian Analysis 2009; 4(1):85-117.
39. Ambler G, Brady AR, Royston P. Simplifying a prognostic model: a simulation study based on clinical data. Statistics in Medicine 2002; 21(24):3803-3822.
40. Steyerberg EW, Vickers AJ, Cook NR, Gerds T, Gonen M, Obuchowski N, Pencina MJ, Kattan MW. Assessing the performance of prediction models: a framework for traditional and novel measures. Epidemiology 2010; 21(1):128-138.
41. Steyerberg EW. Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating, 1. Springer: New York, 2009.
42. Roberts S, Nowak G. Stabilizing the lasso against cross-validation variability. Computational Statistics and Data Analysis 2014; 70(0):198-211.
43. Huang J, Ma S, Zhang CH. Adaptive lasso for sparse high-dimensional regression models. Statistica Sinica 2008; 18(4):1603-1618.
44. Austin E, Pan W, Shen X. Penalized regression and risk prediction in genome-wide association studies. Statistical Analysis and Data Mining 2013; 6(4):315-328.
45. Firth D. Bias reduction of maximum likelihood estimates. Biometrika 1993; 80(1):27-38.
46. Heinze G, Schemper M. A solution to the problem of separation in logistic regression. Statistics in Medicine 2002; 21(16):2409-2419.
47. van der Ploeg T, Austin P, Steyerberg E. Modern modelling techniques are data hungry: a simulation study for predicting dichotomous endpoints. BMC Medical Research Methodology 2014; 14(1):137.
48. Collins GS, Reitsma JB, Altman DG, Moons KGM. Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): The TRIPOD statement. Annals of Internal Medicine 2015; 162(1):55-63.
49. Chawla NV, Bowyer KW, Hall LO, Kegelmeyer WP. SMOTE: synthetic minority over-sampling technique. Journal of Artificial Intelligence Research 2002; 16: 321-357.