A new test and graphical tool to assess the goodness of fit of logistic regression models

Statistics in Medicine

Volumn 35, Issue 5, 2016, Pages 709-720

  Nattino, Giovanni ^a   Finazzi, Stefano ^b   Bertolini, Guido ^a  

^a MARIO NEGRI INSTITUTE FOR PHARMACOLOGICAL RESEARCH   (Italy)

^b UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Calibration test; Dichotomous outcome models; Goodness of fit; Graphical methods; Logistic regression models

Indexed keywords

CALIBRATION; LOGISTIC REGRESSION ANALYSIS; PREDICTION; PROBABILITY; PROCESS MODEL; STATISTICAL MODEL; VALIDATION PROCESS; BENCHMARKING; CLINICAL TRIAL (TOPIC); SAMPLE SIZE; STATISTICS AND NUMERICAL DATA;

BENCHMARKING; CALIBRATION; CLINICAL TRIALS AS TOPIC; LIKELIHOOD FUNCTIONS; LOGISTIC MODELS; SAMPLE SIZE;

EID: 84957111040     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6744     Document Type: Article

References (23)

1. Steyerberg EW, Vickers AJ, Cook NR, Gerds T, Gonen M, Obuchowski N, Pencina MJ, Kattan MW. Assessing the performance of prediction models. Epidemiology. 2010; 21(1):128-138.
2. Hosmer D, Lemeshow S. Applied Logistic Regression, Wiley series in probability and mathematical statistics: applied probability and statistics. Wiley: New York, 1989.
3. Le Cessie S, Van Houwelingen J. A goodness-of-fit test for binary regression models, based on smoothing methods. Biometrics. 1991; 47(4):1267-1282.
4. Royston P. The use of cusums and other techniques in modelling continuous covariates in logistic regression. Statistics in Medicine. 1992; 11(8):1115-1129.
5. Austin PC, Steyerberg EW. Graphical assessment of internal and external calibration of logistic regression models by using loess smoothers. Statistics in Medicine. 2014; 33(3):517-535.
6. Moons KG, Altman DG, Reitsma JB, Ioannidis JP, Macaskill P, Steyerberg EW, Vickers AJ, Ransohoff DF, Collins GS. Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (tripod): explanation and elaboration. Annals of Internal Medicine. 2015; 162(1):W1-W73.
7. Cleveland WS. Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association. 1979; 74(368):829-836.
8. Cox D. Two further applications of a model for a method of binary regression. Biometrika. 1958; 45: 562-565.
9. Harrell F. Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis, Graduate Texts in Mathematics. Springer: New York, 2001.
10. Harrell FE, Lee KL. Using logistic model calibration to assess the quality of probability predictions, division of biometry duke university medical center. http://biostat.mc.vanderbilt.edu/wiki/pub/Main/FrankHarrell/logistCal.pdf.
11. Miller ME, Hui SL, Tierney WM. Validation techniques for logistic regression models. Statistics in Medicine. 1991; 10(8):1213-1226.
12. Hosmer DW, Hosmer T, Le Cessie S, Lemeshow S. A comparison of goodness-of-fit tests for the logistic regression model. Statistics in Medicine. 1997; 16: 965-980.
13. Bertolini G, D'Amico R, Nardi D, Tinazzi A, Apolone G. One model, several results: the paradox of the HosmerULemeshow goodness-of-fit test for the logistic regression model. Journal of Epidemiology and Biostatistics. 2000; 5(4):251-253.
14. Stallard N. Simple tests for the external validation of mortality prediction scores. Statistics in Medicine. 2009; 28: 377-388.
15. Nattino G, Finazzi S, Bertolini G. Comments on: 'graphical assessment of internal and external calibration of logistic regression models by using loess smoothers' by Peter C. Austin and Ewout W. Steyerberg. Statistics in Medicine. 2014; 33(15):2696-2698.
16. Finazzi S, Poole D, Luciani D, Cogo PE, Bertolini G. Calibration belt for quality of care assessment based on dichotomous outcome. PLoS ONE. 2011; 6(2):e16110.
17. Nattino G, Finazzi S, Bertolini G. A new calibration test and a reappraisal of the calibration belt for the assessment of prediction models based on dichotomous outcomes. Statistics in Medicine. 2014; 33(14):2390-2407.
18. McCullagh P, Nelder JA. Generalized Linear Models, Chap. 4. Chapman & Hall: London, 1989; 72-100.
19. Pratt JW. Concavity of the log likelihood. Journal of the American Statistical Association. 1981; 76(373):103-106.
20. 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. http://www.sciencedirect.com/science/article/pii/S0895435696002363.
21. Rossi C, Di Gangi S, Bertolini G. Progetto Margherita - Rapporto 2009. Sestante Edizioni: Bergamo, 2010. http://www.giviti.marionegri.it/MargheritaDue_PrecedentiRapporti.asp.
22. Le Gall J, Lemeshow S, Saulnier F. A new simplified acute physiology score (SAPS II) based on a european/north american multicenter study. JAMA. 1993; 270(24):2957-2963.
23. Paul P, Pennell ML, Lemeshow S. Standardizing the power of the Hosmer-Lemeshow goodness of fit test in large data sets. Statistics in Medicine. 2013; 32(1):67-80.