A comparative investigation of methods for logistics regression with separated or nearly separated data

Statistics in Medicine

Volumn 25, Issue 24, 2006, Pages 4216-4226

  Heinze, Georg ^a  

^a MEDICAL UNIVERSITY OF VIENNA   (Austria)

Author keywords

Bias reduction; Exact logistic regression; Infinite estimates; Modified score function; Penalized likelihood; Sparse data

Indexed keywords

ARTICLE; COMPUTER ANALYSIS; CONFIDENCE INTERVAL; ERYTHROCYTE SEDIMENTATION RATE; INCONTINENCE; INFERENTIAL STATISTICS; INTERMETHOD COMPARISON; LOGISTIC REGRESSION ANALYSIS; PREMATURITY; PROBABILITY; STATISTICAL MODEL;

AMNIOTIC FLUID; BLOOD SEDIMENTATION; DATA INTERPRETATION, STATISTICAL; FIBRINOGEN; GAMMA-GLOBULINS; HUMANS; INFANT, NEWBORN; INFANT, PREMATURE; LIKELIHOOD FUNCTIONS; LOGISTIC MODELS; LUNG DISEASES; ODDS RATIO; UREAPLASMA UREALYTICUM; URINARY INCONTINENCE;

EID: 33845900763     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.2687     Document Type: Article

References (33)

1. Schaefer RL. Bias correction in maximum likelihood logistic regression. Statistics in Medicine 1983; 2:71-78.
2. Cordeiro GM, McCullagh P. Bias correction in generalized linear models. Journal of the Royal Statistical Society, Series B 1991; 53:629-643.
3. Leung DH-Y, Wang YG. Bias reduction using stochastic approximation. Australian and New Zealand Journal of Statistics 1998; 40:43-52.
4. Cordeiro GM, Cribari-Neto F. On bias reduction in exponential and non-exponential family regression models. Communications in Statistics - Simulation and Computation 1998; 27:485-500.
5. Bull SB, Greenwood CMT, Hauck WW. Jackknife bias reduction for polychotomous logistic regression. Statistics in Medicine 1997; 16:545-560.
6. Hauck WW, Donner A. Wald's test as applied to hypotheses in logit analysis. Journal of the American Statistical Association 1977; 72:851-853.
7. Heinze G. The impact of separation in logistic regression on maximum likelihood and other estimation methods. Unpublished Doctoral Thesis, University of Vienna, Vienna, Austria, 1998.
8. Day N, Kerridge DF. A general maximum likelihood discriminant. Biometrics 1967; 23:313-328.
9. Albert A, Anderson JA. On the existence of maximum likelihood estimates in logistic regression models. Biometrika 1984; 71:1-10.
10. Hirji KF, Mehta CR, Patel NR. Computing distributions for exact logistic regression. Journal of the American Statistical Association 1987; 82:1110-1117.
11. Hirji KF, Tsiatis AA, Mehta CR. Median unbiased estimation for binary data. The American Statistician 1989; 43:7-11.
12. Mehta CR, Patel NR. Exact logistic regression: theory and examples. Statistics in Medicine 1995; 14:2143-2160.
13. Firth D. Bias reduction of maximum likelihood estimates. Biometrika 1993; 80:27-38.
14. Heinze G, Schemper M. A solution to the problem of separation in logistic regression. Statistics in Medicine 2002; 21:2409-2419.
15. Bull S, Mak C, Greenwod CMT. A modified score function estimator for multinomial logistic regression in small samples. Computational Statistics and Data Analysis 2002; 39:57-74.
16. Cytel Software Corporation. LogXact-5. Cytel Software Corporation: Cambridge, MA, U.S.A., 2002.
17. SAS Institute Inc. SAS for Windows, version 9. SAS Institute Inc.: Cary, NC, U.S.A., 2003.
18. Cox DR. Analysis of Binary Data. Methuen: London, 1970.
19. Mehta C, Patel N, Senchaudhuri P. Efficient Monte Carlo methods for conditional logistic regression. Journal of the American Statistical Association 2000; 95:99-108.
20. Heinze G, Ploner M. Fixing the nonconvergence bug in logistic regression with SPLUS and SAS. Computer Methods and Programs in Biomedicine 2003; 71:191-187.
21. Berger A, Witt A, Haiden N, Kretzer V, Heinze G, Kohlhauser C. Microbial invasion of the amniotic cavity at birth is associated with adverse short-term outcome of preterm infants. Journal of Perinatal Medicine 2003; 31:115-121.
22. Potter DM. A permutation test for inference in logistic regression with small- and moderate-sized data sets. Statistics in Medicine 2005; 24:693-708.
23. Collett D. Modelling Binary Data (2nd edn). Chapman & Hall: London, 2003.
24. King EN, Ryan TP. A preliminary investigation of maximum likelihood logistic regression versus exact logistic regression. The American Statistician 2002; 56:163-170.
25. Pierce DA, Peters D. Improving on exact tests by approximate conditioning. Biometrika 1999; 86:265-277.
26. Insightful Corp. S-PLUS for Windows, version 6.2. Insightful Corp.: Seattle, WA, U.S.A., 2003.
27. Heinze G, Ploner M. A SAS macro, S-Plus library and R package to perform logistic regression without convergence problems. Technical Report 2/ 2004, Department of Medical Computer Sciences, Medical University of Vienna, Vienna, 2004.
28. Venzon DJ, Moolgavkar SH. A method for computing profile-likelihood based confidence intervals. Applied Statistics 1988; 37:87-94.
29. Gulyaeva N, Zaslavsky A, Lechner P, Chlenov M, McConnell O, Chait A, Kipnis V, Zaslavsky B. Relative hydrophobicity and lipophilicity of drugs measured by aqueous two-phase partitioning, octanol-buffer partitioning and HPLC. A simple model for predicting blood-brain distribution. European Journal of Medicinal Chemistry 2003; 38:391-396.
30. Chauchemez B, Extramiana F, Cauchemez S, Cosson S, Zouzou H, Meddane M, D'Allonnes LR, Lavergne T, Leenhardt A, Coumel P, Houdart E. High-flow perfusion of sheaths for prevention of thromboembolic complications during complex catheter ablation in the left atrium. Journal of Cardiovascular Eletrophysiology 2004; 15:276-283.
31. Bonderman D, Jakowitsch J, Adlbrecht C, Schemper M, Kyrie PA, Schoenauer V, Exner M, Klepetko W, Kneussl MP, Maurer G, Lang I. Medical conditions increasing the risk of chronic thromboembolic pulmonary hypertension. Thrombosis and Haemostasis 2005; 93:512-516.
32. Gorak E, Geller N, Srinivasan R, Espinoza-Delgado I, Donohue T, Barrett AJ, Suffredini A, Childs R. Engraftment syndrome after nonmyeloablative allogeneic hematopoietic stem cell transplantation: incidence and effects on survival. Biology of Blood and Marrow Transplantation 2005; 11:542-550.
33. Heintel D, Kienle D, Shehata M, Kroeber A, Kroemer E, Schwarzinger I, Mitteregger D, Le I, Gleiss A, Mannhalter C, Chott A, Schwarzmeier J, Fonatsch C, Gaiger A, Doehner A, Stilgenbauer S, Jaeger U. High expression of lipoprotein lipase in poor risk b-cell chronic lymphocytic leukemia. Leukemia 2005; 19:1216-1223.