Heinze G, Schemper M. A solution to the problem of separation in logistic regression. Stat Med 21: 2409-2419

Section of Clinical Biometrics, Department of Medical Computer Sciences, University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria.
Statistics in Medicine (Impact Factor: 1.83). 08/2002; 21(16):2409-19. DOI: 10.1002/sim.1047
Source: PubMed


The phenomenon of separation or monotone likelihood is observed in the fitting process of a logistic model if the likelihood converges while at least one parameter estimate diverges to +/- infinity. Separation primarily occurs in small samples with several unbalanced and highly predictive risk factors. A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates is shown to provide an ideal solution to separation. It produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald tests and confidence intervals are available but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. The clear advantage of the procedure over previous options of analysis is impressively demonstrated by the statistical analysis of two cancer studies.

Download full-text


Available from: Georg Heinze, Dec 22, 2014
  • Source
    • "Artificial data, which have no influence on model inferences, are 'added' to generate stable estimates in the context of a large number of empty cells. We constructed unadjusted and adjusted regression models for age, education, and cigarette smoking, and calculated profile-likelihood based 95% confidence intervals (Heinze and Schemper, 2002). In sensitivity analyses, we incorporated 'lag times,' by restricting the sample to women residing at the study address for ≥5 years or ≥10 years. "
    [Show abstract] [Hide abstract]
    ABSTRACT: We conducted a pilot study of associations between drinking water contaminated by inorganic arsenic (iAs), mostly <10μg/L, and self-reported chronic diseases in 297 pregnant women. Adjusted for confounding variables, we identified a positive association between iAs and heart disease (OR=1.63, 95%CI 0.81-3.04, p=0.094), which was stronger for women living at their current residence ≥10 years (OR=2.47, 95%CI 0.87-10.43, p=0.058). Confounder-adjusted associations were also suggested for iAs with kidney disease (OR=1.32, 95%CI 0.77-2.21, p=0.265) and with high blood pressure (OR=1.36, 95%CI 0.68-2.39, p=0.300). A post hoc power analysis indicated the need for a larger study with more statistical power.
    Full-text · Article · Nov 2015
  • Source
    • "How - ever , when the occurrence probability is extremely small ( or large) , or if the number of samples is not enough for the number of parameters , it is sometimes impossible to obtain accurate estimates with this method . The exact method is one way of resolving these issues ( Mehta and Patel 1995 ) ( Heinze and Schemper 2002) . "
    [Show abstract] [Hide abstract]
    ABSTRACT: In 2014, we published an article titled "Novel uterine sarcoma preoperative diagnosis score predicts the need for surgery in patients presenting with a uterine mass" on the preoperative diagnosis of uterine sarcoma, in the SpringerPlus (Nagai et al. in SpringerPlus 2014, 3:678. doi:10.1186/2193-1801-3-678). Subsequently, we received several suggestions from readers, which were used to modify the statistical analysis methods and create a more precise preoperative diagnostic scoring system, which we present here as a supplemental report. The subjects were 63 patients who underwent surgical therapy for suspected uterine sarcoma (sarcoma group: 15 patients, benign group: 48 patients). Logistic regression analysis using the exact method was performed considering the subjects' preoperative age, serum lactate dehydrogenase levels, magnetic resonance imaging findings, and endometrial cytology findings. We then used parameter estimates obtained from this analysis to revise the PREoperative Sarcoma Score (PRESS). The revised PRESS (rPRESS) has a maximum score of 10 points and an optimal cut-off value of 4 points, as derived from a receiver operating characteristic curve. Using this, the accuracy, positive predictive value, and negative predictive value were 93.7, 92.3, and 94.0 %, respectively. The diagnostic precision of the rPRESS is better than that of the original PRESS.
    Full-text · Article · Sep 2015 · SpringerPlus
  • Source
    • "The problem of potential dependency could be resolved in generalized linear mixed models (GLMM) by including female identity and pond as random factors. However, our data included several incidences of perfect prediction, that is, when all of the females in a pond scored either positive or negative assortative, which interferes with parameter estimation in GLMM (Heinze and Schemper 2002). An appropriate correction for the bias introduced by perfect prediction has not yet been developed for mixed models (G. "
    [Show abstract] [Hide abstract]
    ABSTRACT: Assortative mating promotes reproductive isolation and allows allopatric specia-tion processes to continue in secondary contact. As mating patterns are determined by mate preferences and intrasexual competition, we investigated male–male competition and behavioral isolation in simulated secondary contact among allopatric populations. Three allopatric color morphs of the cichlid fish Tropheus were tested against each other. Dyadic male–male contests revealed dominance of red males over bluish and yellow-blotch males. Reproductive isolation in the presence of male–male competition was assessed from genetic parent-age in experimental ponds and was highly asymmetric among pairs of color morphs. Red females mated only with red males, whereas the other females performed variable degrees of heteromorphic mating. Discrepancies between mating patterns in ponds and female preferences in a competition-free, two-way choice paradigm suggested that the dominance of red males interfered with positive assortative mating of females of the subordinate morphs and provoked asymmet-ric hybridization. Between the nonred morphs, a significant excess of negative assortative mating by yellow-blotch females with bluish males did not coincide with asymmetric dominance among males. Hence, both negative assortative mating preferences and interference of male–male competition with positive assorta-tive preferences forestall premating isolation, the latter especially in environments unsupportive of competition-driven spatial segregation.
    Full-text · Article · Apr 2015 · Ecology and Evolution
Show more