The DOI matches its Crossref record; 20 of the 20 references it cites were found in a registry or an index.
A Solution to the Problem of Monotone Likelihood in Cox Regression
Open accessAbstract
Summary.The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to ±∞. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993,Biometrika80, 27–38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald‐type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Regression Models and Life-Tables
Cox, D. R. (1972) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1972.tb00899.x · Cited by 39,793
Regression Models and Life-Tables
Cox, D. R. (1992) · Springer Series in Statistics · doi:10.1007/978-1-4612-4380-9_37 · Cited by 26,297
(2005) · Statistics for Biology and Health · doi:10.1007/0-387-27255-0_9 · Cited by 20,133
McCullagh, P., & Nelder, J. A. (1989) · doi:10.1007/978-1-4899-3242-6 · Cited by 16,836
Cox, D. R., & Oakes, D. (2018) · Chapman & Hall/CRC eBooks · doi:10.1201/9781315137438 · Cited by 6,234
Bias reduction of maximum likelihood estimates
FIRTH, D. (1993) · Biometrika · doi:10.1093/biomet/80.1.27 · Cited by 5,035
Breslow, N., Cox, D. R., & Oakes, D. (1985) · Biometrics · doi:10.2307/2530888 · Cited by 4,333
Modelling for Survival Data in Medical Research
(1995) · Technometrics · doi:10.1080/00401706.1995.10485920 · Cited by 2,145
Modelling Survival Data in Medical Research
Collett, D. (1994) · Springer eBooks · doi:10.1007/978-1-4899-3115-3 · Cited by 1,065
Analysing Survival Data From Clinical Trials and Observational Studies
(1996) · Technometrics · doi:10.1080/00401706.1996.10484530 · Cited by 663
Cited by
Subclinical Hypothyroidism and the Risk of Coronary Heart Disease and Mortality
Rodondi, N., den Elzen, W. P. J., Bauer, D. C., Cappola, A. R., Razvi, S., Walsh, J. P., Åsvold, B. O., Iervasi, G., Imaizumi, M., Collet, T.-H., et al. (2010) · JAMA · doi:10.1001/jama.2010.1361 · Cited by 1,216
Taur, Y., Xavier, J. B., Lipuma, L., Ubeda, C., Goldberg, J., Gobourne, A., Lee, Y. J., Dubin, K. A., Socci, N. D., Viale, A., et al. (2012) · Clinical Infectious Diseases · doi:10.1093/cid/cis580 · Cited by 1,020
Co-expression of CD39 and CD103 identifies tumor-reactive CD8 T cells in human solid tumors
Duhen, T., Duhen, R., Montler, R., Moses, J., Moudgil, T., de Miranda, N. F., Goodall, C. P., Blair, T. C., Fox, B. A., McDermott, J. E., et al. (2018) · Nature Communications · doi:10.1038/s41467-018-05072-0 · Cited by 938
A single dose of neoadjuvant PD-1 blockade predicts clinical outcomes in resectable melanoma
Huang, A. C., Orlowski, R. J., Xu, X., Mick, R., George, S. M., Yan, P. K., Manne, S., Kraya, A. A., Wubbenhorst, B., Dorfman, L., et al. (2019) · Nature Medicine · doi:10.1038/s41591-019-0357-y · Cited by 686
Subclinical hyperthyroidism and the risk of coronary heart disease and mortality
Collet, T.-H., Gussekloo, J., Bauer, D. C., den Elzen, W. P. J., Cappola, A. R., Balmer, P., Iervasi, G., Åsvold, B. O., Sgarbi, J. A., Völzke, H., et al. (2012) · Archives of Internal Medicine · doi:10.1001/archinternmed.2012.402 · Cited by 572
Metadata
- Authors
- Heinze, G., & Schemper, M.
- Venue
- Biometrics
- Publisher
- Oxford University Press (OUP)
- Published
- 2001-03
- Volume
- 57
- Issue
- 1
- Pages
- 114-119
- ISSN
- 0006-341X (ISSN-L)
- 1541-0420
- OpenAlex
- W2112600232
- Cited by
- 396
- References
- 20
- FWCI
- 2.87
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A Solution to the Problem of Monotone Likelihood in Cox Regression. https://app.cochat.ai/papers/10.1111/j.0006-341x.2001.00114.x
- The paper
- Heinze, G., & Schemper, M. (2001). A Solution to the Problem of Monotone Likelihood in Cox Regression. Biometrics. https://doi.org/10.1111/j.0006-341x.2001.00114.x
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
