{ "id": "epdkqahrzs", "slug": "conditional-logistic-regression", "title": "Conditional logistic regression", "updated": "2026-10-15", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math" }, { "id": "physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics" }, { "id": "physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics.stats_statistical_inference" }, { "id": "physical.math.statistics.stats_statistical_inference.regression-analysis", "label": "Regression analysis", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics.stats_statistical_inference.regression-analysis" } ], "geo": [ { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.regression-analysis", "label": "Non-geographic · 1946 to 2000: Regression analysis", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.regression-analysis", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math" }, { "id": "geo.nongeo.t1946.physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.regression-analysis", "label": "Regression analysis", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.regression-analysis" } ] } ], "excerpt": "Conditional logistic regression is a regression method for binary outcomes in matched or finely stratified data, the predominant analysis for matched case-control studies, known in economics as the fixed-effects logit.", "snippet": "Conditional logistic regression is a regression method for binary outcomes in matched or finely stratified data, the predominant analysis for matched case-control studies, known in economics as the fixed-effects logit.", "node": "physical.math.statistics.stats_statistical_inference.regression-analysis", "markdown": "# Conditional logistic regression\n\nConditional logistic regression is a regression method for binary outcomes in matched or finely stratified data, such as matched case-control studies, that estimates covariate effects by conditioning on each stratum so that stratum-specific intercepts drop out of the likelihood. It is the predominant method of analysis for individually matched case-control studies, and it yields a conditional odds ratio rather than a marginal one.[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC2827892/) It is to be distinguished from two alternatives. Unconditional logistic regression that includes a separate intercept for each stratum is inconsistent when strata are small and the number of nuisance intercepts grows with sample size[2](https://www.mayo.edu/research/documents/biostat-65pdf/doc-10027676) • [3](https://www.sciencedirect.com/science/article/abs/pii/S0378375800002172), which is the incidental-parameters problem that conditioning avoids. A pooled model that simply ignores the matching is not generally equivalent and may be biased; whether it is suitable depends on the matching design and covariates.\n\n| Key fact | Detail |\n|---|---|\n| What it estimates | Conditional odds ratios for covariates within matched sets; the intercept and effects of matching variables are not estimated[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC2827892/) • [4](https://people.stat.sc.edu/hoyen/STAT705/Notes/Lecture12.pdf) |\n| Model form | Each matched set has its own intercept \\( \\alpha_{k} \\) with common slopes \\( \\beta \\); conditioning removes the \\( \\alpha_{k} \\)[5](https://library.virginia.edu/data/articles/matched-case-control-studies-and-conditional-logistic-regression) |\n| Computational identity | Identical likelihood to a stratified Cox model with constant time and exact partial likelihood; R's clogit() calls coxph()[6](https://search.r-project.org/CRAN/refmans/survival/html/clogit.html) |\n| Informative data | In 1:1 matching, only discordant pairs contribute; with \\( n_{10} \\) counting pairs in which the case is exposed and the control is not, and \\( n_{01} \\) the reverse, the odds ratio is \\( n_{10}/n_{01} \\)[4](https://people.stat.sc.edu/hoyen/STAT705/Notes/Lecture12.pdf) |\n| Why not unconditional ML | With many strata, stratum dummies create the Neyman-Scott incidental-parameters problem and biased, inconsistent estimates[3](https://www.sciencedirect.com/science/article/abs/pii/S0378375800002172) |\n| Software | clogit() in R (survival), clogit in Stata, PROC PHREG with ties=discrete in SAS[6](https://search.r-project.org/CRAN/refmans/survival/html/clogit.html) • [7](https://www.stata.com/manuals14/rclogit.pdf) • [2](https://www.mayo.edu/research/documents/biostat-65pdf/doc-10027676) |\n\n## How it works\n\nThe stratum-specific model is \\( \\mathrm{logit}[\\pi_{k}(X)] = \\alpha_{k} + \\beta' \\cdot X \\): each matched set or stratum \\( k \\) has its own intercept \\( \\alpha_{k} \\), but the slope coefficients \\( \\beta \\) are common across strata.[4](https://people.stat.sc.edu/hoyen/STAT705/Notes/Lecture12.pdf) Because there is typically one case per stratum, the \\( \\alpha_{k} \\) cannot be estimated well by unconditional maximum likelihood, so they are removed by conditioning on a sufficient statistic, usually the observed numbers of cases and controls in each stratum.[4](https://people.stat.sc.edu/hoyen/STAT705/Notes/Lecture12.pdf) The conditional likelihood for stratum \\( k \\) is the probability of the observed case assignment relative to all \\( c_{k} = n_{k}!/(n_{1k}!\\,(n_{k}-n_{1k})!) \\) possible assignments of \\( n_{1k} \\) cases among \\( n_{k} \\) subjects.[8](https://wnarifin.github.io/lecture/mstat/conditional.pdf) Written out over \\( n \\) strata, each with one case, it is[9](https://link.springer.com/article/10.1186/s12859-024-05850-2)\n\n\\[ L(\\beta) = \\prod_{i=1}^{n} \\frac{\\exp\\{X_{i1}^{\\top} \\cdot \\beta\\}}{\\sum_{l=1}^{K}\\exp\\{X_{il}^{\\top} \\cdot \\beta\\}} \\]\n\nwith the stratum-specific intercepts treated as nuisance parameters that cancel. For a single risk set the contribution is \\( \\exp[\\beta \\cdot x_{\\mathrm{case}}]/\\sum_{j}\\exp[\\beta \\cdot x_{j}] \\), with score \\( x_{\\mathrm{case}} - x_{\\mathrm{weighted}} \\), and estimation proceeds by Newton-Raphson.[10](https://www.jhanley.biostat.mcgill.ca/bios602/CondnlLogisticRegrn/ch-notes-29.pdf) In 1:1 matching the conditional likelihood is proportional to a binomial likelihood, the conditional maximum likelihood estimate of the log-odds ratio is \\( \\log(n_{10}/n_{01}) \\), and the conditional score test for \\( \\beta = 0 \\) is McNemar's statistic, \\( Z^{2} = (n_{10} - n_{01})^{2}/(n_{10} + n_{01}) \\).[11](https://people.musc.edu/~bandyopd/bmtry711.11/lecture_26.pdf) The same likelihood has a second life in survival analysis: a stratified Cox model with each case/control group in its own stratum, time set to a constant, status coded 1 for case and 0 for control, and the exact partial likelihood has the same likelihood formula as conditional logistic regression.[6](https://search.r-project.org/CRAN/refmans/survival/html/clogit.html)\n\n## How it is done\n\nThe workflow is straightforward in standard packages. Data are arranged one row per subject, with a case indicator, covariates, and a stratum identifier for each matched set or unique combination of matching variables.[12](https://019b2da8-edfb-a262-61be-7973c056d9ae.share.connect.posit.cloud/blr-conditional.html)\n\n- **R.** clogit() in the survival package uses a formula of the form case.status ~ exposure + strata(matched.set), with the exact conditional likelihood as default; it creates dummy times (all 1) and calls coxph().[6](https://search.r-project.org/CRAN/refmans/survival/html/clogit.html)\n- **Stata.** clogit fits matched case-control data with 1:1, 1:k2i, or k1i:k2i matching, and the matching ratio can vary across groups; a recursive algorithm computes the likelihood with no limit on group size.[7](https://www.stata.com/manuals14/rclogit.pdf)\n- **SAS.** PROC PHREG with ties=discrete exploits the Cox-likelihood identity[2](https://www.mayo.edu/research/documents/biostat-65pdf/doc-10027676); NCSS likewise fits the model through Cox regression, recommending the Breslow tie method for 1:1 and 1:n matching and Efron's method for m:n matching.[13](https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Conditional_Logistic_Regression.pdf)\n\nOdds ratios are reported as \\( \\mathrm{OR}(x_{i}) = e^{\\beta_{i}} \\), with significance assessed by the Wald statistic \\( W = \\hat{\\beta}/\\mathrm{SE}(\\hat{\\beta}) \\) or the likelihood ratio test \\( G = 2(\\ell_{1} - \\ell_{0}) \\), where \\( \\ell_{0} \\) and \\( \\ell_{1} \\) are the null and fitted log-likelihoods; simulation studies usually show the likelihood ratio test performs better.[8](https://wnarifin.github.io/lecture/mstat/conditional.pdf) • [13](https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Conditional_Logistic_Regression.pdf) The output contains no intercept, and the model does not estimate associations between the matching variables and the outcome.[12](https://019b2da8-edfb-a262-61be-7973c056d9ae.share.connect.posit.cloud/blr-conditional.html) Regression diagnostics for conditional logistic regression include likelihood-displacement measures for identifying influential matched sets.[2](https://www.mayo.edu/research/documents/biostat-65pdf/doc-10027676)\n\n## Origin\n\nN. E. Breslow and colleagues gave an influential development of conditional logistic regression for matched case-control studies in 1978, in \"Estimation of Multiple Relative Risk Functions in Matched Case-Control Studies\" in the American Journal of Epidemiology, though earlier use of the method went unrecognized for decades.[14](https://doi.org/10.1093/oxfordjournals.aje.a112623) A historical review notes that the model's earliest use went unrecognized for decades.[15](https://jhanley.biostat.mcgill.ca/Reprints/HanleyFirstCondnlLogisticRegression.pdf) In economics and other social sciences, the same model is known as the fixed-effects logit for panel data, introduced by [Gary Chamberlain](https://www.edgepedia.org/gary-chamberlain) in \"Analysis of Covariance with Qualitative Data\" (The Review of Economic Studies, 1980).[16](https://doi.org/10.2307/2297110) • [7](https://www.stata.com/manuals14/rclogit.pdf) Later methodological work shaped practice: Mitchell Gail, Jay Lubin, and Lawrence Rubinstein introduced a fast recursion for conditional likelihood calculations in 1981 ([Biometrika](https://www.edgepedia.org/biometrika)), later incorporated into version 2.36-11 of the R survival package[17](https://doi.org/10.1093/biomet/68.3.703) • [6](https://search.r-project.org/CRAN/refmans/survival/html/clogit.html), and John Connett, Judith Smith, and Richard McHugh provided the large-sample sample-size formula for pair-matched studies in 1987.[18](https://doi.org/10.1002/sim.4780060107)\n\n## Variants\n\n**Matching ratios.** The method is not limited to 1:1 pairs; one case can be matched to two or more controls, and Stata's clogit handles general k1i:k2i matching with varying ratios.[5](https://library.virginia.edu/data/articles/matched-case-control-studies-and-conditional-logistic-regression) • [7](https://www.stata.com/manuals14/rclogit.pdf) More than five controls per matched set usually does not make sense.[5](https://library.virginia.edu/data/articles/matched-case-control-studies-and-conditional-logistic-regression)\n\n**Frequency matching and complex sampling.** A finite-population sampling model yields a weighted conditional logistic likelihood that accommodates frequency matching, counter-matching, case-cohort, randomized recruitment, and quota sampling designs.[19](https://dornsife.usc.edu/larry-goldstein/wp-content/uploads/sites/221/2023/06/cond.pdf) Counter-matching, which samples controls using exposure-related information, improves efficiency: under the null, about three times as many frequency-matched controls were needed to match the efficiency of a 1:1 counter-matched design in one simulation.[19](https://dornsife.usc.edu/larry-goldstein/wp-content/uploads/sites/221/2023/06/cond.pdf)\n\n**Panel data.** The fixed-effects logit fit by clogit is the same model, applied to repeated binary outcomes within subjects.[7](https://www.stata.com/manuals14/rclogit.pdf) The [case-crossover design](https://www.edgepedia.org/case-crossover-design), in which each subject serves as his or her own control, is a particular matched case-control design analyzed with the same tool.[20](https://link.springer.com/article/10.1186/1471-2105-16-S6-S1)\n\n**Penalized and Bayesian extensions.** Stephen Reid and Rob Tibshirani's clogitL1 package (2014) provided lasso and elastic net regularization paths for the conditional model via cyclic coordinate descent.[21](https://doi.org/10.18637/jss.v058.i12) The 2024 R package penalizedclr implements penalized conditional logistic regression with different lasso or ridge penalties for different blocks of covariates, aimed at multi-omics integration, with stability selection for variable selection[9](https://link.springer.com/article/10.1186/s12859-024-05850-2); the block-penalty idea follows the IPF-LASSO of Anne-Laure Boulesteix and colleagues (2017)[22](https://doi.org/10.1155/2017/7691937) and stability selection that of Nicolai Meinshausen and [Peter Bühlmann](https://www.edgepedia.org/peter-buhlmann) (2010).[23](https://doi.org/10.1111/j.1467-9868.2010.00740.x) Jacob Tennenbaum and Adam Kapelner introduced a Bayesian conditional logistic regression (package bclogit, 2026) that salvages information from concordant pairs, which traditional conditional likelihood discards, by building an empirical Bayes prior on nuisance covariate coefficients from a concordant-pair pre-model; the treatment coefficient itself is never shrunk by that prior.[24](https://cran.r-project.org/web/packages/bclogit/refman/bclogit.html) Log-F-penalized conditional logistic regression (2026) addresses small-sample bias in 1:M designs and can be implemented by adding a small number of artificial exposure-discordant matched sets, so standard software suffices.[25](https://arxiv.org/html/2607.28899)\n\n## Applications\n\nMatched case-control studies in epidemiology are the main application. Worked examples include a low-birth-weight study in which clogit gave an odds ratio of 2.75 (95% CI 1.22 to 6.18) for smoking[5](https://library.virginia.edu/data/articles/matched-case-control-studies-and-conditional-logistic-regression) and a 1:2 matched myocardial infarction example (39 patients, 117 subjects) with an odds ratio of 1.047 per mmHg systolic blood pressure.[26](https://dmrocke.ucdavis.edu/Class/EPI204-Spring-2021/Lecture7ConditionalLikelihood.pdf) Population-science uses include a 2018 U.S. Natality analysis in which previous preterm birth gave an odds ratio of 3.07 (95% CI 1.65 to 5.71) for NICU admission, with cases and controls matched on maternal education and age.[12](https://019b2da8-edfb-a262-61be-7973c056d9ae.share.connect.posit.cloud/blr-conditional.html) In economics and sociology, the fixed-effects logit is used for panel binary outcomes[7](https://www.stata.com/manuals14/rclogit.pdf), and penalized versions are applied to prediction from matched multi-omics data.[9](https://link.springer.com/article/10.1186/s12859-024-05850-2)\n\nIn 1:1 matching, concordant pairs (both case and control exposed, or both unexposed) contribute no information about the effect; only discordant pairs inform \\( \\beta \\).[4](https://people.stat.sc.edu/hoyen/STAT705/Notes/Lecture12.pdf) • [11](https://people.musc.edu/~bandyopd/bmtry711.11/lecture_26.pdf) Power therefore depends on the number of discordant pairs, not the total number of pairs. Sample-size tables for pair-matched studies with binary outcome are based on exact binomial tests, using a modification of the Connett large-sample formula and a practical strategy for handling the nuisance parameter, the proportion of discordant pairs.[27](https://onlinelibrary.wiley.com/doi/10.1002/sim.4780120709) • [18](https://doi.org/10.1002/sim.4780060107)\n\n## Limitations and alternatives\n\n**No intercept, no absolute risk.** Because the likelihood conditions on each matched set, no intercept is estimated and a baseline average outcome cannot be recovered within strata.[28](https://rawcdn.githack.com/mcarabali1/EPIB-704/49ee454d3028cb175556ba9382dce915d3d9cf6c/slides/L14matchingandconditionallogisticregression.pdf) If a marginal causal effect is the parameter of interest, conditional logistic regression cannot be used, as it estimates only the conditional odds ratio.[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC2827892/)\n\n**Matching variables are lost.** Once factors are matched on, their effects cannot be estimated; they become nuisance parameters whose effects drop out of the conditional likelihood.[4](https://people.stat.sc.edu/hoyen/STAT705/Notes/Lecture12.pdf) • [11](https://people.musc.edu/~bandyopd/bmtry711.11/lecture_26.pdf) In panel applications, variables that do not change within groups are collinear with the fixed effects and cannot be estimated.[7](https://www.stata.com/manuals14/rclogit.pdf)\n\n**Unconditional regression with stratum dummies.** Maximum likelihood is inconsistent when the number of nuisance intercepts grows with sample size (the Neyman-Scott or Andersen incidental-parameters problem)[3](https://www.sciencedirect.com/science/article/abs/pii/S0378375800002172), and in matched designs an analysis that ignores matching can bias the estimated odds ratio in either direction, depending on the design and the data.[28](https://rawcdn.githack.com/mcarabali1/EPIB-704/49ee454d3028cb175556ba9382dce915d3d9cf6c/slides/L14matchingandconditionallogisticregression.pdf) For frequency-matched designs with categorical matching factors, however, correctly specified unconditional logistic regression can be more efficient than conditional logistic regression; conditional fitting remains more practical because it is less dependent on modeling choices.[29](https://www.stat.ubc.ca/~john/papers/WanSIM2022.pdf)\n\n**Sparse data.** Conditional maximum likelihood can produce infinite odds-ratio estimates and a monotone likelihood in small or sparse stratified data[30](https://onlinelibrary.wiley.com/doi/10.1002/sim.3794); in a DES example where seven of eight cases were exposed and no controls were, standard clogit() failed to converge.[25](https://arxiv.org/html/2607.28899) Firth-type penalized conditional likelihood gave almost unbiased log odds ratios in small-sample simulation, with close-to-nominal interval coverage[30](https://onlinelibrary.wiley.com/doi/10.1002/sim.3794), building on David Firth's 1993 bias-reduction method.[31](https://doi.org/10.1093/biomet/80.1.27) Goodness-of-fit assessment for conditional logistic regression is difficult and not available in standard software.[8](https://wnarifin.github.io/lecture/mstat/conditional.pdf)\n\n## References\n\n1. [Why Match? Investigating Matched Case-Control Study Designs with Causal Effect Estimation (Rose & van der Laan)](https://pmc.ncbi.nlm.nih.gov/articles/PMC2827892/)\n2. [A SAS macro for conditional logistic regression in matched case-control studies (Mayo Biostatistics report)](https://www.mayo.edu/research/documents/biostat-65pdf/doc-10027676)\n3. [The unreasonable effectiveness of a biased logistic regression procedure in the analysis of pair-matched case-control studies](https://www.sciencedirect.com/science/article/abs/pii/S0378375800002172)\n4. [Conditional Logistic Regression, Stat 705 lecture notes, University of South Carolina](https://people.stat.sc.edu/hoyen/STAT705/Notes/Lecture12.pdf)\n5. [Matched Case-Control Studies and Conditional Logistic Regression | UVA Library](https://library.virginia.edu/data/articles/matched-case-control-studies-and-conditional-logistic-regression)\n6. [R: Conditional logistic regression (survival package documentation)](https://search.r-project.org/CRAN/refmans/survival/html/clogit.html)\n7. [Stata 14 documentation: clogit, Conditional (fixed-effects) logistic regression](https://www.stata.com/manuals14/rclogit.pdf)\n8. [Conditional Logistic Regression (Dr Wan Nor Arifin, Universiti Sains Malaysia, updated Jun 24, 2024)](https://wnarifin.github.io/lecture/mstat/conditional.pdf)\n9. [penalizedclr: an R package for penalized conditional logistic regression for integration of multiple omics layers](https://link.springer.com/article/10.1186/s12859-024-05850-2)\n10. [Course notes ch. 29: Conditional likelihood for matched sets (Hanley, McGill BIOS 602)](https://www.jhanley.biostat.mcgill.ca/bios602/CondnlLogisticRegrn/ch-notes-29.pdf)\n11. [Conditional Logistic Regression (MUSC Biometry 711 lecture notes, Bandyopadhyay)](https://people.musc.edu/~bandyopd/bmtry711.11/lecture_26.pdf)\n12. [6.20 Conditional logistic regression for matched case-control data (Introduction to Regression Methods for Public Health Using R)](https://019b2da8-edfb-a262-61be-7973c056d9ae.share.connect.posit.cloud/blr-conditional.html)\n13. [Conditional Logistic Regression, NCSS statistical software documentation](https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Conditional_Logistic_Regression.pdf)\n14. [N. E. BRESLOW and colleagues (1978). ESTIMATION OF MULTIPLE RELATIVE RISK FUNCTIONS IN MATCHED CASE-CONTROL STUDIES. American Journal of Epidemiology.](https://doi.org/10.1093/oxfordjournals.aje.a112623)\n15. [Studies in the history of probability and statistics, LI: the first conditional logistic regression (Hanley)](https://jhanley.biostat.mcgill.ca/Reprints/HanleyFirstCondnlLogisticRegression.pdf)\n16. [Gary Chamberlain (1980). Analysis of Covariance with Qualitative Data. The Review of Economic Studies.](https://doi.org/10.2307/2297110)\n17. [MITCHELL H. GAIL, JAY H. LUBIN, LAWRENCE V. RUBINSTEIN (1981). Likelihood calculations for matched case-control studies and survival studies with tied death times. Biometrika.](https://doi.org/10.1093/biomet/68.3.703)\n18. [John E. Connett, Judith A. Smith, Richard B. McHugh (1987). Sample size and power for pair‐matched case‐control studies. Statistics in Medicine.](https://doi.org/10.1002/sim.4780060107)\n19. [Conditional logistic analysis of case-control studies with complex sampling (Langholz, Goldstein et al.)](https://dornsife.usc.edu/larry-goldstein/wp-content/uploads/sites/221/2023/06/cond.pdf)\n20. [Sparse conditional logistic regression for analyzing large-scale matched data from epidemiological studies: a simple algorithm (BMC Bioinformatics)](https://link.springer.com/article/10.1186/1471-2105-16-S6-S1)\n21. [Stephen Reid, Rob Tibshirani (2014). Regularization Paths for Conditional Logistic Regression: TheclogitL1Package. Journal of Statistical Software.](https://doi.org/10.18637/jss.v058.i12)\n22. [Anne-Laure Boulesteix and colleagues (2017). IPF-LASSO: Integrative L 1 -Penalized Regression with Penalty Factors for Prediction Based on Multi-Omics Data. Computational and Mathematical Methods in Medicine.](https://doi.org/10.1155/2017/7691937)\n23. [Nicolai Meinshausen, Peter Bühlmann (2010). Stability Selection. Journal of the Royal Statistical Society Series B (Statistical Methodology).](https://doi.org/10.1111/j.1467-9868.2010.00740.x)\n24. [Help for package bclogit (version 1.1)](https://cran.r-project.org/web/packages/bclogit/refman/bclogit.html)\n25. [Log-F-penalized Conditional Logistic Regression for Sparse Data](https://arxiv.org/html/2607.28899)\n26. [Matching and Conditional Likelihood (David M. Rocke, UC Davis)](https://dmrocke.ucdavis.edu/Class/EPI204-Spring-2021/Lecture7ConditionalLikelihood.pdf)\n27. [Exact conditional and unconditional sample size for pair-matched studies with binary outcome: A practical guide (Royston, Statistics in Medicine, 1993)](https://onlinelibrary.wiley.com/doi/10.1002/sim.4780120709)\n28. [Matching and conditional logistic regression, EPIB-704 slides (McGill)](https://rawcdn.githack.com/mcarabali1/EPIB-704/49ee454d3028cb175556ba9382dce915d3d9cf6c/slides/L14matchingandconditionallogisticregression.pdf)\n29. [Conditional or unconditional logistic regression for frequency matched case-control design? (Wan et al., Statistics in Medicine 2022)](https://www.stat.ubc.ca/~john/papers/WanSIM2022.pdf)\n30. [Bias-reduced and separation-proof conditional logistic regression with small or sparse data sets (Heinze & Schemper, Statistics in Medicine 2010)](https://onlinelibrary.wiley.com/doi/10.1002/sim.3794)\n31. [DAVID FIRTH (1993). Bias reduction of maximum likelihood estimates. Biometrika.](https://doi.org/10.1093/biomet/80.1.27)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Statistics and probability › Statistical inference, estimation, sampling, and testing › Regression analysis*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [ "https://people.musc.edu/~bandyopd/bmtry711.11/lecture_26.pdf" ], "url": "https://www.edgepedia.org/conditional-logistic-regression", "markdown_url": "https://www.edgepedia.org/conditional-logistic-regression.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. 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