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'''Conditional logistic regression''' is an extension of [[logistic regression]] that allows one to take into account [[stratification (clinical trials)|stratification]] and [[Matching (statistics)|matching]]. Its main field of application is [[observational studies]] and in particular [[epidemiology]]. It was devised in 1978 by [[Norman Breslow]], [[Nick Day (statistician)|Nicholas Day]], [[Katherine Halvorsen]], [[Ross L. Prentice]] and C. Sabai.<ref name="pmid727199">{{cite journal|vauthors=Breslow NE, Day NE, Halvorsen KT, Prentice RL, Sabai C| title=Estimation of multiple relative risk functions in matched case-control studies. | journal=Am J Epidemiol | year= 1978 | volume= 108 | issue= 4 | pages= 299–307 | pmid=727199 | doi= 10.1093/oxfordjournals.aje.a112623| url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=727199 }} </ref> It is the most flexible and general procedure for matched data.
==Motivation==
Observational studies use [[stratification (clinical trials)|stratification]] or [[Matching (statistics)|matching]] as a way to control for [[confounding]]. Several tests existed before conditional logistic regression for matched data as shown in [[
Logistic regression can take into account stratification by having a different constant term for each stratum. Let us denote <math>Y_{i\ell}\in\{0,1\}</math> the label (e.g. case status) of the <math>\ell</math>th observation of the <math>i</math>th stratum and <math>X_{i\ell}\in\mathbb{R}^p</math> the values of the corresponding predictors. Then, the likelihood of one observation is
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