Editing Case–control study (section)

==Analysis==
Case–control studies were initially analyzed by testing whether or not there were significant differences between the proportion of exposed subjects among cases and controls.<ref name="Rodrigues_1990">{{cite journal | last1=Rodrigues |first1=L. |last2=Kirkwood |first2=B. R. | title = Case–control designs in the study of common diseases: updates on the demise of the rare disease assumption and the choice of sampling scheme for controls | journal = Int. J. Epidemiol. | volume = 19 | issue = 1 | pages = 205–13 | year = 1990 | pmid = 2190942 | doi =  10.1093/ije/19.1.205}}</ref> Subsequently, Cornfield<ref name="pmid7046823">{{cite journal | vauthors = Greenhouse SW | title = Jerome Cornfield's contributions to epidemiology | journal = Biometrics | volume = 38 Suppl | pages = 33–45 | year = 1982 | pmid = 7046823 | doi =  10.2307/2529852| jstor = 2529852 }}</ref> pointed out that, when the disease outcome of interest is rare, the [[odds ratio]] of exposure can be used to estimate the [[relative risk]] (see [[rare disease assumption]]). The validity of the odds ratio depends highly on the nature of the disease studied, on the sampling methodology and on the type of follow-up. Although in classical case–control studies, it remains true that the odds ratio can only approximate the relative risk in the case of rare diseases, there is a number of other types of studies (case–cohort, nested case–control, cohort studies) in which it was later shown that the [[odds ratio]] of exposure can be used to estimate the [[relative risk]] or the [[incidence rate ratio]] of exposure without the need for the rare disease assumption.<ref name="Rodrigues_1990" /><ref name="pmid1251836">{{cite journal |last=Miettinen |first=O. | title = Estimability and estimation in case–referent studies | journal = Am. J. Epidemiol. | volume = 103 | issue = 2 | pages = 226–35 | year = 1976 | pmid = 1251836 | doi=10.1093/oxfordjournals.aje.a112220}}</ref><ref>{{cite book |last1=Rothman |first1=K. J. |last2=Greenland |first2=S. |last3=Lash |first3=T. L. |title=Modern Epidemiology |edition=3rd |publisher=Wolters Kluwer, Lippincott Williams & Wilkins |year=2008 |isbn=978-0-7817-5564-1 }}</ref>

When the logistic regression model is used to model the case–control data and the odds ratio is of interest, both the prospective and retrospective likelihood methods will lead to identical maximum likelihood estimations for covariate, except for the intercept.<ref name= "Prentice1979"/> The usual methods of estimating more interpretable parameters than odds ratios—such as risk ratios, levels, and differences—is biased if applied to case–control data, but special statistical procedures provide easy to use consistent estimators.<ref>{{Cite journal|last1=King|first1=Gary|last2=Zeng|first2=Langche|date=2002-05-30|title=Estimating risk and rate levels, ratios and differences in case–control studies|url=http://doi.wiley.com/10.1002/sim.1032|journal=Statistics in Medicine|language=en|volume=21|issue=10|pages=1409–1427|doi=10.1002/sim.1032|pmid=12185893 |s2cid=11387977 |issn=0277-6715|url-access=subscription}}</ref>