Logistic regression analysis studies the association between a binary dependent variable and a set of independent (explanatory) variables using a logit model.
Conditional logistic regression (CLR) is a specialized type of logistic regression usually employed when case subjects with a particular condition or attribute are each matched with n control subjects without the condition. In general, there may be 1 to m cases matched with 1 to n controls. However, the most common design is 1:1 matching, followed by 1:n matching in which nvaries from 1 to 5
Ref. https://ncss-wpengine.netdna-ssl.com/wp content/themes/ncss/pdf/Procedures/NCSS/Conditional_Logistic_Regression.pdf
In CLR we must remember that observations are not independent, and participants in different treatment groups have been matched for at least 1 characteristic, and this must be taken into account in the analysis.
The philosophy is the same with logistic regression with the exception that the estimates from conditional logistic regression are conditional on the matched treatment groups or on the cases being linked to the controls in a matched case-control study. This type of analysis is required in individually matched studies.
However, it is different when studies use frequency matching, which deals with selecting individuals for different groups to have the same overall distribution on a matching variable. In this case, it is acceptable to use unconditional (ordinary) logistic regression and include the matching factor in the model.
The philosophy is the same with logistic regression with the exception that the estimates from conditional logistic regression are conditional on the matched treatment groups or on the cases being linked to the controls in a matched case-control study. This type of analysis is required in individually matched studies.
However, it is different when studies use frequency matching, which deals with selecting individuals for different groups to have the same overall distribution on a matching variable. In this case, it is acceptable to use unconditional (ordinary) logistic regression and include the matching factor in the model.
In conditional logistic regression model, likelihood is formulated in a way that subjects from different treatment groups (or case controls) are only compared within the same matched set; this is called conditional likelihood. The general form of a conditional logistic regression model with a single binary exposure is:
Log odds = a + set + beta1 exposure
- Where (a + set) represents constant term in each set of matched individuals, and beta1 exposure represents estimate of effect
of exposure of interest.
- Constant in each set is eliminated from the model using conditional likelihood, and only the effect of the exposure and other potential predictors are retained. This means that there is no constant term as in the usual logistic regression in the output from a con- ditional logistic regression.
- Where (a + set) represents constant term in each set of matched individuals, and beta1 exposure represents estimate of effect
of exposure of interest.
- Constant in each set is eliminated from the model using conditional likelihood, and only the effect of the exposure and other potential predictors are retained. This means that there is no constant term as in the usual logistic regression in the output from a con- ditional logistic regression.
- When modeling our data with conditional logistic regression, we can additionally include other potential
predictor variables or confounders and test for interac- tions in the same way that this is done using ordinary lo- gistic regression
Ref http://dx.doi.org/10.1016/j.ajodo.2017.04.009
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