The Conditional Logistic Regression Model (Breslow and Day, 1980)

The Conditional Logistic Regression Model (Breslow and Day, 1980)

<p>Appendix</p><p>The Conditional Logistic Regression model (Breslow and Day, 1980)</p><p>In matched case-control studies, conditional logistic regression for matched sets is used to investigate the relationship between an outcome of being a case (patient) or a control and a set of prognostic factors, as described by Breslow and Day46. (Breslow NE. and Day NE Statistical Methods in Cancer Research. Volume I The analysis of case-controls studies. Lyon: IARC Scientific Publications, numero 32, 1980). The model was constructed to respond to the following question: Do genotypes/or alleles have different risks of developing affective disorder? By constructing a Conditional Logistic Regression model for matched sets, with diagnosis (patient /control) as dependant variable and genotypes/or alleles entered as covariates, we tested the effects genotypes/alleles on disorder.</p><p>Stratification, Mantel-Haenszel and Breslow Day tests (Breslow and Day, 1980)</p><p>Both confounding and effect modification are evaluated through the process of stratification. Stratification is a technique to control confounding factors in the analysis of a study that involves the evaluation of the association within strata of the confounding variable.</p><p> cases controls exposed a b Non c d exposed</p><p>Suppose that cases and controls are stratified on the basis of one or more variables into k subgroups. The Mantel-Haenszel estimate of the odds ratio, adjusted for the effects of the stratification variables (OR MH), is calculated as:</p><p>ORMH= i=1 to k (aidi/T)/ (bici/T), (T=a+b+c+d). The quantities in the numerator and denominator are summed separately over each of the individual strata. The crude OR is calculated as: ORcrude= ad/bc The magnitude of confounding can be evaluated by observing the degree of discrepancy between the crude (ORcrude) and adjusted (ORMH) estimates. (Tolerated difference is not more than 15%). If ORcrude and ORMH are identical, there is no confounding effect by the stratification variable (gender in our study).</p><p>To evaluate the likelihood that the association between exposure and disease, after adjustment for a potential 2 confounding factor (gender in our study) is due to chance, the Mantel-Haenszel chi-square statistic c MH can be calculated as follows:</p><p>  a-  (a+b) (a+c)  2 T</p><p> (a+b)(c+d)(a+c)(b+d) T2(T-1)</p><p>When the association between the exposure and disease under study varies by level of a third factor (gender /center in our study), there is a modifier effect. To evaluate the uniformity of the stratum-specific estimates, a chi- square test for homogeneity was proposed by Breslow and Day that test the null hypothesis that the degree of variability in the series of stratum-specific estimates is consistent with random variation. 2 (i=1 to k) ai-Ai(ORg) /var(ai;ORg) k=number of strata, ai=number of observed exposed cases in stratum i; Ai(ORg)=number of attended exposed cases, according to the ORg (global Odd ratio).</p>

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