Inverse of the large strata variance weights Mantel Haenszel weights Inverse

# Inverse of the large strata variance weights mantel

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Inverse of the large strata variance weights Mantel Haenszel weights. Inverse variance weights have the form: If there are no cases observed among either the exposed or unexposed in a stratum, calculation of the variance for that stratum involves a division by 0. When the number of cases observed among either the exposed or unexposed group is small, the large strata variance formula may be inaccurate. N b b - N + N a a - N 1 = )] R I C ( [ Var 1 = ' w 0i i i 0i 1i i i 1i i ^ i ˆ ln
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 15 Choices of Weights Mantel Haenszel Weights Thus, to make the best use of our data, we prefer the Mantel Haenszel weights: Using the Mantel Haenszel weights, the summary cumulative incidence ratio is: T N b = ' w i 1i i i T N b T N a = T N b N b N a T N b w R I C ' w = R I C i 1i i I 1 = i i 0i i I 1 = i i 1i i I 1 = i 0i i 1i i i 1i i I 1 = i i I 1 = i i i I 1 = i MH = ' ˆ ˆ Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 16 Evans County Study CIR MH Estimation The Mantel Haenszel summary cumulative incidence ratio is: After adjusting for confounding by age and ECG status, the estimated risk ratio changed from 2.45 to 1.70. Confounding by either or both of these variables led to an overestimation of the risk ratio. Assuming there is no confounding by other variables, no residual confounding by these variables, no selection bias and no information bias, these data indicate that men with high CAT levels have a 70% higher 7 year cumulative incidence of CHD than men with low CAT levels. 1.70 = 8.90 15.10 = 90 58 * 5 + 161 39 * 15 + 76 17 * 7 + 282 8 * 17 90 32 * 14 + 161 122 * 9 + 76 59 * 3 + 282 274 * 1 = R I C MH ˆ
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 17 95% CI for ln (CIR MH ) To construct the 95% confidence interval for ln (CIR MH ), we use the usual formula: Where MH MH R I C Var 1.96 R I C ˆ ln ˆ ln I i i i i I i i i i I i i i i i i i i T N b T N a T T b a N N M ˆ ln 1 1 1 0 1 2 0 1 1 MH R I C Var Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 18 Evans County Study CIR MH Confidence Interval Estimation In this example, Thus, the 95% confidence interval for ln (CIR MH ) is: and the 95% confidence interval for CIR MH is: e (0.020, 1.036) = (1.02, 2.82) 0.067 = R) I C ar V ˆ (ln ˆ 1.036) (0.020, 0.067 1.96 0.528 = 0.067 1.96 (1.70) ln
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 19 Evans County Study CIR MH Confidence Interval Interpretation Assuming no residual confounding by age or ECG status, no confounding by other variables, no selection bias and no information bias, we conclude that there is evidence of a significant elevation in the 7 year cumulative incidence of CHD associated with high CAT level compared with lower levels, ranging in magnitude from 2% to nearly a three fold higher cumulative incidence with 95% confidence.

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