The crude 7 year cumulative incidence ratio 245 158 379 was incorrectly

# The crude 7 year cumulative incidence ratio 245 158

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The crude 7 year cumulative incidence ratio 2.45 (1.58, 3.79) was incorrectly centered and far too narrow due to confounding by age and/or ECG status. Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 20 Cumulative Incidence Difference Point and Interval Estimates To calculate the estimated summary cumulative incidence difference, we use a weighted average of the stratum specific differences: Where: w i ' = the weight for the estimated cumulative incidence difference in the i th stratum = the estimated cumulative incidence difference in the i th stratum D I C i ˆ ' ' = ' w D I ˆ C w D I ˆ C w ' w = D I ˆ C * w = D I ˆ C i I =1 i i i I =1 i i i I =1 i i I =1 i i i I =1 i
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 21 Choice of Weights Summary Cumulative Incidence Difference Mantel Haenszel weights are not used for difference measures of association. Rather, we take weights as the inverse of the variance of the stratum specific estimates of the CID. Recall that Thus, the weight for stratum i is: N ) b - N ( b + N ) a - N ( a = ) D I (C ar V 3 0i i 0i i 3 1i i 1i i i ˆ ˆ )] b - N ( b N + ) a - N ( a N [ N N = ) D I C ( ar V 1 = ' w i 0i i 3 1i i i1 i 3 0i 3 0i 3 1i i i ˆ ˆ Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 22 Evans County Study CID inv var Estimation The summary cumulative incidence difference: Assuming no confounding by additional variables, no residual confounding by age and ECG status, no selection bias, and no information bias, these data indicate that men with high CAT levels have an 8.5% higher cumulative incidence of CHD than men with low CAT levels. Recall that the crude CID was estimated to be 13.1%. Adjustment for age and ECG status led to a reduction in the estimated cumulative incidence difference by (8.5 13.1)/8.5 = 54%. 0.085 = 137.42 + 183.97 + 96.89 + 72.02 (0.085) (137.42) + (0.108) (183.97) + (0.058) (96.89) + (0.063) (72.02) = ' w D I C w = D I C i I 1 = i i i I 1 = i ' ˆ ˆ
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 23 95% CI for CID inv var The 95% confidence interval for the summary incidence rate difference is calculated in the usual way: ) D I ar(C V 1.96 D I C VAR INV VAR INV ˆ ˆ ˆ Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 24 Variance of the CID inv var There is a simple expression for the estimated variance of a summary cumulative incidence difference when the inverse of the stratum specific variances are used as weights. when X is an inverse variance weighted average of the stratum specific quantities As stated previously, given sufficient data so that the large strata variance formula applies, using the inverse variances of the stratum specific estimates as gives the most efficient, i.e. minimum variance, summary incidence rate difference available. ' w 1 = ar(X) V ˆ i I =1 i
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2018 25 Evans County Study CID inv var CI Estimation and Interpretation In this example, Thus, the 95% confidence interval for CID is: The cumulative incidence difference for 7 year cumulative incidence of CHD, adjusted for age and ECG status, lies between a slight deficit risk to an excess risk of 17%. The

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