932953 1085191104 006214 721393 1222181240

932953 1085191104 006214 721393 1222181240

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Var(ln(CIR≤55))= 2860/(93*2953) + 1085/(19*1104) = 0.06214Var(ln(CIR>55))= 1321/(72*1393) + 1222/(18*1240) = 0.06792Z2 =[(0.604-0.932)2 /[0.06214]+ [(1.27-0.932)2]/ [0.06792] = 1.731 + 1.682 = 3.41 ~ χ2with 1 dfp-value =0.065At the alpha=0.05 level, we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that there is effect measure modification by age on the multiplicative scale for the association between ever smoking compared to never smoking and the cumulative incidence of oral or bladder cancer (assuming no confounding, selection bias, or information bias). However, note that the p-value is quite close to 0.05 and studies are often underpowered for tests of homogeneity. e. For the stratified data, perform the test of homogeneity for the cumulative incidence difference. State the null and alternative hypotheses. Interpret your findings.
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H0: There is no effect measure modification of the association between ever versus never smoking and oral or bladder cancer across the strata of age on the additive scale (CID≤55= CID>55)H1: There is effect measure modification of the association between ever versus never smoking and oral or bladder cancer across the strata of age on the additive scale (CID≤55≠ CID>55)Xi= CIDiXsumm=CIDSUMMVar(Xi)=Var(CIDi)Degrees of freedom = # of strata - 1 = 2-1 = 1 degree of freedomwhere From question 2b:CID≤55= 0.0143 over the 22-year study periodCID>55= 0.0372 over the 22-year study periodw≤55= (29533* 11043) / [(11043 * 93 * {2953-93}) + (29533* 19 * {1104-19})] = 38,986.93w>55= (13933* 12403) / [(12403 * 72 * {1393-72}) + (13933* 18 * {1240-18})] = 21,402.46CIDSumm= [(38968.93*0.0143) + (21402.46*0.0372)] / [21402.46 + 38968.93] = 0.0224 over the 22-year study periodVar(CIDi)= = 1/wiVar(CID≤55) = 1/38,986.93=2.565 E-05Var(CID>55) = 1/21,402.46=4.672 E-05Z2 =[(0.0143-0.0224)2 / 2.565 E-05] + [(0.0372-0.0224)2/ 4.672 E-05] = 2.558 + 4.688 = 7.24 ~ χ2with 1 dfp-value =0.007At the alpha=0.05 level, we reject the null hypothesis. We have sufficient evidence to conclude that there is effect measure modification by age on the additive scale for the association between ever smoking compared to never smoking and the cumulative incidence of oral or bladder cancer (assuming no confounding, selection bias, or information bias).f. Given these results, would you present a MH summary CIR or summary CID?Though we did not reject the null hypothesis of no effect measure modification on the multiplicative scale for the association between smoking and the cumulative incidence of oral or bladder cancer, we can see that the CIR among men who are older than 55 years (3.56 over the
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22-year study period) is nearly double the CIR among men who are 55 years or younger (1.83 over the 22-year study period). Additionally, studies are often underpowered to detect statistically significant effect measure modification. As a result, presenting an MH summary CIR may be inappropriate. Instead, we may want to present CIR stratified by age. Or, if we want to present a summary CIR, we could standardize by using population-based weights (which we willdiscuss this in a future lecture).
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  • Summer '14
  • FrancisCook

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