IRRMH = 1 ↔ IRDSumm = 0HA: The rate of diarrhea does differ between those children who are less than 75% of their expected weight for age compared to children who are 90% or more of their expected weight for age, after stratifying by sex.IRRMH ≠ 1 ↔ IRDSumm ≠ 0Values for a, b, and N can be found in the previous table.X= 75+79= 154E(X|H0)= 20.5(225)/68.8+18.01(216)/58.84= 133.4499744451Var(X|H0)= 20.5(48)(225)/68.82+18.01(40.83)(216)/58.842= 93.0618738684Z2= (154-133.450)2/93.062= 4.54The epi calculator gets a Z-square= 4.58p-value= 0.0324These data are not consistent with the state of nature described by the null. We can reject the null hypothesis at the alpha=0.05 level and conclude that there is statistically significant evidence that after stratifying by sex, the rate of diarrhea does differ between those children who are less than 75% of their expected weight for age compared to children who are 90% or more of their expected weight for age, assuming no residual confounding, confounding from other variables, selection bias, or informationbias.d.Do you think sex is a confounder based on the above analyses?In order for sex to be a confounder of the relationship between WFA and diarrheal disease, there would need to be an open backdoor path through sex. A simple version ofthis is if sex is a common cause of WFA and diarrheal disease.
Confounders will also have three properties: 1) they are associated with the exposure in the study base, 2) they are associated with the outcome in the unexposed, and 3) they are not a downstream consequence of the exposure or outcome. We can empirically check conditions 1) and 2), and must use substantive knowledge to decide about 3). Importantly, not all variables with these properties will be confounders, so the ‘backdoor path’ (causal) definition described above should be used to get an understanding of the structure of the relationship.From the information provided above, we can see that sex is weakly associated with diarrhea in children ≥90% WFA (IRR=0.93) and weakly associated with weight for age (IRR=1.03). Additionally, sex is not a downstream consequence of weight for age or diarrhea. However, the associations between sex with the exposure and outcome are both very weak and may be the result of sampling variability. From this information, sex is not likely to be a strong confounder.Finally, we can note that the crude and adjusted analyses produced almost identical results. This is indirect, but not irrefutable, evidence that sex is unlikely to be a strong confounder.2. A cigarette smoking history was obtained from 6,690 Japanese-American men examined from 1965 through 1968. During the 22-year follow-up period, 37 incident cases of oral or bladder cancer were observed among the 2,344 never smokers, and 165 incident cases or oral or bladder cancer were observed among the 4,346 past and current smokers, as shown in the table below (Chyou PH, Nomura AMY, Stemmermann GN. Am J Public Health 1992;83:37-40). Assume no loss to follow-up and no competing causes of death for this and all remaining questions about these data.
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