A Practical Approach, Second Edition=Ronald D. Ho.pdf

HUMAN STUDIES 825but also the magnitude of an effect. The 95% confidence interval of the odds ratio can be calculatedby using Miettinen’s method (test based estimate) according to the following formula, althoughother methods are available:95%CI of OR = OR ±Let us take the example in Table 20.2 — the OR is 0.77 and the 95% CI is 0.63 to 0.94, while inthe smaller material the OR is nearly the same (0.76), but the 95% CI is much larger (0.40 to 1.44).From the former estimate, it can be said that most likely the OR is reduced by at least 6% and possiblyby as much as 37%, while from the latter estimate, the OR could be increased by up to 44%.It should be observed that the odds ratio is not a direct estimate of the risk or the risk decreasefor a smoking woman to have an infant with Down syndrome, but when very rare occurrences(such as Down syndrome) are studied, the estimate will be quite adequate. If we suppose that thepopulation risk of having an infant with Down syndrome is 1 in 700, it means that the 752 caseswere drawn from a total of some 526,400 births. Among them (judged from the smoking rateamong controls), 155,400 smoked and 371,000 did not. The risk of having an infant with Downsyndrome among smokers is thus 1.18 per 1000, and among nonsmokers it is 1.53 per 1000. Therisk ratio will be 0.77, exactly the odds ratio that was estimated.2. Stratified Analysis — A Method to Control for ConfoundingIn the example in Table 20.2, we saw a difference in smoking rate among case and control women.Is this difference causal? Does smoking really prevent the birth of a Down infant, or is it a secondaryeffect of a so-called confounder, that is, a variable that affects both smoking rate and the risk ofhaving a Down infant?Table 20.3 addresses this problem. Here the material has been divided into 5-year maternal ageclasses. From the control data it is apparent that smoking declines with age, and it is well knownthat the risk of having an infant with Down syndrome increases with age. The seemingly protectiveeffect of smoking may therefore be secondary to these differences in smoking distribution andDown infant risk between age classes.There are different methods to control for such a confounder (or a set of confounders). One isto match cases and controls, so each case and control will form a pair with the same maternal age.Another is to make a stratified analysis. The data in Table 20.3 can be looked upon as a series of2×2 tables, one for each age class or stratum. The Mantel-Haenszel method makes it possible tosum up the differences over the strata and to calculate a χ 2 (based on one degree of freedom, df)common for all strata.The method is as follows, using the designations of Table 20.2 for each 2×2 table, with E(a)designating the expected value of a (= n 1 n 3 /n). The subscript i refers to the ith 2×2 table:s = Σ[a i – E(a i )]The variance estimate of a i is:Vaiv = Σ(Va i )R 1 = Σ(a i *d i /n i )R 2 = Σ(c i *b i /n i )2( χ1196 .)n * n n * n=2n * n −i( )( 1 1)1 2 3 4χ 2 = s 2 /v. This χ 2 is based on only 1 df.© 2006 by Taylor & Francis Group, LLC