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more and bigger tables - Choice lowest quintile is...

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Farrelll et al (2004) Prevalence of Metabolic Syndrome across Cardiorespiratory Fitness Levels in Women, Obesity Research 12 (5): 824-830 What are interesting hypothesis? Null? There is no association between fitness level and Metabolic syndrome Alternative? As fitness level increases, prevalence in MS decreases There is big drop from lowest to 2 nd quintile and continues to decrease Estimates of p The crude (unadjusted) prevalence of the metabolic syndrome (not shown) was 20.2%, 7.4%, 6.9%, 4.1% and 2.7% across CRF quintiles” 95% Exact Confidence intervals: In STATA Estimates of RD Comparative measures Choice: lowest quintile is “reference category” In this example, it is prevalence rate difference In STATA This is Q2 vs Q1 Estimates of RR Comparative measures Choice: lowest quintile is “reference category” Estimates of OR Comparative measures Choice: lowest quintile is “reference category” Using CIs To test Sometimes people do to see the CI overlapping in order to test the hypothesis If they CI overlap each other, there is no association and if they don’t overlap there is association. However, CI depends on 2 things: Precision of the group and Precision of reference group
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Dots are actual proportion in data and line is Confidence interval In this particular data, reference category is smallest. So, it has the least information on Metabolic Syndrome If we rely on this, we could be making mistakes There may be fairly strong evidence that there is difference among the group In STATA Comparison between Q3 and Q4 There is significant difference But when we compare earlier with the Q1 there was no association. When we compare Q3 and Q4, there is strong evidence that MS is associated with fitness. (p=0.007) We estimate that the risk of prevalence of MS among Q3 is 1.7 times higher than Q3. Moral Cannot rely on overlap of CIs, especially when each compares to third group, to test differences between groups If you want to make a statement about the comparison between two groups o Estimate a parameter (RD, RR, OR) that compares them and its CI, or o Test whether they are different. Consider the following 2 * 5 table Reordered as there is no longer trend of decreasing proportion of MS with increase in fitness. In picture Same story? Not the same story In first plot, there is evidence that MS decreases with Fitness In second plot, there is no such evidence If we are interested in whether the proportion with metabolic syndrome increases or decreases with increasing quintile of fitness o H0: no difference between quintile groups p1 = p2=p3=p4=p5 o HA : positive or negative trend (two sided) p1 ≤ p2 ≤ p3 ≤ p4 ≤ p5 p1 ≥ p2 ≥ p3 ≥ p4 ≥ p5 First table and plot gives strong evidence HA is true, second gives strong evidence, even though the same numbers (in different orders) Cochran-Armitage Trend Test Really a regression on 1,2,3,4,5 but has good power for many trend hypothesis
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