1. Measuring Associations Between Exposure and Outcomes Chapter 3, Szklo and Nieto

2. Measures of Association can be based on: Absolute differences Between Groups (e.g., disease risk among exposed – disease risk among unexposed) Relative differences or ratios Between Groups (e.g., disease risk ratio or relative risk: disease risk in exposed/disease risk in unexposed)

3. Absolute differences Public Health activities Preventive activities Measure of association when the outcome of interest is continuous Examples: PAR, Mean Differences

4. Relative differences or ratios For discrete variable To assess causal associations Examples: Relative Risk/Rate, Relative odds

5. Types of Variables Discrete/categorical –Dichotomous, binary Absolute Difference? Relative Difference Continuous –Difference between means

6. Cohort Study Cohort Study Diseased Non- diseased Totals: Risk odds Exposure Exposedaba+b a / a+b a / b Unexposedcdc+d c /c+d c / d Totals: Disease a+cb+da+b+c+d

7. Odds in Exposed and Unexposed Odds in exposed=( a / a+b) / 1- (a / a+b ) =(a / a+b) / (b / a+b) = a/b Odds in unexposed=( c / c+d) / 1- (c / c+d ) =(c / c+d) / (d / c+d) = c/d

8. Relative Risk RR= a / a+b / c / c+d OR= a / b / c / d = a*d / b*c Odds ratio is a cross-product ratio

9. Rare Disease - MI MIFree of MITotals: Exposure High Blood Pressure 180 982010000 Normal Pressure 30 997010000

10. Probability + =q + = 180/10000 = 0.0180 Probability - = q - = 30/10000 = 0.0030 Odds dis + = 180/9820 = 0.01833 Odds dis - = 30/9970 = 0.00301 RR=6 OR=6.09

11. Common Disease – Vaccine Reactions Local Reactions Free of Reactions Totals: Exposure Vaccinated 65019202570 Placebo1702240

12. RR = 650 / 2570 / 170 / 2410 = 0.2529 / 0.0705 = 3.59 OR = 650 / 1920 / 170 / 2240 = 0.3385 / 0.0759 = 4.46

13. Built – in bias OR = ( q + / 1 - q + ) / ( q - / 1 - q – ) = q + / q - * ( 1 - q - / 1- q + ) = RR * ( 1 - q - / 1- q + )

14. Built – in bias Use of the odds ratio as an estimate of the relative risk biases it in a direction opposite to the null hypothesis. (1 - q - / 1- q + ) defines the bias responsible for the discrepancy between the RR & OR.

15. When the disease is relatively rare, this bias is negligible. When the incidence is high, the bias can be substantial.

16. OR is a valuable measure of association : 1. It can be measured in case – control studies. 2. It is directly derived from logistic regression models 3. The OR of an event is the exact reciprocal of the OR of the nonevent. (survival or death OR both are informative) 4. when the baseline risk is not very small, RR can be meaningless.

17. Cross-sectional Studies In the stationary population: Prevalent RR= Prev+ / prev- = ( q+ * Dur+ * (1- prev+)) / ( q- * Dur- * (1- prev-)) PPR = RR x dur + x {1-prev+} dur - {1-prev-}

18. Cross-sectional Studies A point prevalence ratio may be able to estimate the relative risk depending on –the ratio of the durations of disease among the exposed with disease + the unexposed with disease - –the ratio of the values 1-prevalence among the exposed + 1-prevalence among the unexposed -

19. The two bias factors that differentiate the PRR from the relative risk: 1. Dur+/Dur- survival or duration bias 2. (1- prev+/ 1- prev -) complement bias 1 & 2 (S.B) Incidence – prevalence bias

20. We can estimate RR in cross sectional study when the exposure don’t modify the duration of the disease and the disease is rare. Since (1- prev+/ 1- prev -)< 1: PRR underestimates RR We should consider temporality

21. Case-Control Study The OR of disease and the OR of exposure are mathematically equivalent. In case control study we calculate the OR of exposure as it’s algebraically identical to the OR of disease. OR exp = a /c / b/ d = a*d/ b*c = a / b / c / d = OR dis

22. Case-Control Study The fact that the OR exp is identical to the OR dis explains why the interpretation of the odds ratio in case control studies is prospective.

23. Odds Ratio as an Estimate of the Relative Risk: The disease under study has low Incidence thus resulting in a small built-in bias : OR is an estimate of RR The case – cohort approach allows direct estimation of RR by OR and does not have to rely on rarity assumption. When the OR is used as a measure of association in itself, this assumption is obviously is not needed

24. Calculation of the OR when there are more than two exposure categories To calculate the OR for different exposure categories, one is chosen as the reference category (biologically or largest sample size)

25. Cases of Craniosynostosis and normal Control according to maternal age Maternal age CasesControlsOdds exp in case Odds exp in control OR <20128912/1289/891 20-244724247/12242/891.44 25-295625556/12255/891.63 >295817358/12173/892.49

26. When the multilevel exposure variable is ordinal, it may be of interest to perform a trend test

27. Assessing the Strength of association Since risk factors vary in terms of their physiologic modus operandi as well as their exposure levels and units, comparisons of the measure of association as relative importance of them are unwarranted.

28. An alternative way to assess the strength of the association of a given Risk factor with An outcome is to estimate the exposure intensity necessary for that factor to produce an association of the same magnitude as that of well- established risk factors or vise-versa.