Sas Analysis

This chapter concentrates on risk ratio and prevalence ratios. Both risk ratios and prevalence ratios are ratios

of proportions. When comparing proportion from independent groups, we adopt the following notation:

Disease + Disease -

Exposure + 1 1 1 A B N

re Exposu ! 0 0 0 A B N

1 0 M M N

1 In this notation, A indicates "case" and B indicates "noncase." Subscript denotes "exposed" and subscript 0

0 1 0 denotes "non-exposed." For example, A indicates the number of exposed cases and B indicates the number

1 0 of non-exposed non-cases. There are N exposed individuals and N non-exposed individuals. There are N

individuals in the study.

Let represent the incidence proportion (risk) estimator in the exposed group, and let represent the risk

estimator in the nonexposed group: and .

Let N (lowercase phi) represent the risk ratio parameter and (phi hat) represent the risk ratio estimator:

1 The above formulas apply to prevalences as well, in which case p represents the prevalence in the exposed

0 group, p represents the prevalence in the nonexposed group, and N represents the represents the prevalence

ratio parameter. The prevalence ratio is equal to the risk ratio when (a) the average duration of disease is

the same in the groups, (b) the disease is "rare" (say, risk . 5%) , and (c) the disease does not influence the

presence of the exposure.

Illustrative example (toxic.sav). A chemotherapeutic agent used for bone marrow ablation in

preparation for transplantation comes in either generic or non-generic form. Patients at a particular hospital

received either the generic or non-generic formulation.* The study outcome was cerebellar toxicity. Crosstabulation

revealed:

Toxicity + Toxicity -

Generic + 11 14 25

Generic - 3 31 34

14 31 59

Thus, , , and .

Interpretation: The risk ratio of 4.99 (about 5) indicates that risk in the exposed group is 5-times that of the

non-exposed group. The segment of the risk ratio above (or below) 1 quantifies the relative increase (or

decrease) in risk associated with exposure. For example, the risk ratio of 5 reveals a 5 ! 1.00 = 400(100%) =

400% increase in risk with exposure.

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Confidence Interval for the Risk Ratio

To calculate a 95% confidence interval for the risk ratio parameter, convert the risk ratio estimate to a

natural log (ln) scale. (Use