In Table 10–3, the crude value of the risk ratio is 1.44, which is between the values for the risk ratio in the two age strata. Could the crude risk ratio have been outside the range of the stratum-specific values, or must it always fall within the range of the stratum-specific values? Why or why not?

The pooled estimate for the risk ratio from Table 10–3 was 1.33, also within the range of the stratum-specific values. Does the pooled estimate always fall within the range of the stratum-specific estimates of the risk ratio? Why or why not?

If you were comparing the effect of exposure at several levels and needed to control confounding, would you prefer to compare a pooled estimate of the effect at each level or a standardized estimate of the effect at each level? Why?

Prove that an SMR is directly standardized to the distribution of the exposed group; that is, prove that an SMR is the ratio of two standardized rates that are both standardized to the distribution of the exposed group.

Suppose that an investigator conducting a randomized trial of an old and a new treatment examines baseline characteristics of the subjects (eg, age, sex, stage of disease) that may be confounding factors and finds that the two groups are different with respect to several characteristics. Why is it unimportant whether these differences are “statistically significant”?

Suppose one of the differences in question 5 is statistically significant. A significance test is a test of the null hypothesis, which is a hypothesis that chance alone can account for the observed difference. What is the explanation for baseline differences in a randomized trial? What implication does that explanation have for dealing with these differences?

The larger a randomized trial, the smaller the expected confounding. Why? Explain why the size of a study does not affect confounding in nonexperimental studies.

Imagine a stratum of a case-control study in which all subjects were unexposed. What is the mathematic contribution of that stratum to the estimate of the pooled odds ratio (see Equation 10–6)? What is the mathematic contribution of that stratum to the variance of the pooled odds ratio (see bottom equation in Table 10–4)?