### 9.6.7Investigating the effect of baseline risk

One potentially important source of heterogeneity among a series of studies is when the underlying average risk of the outcome event varies between the studies. The baseline risk of a particular event may be viewed as an aggregate measure of case-mix factors such as age or disease severity. It is generally measured as the observed risk of the event in the control group of each study (the control group risk (CGR)). The notion is controversial in its relevance to clinical practice since baseline risk represents a summary of both known and unknown risk factors. Problems also arise because baseline risk will depend on the length of follow-up, which often varies across studies. However, baseline risk has received particular attention in meta-analysis because the information is readily available once dichotomous data have been prepared for use in meta-analyses. Sharp provides a full discussion of the topic (Sharp 2000).

Intuition would suggest that participants are more or less likely to benefit from an effective intervention according to their risk status. However, the relationship between baseline risk and intervention effect is a complicated issue. For example, suppose an intervention is equally beneficial in the sense that for all patients it reduces the risk of an event, say a stroke, to 80% of the baseline risk. Then it is not equally beneficial in terms of absolute differences in risk in the sense that it reduces a 50% stroke rate by 10 percentage points to 40% (number needed to treat = 10), but a 20% stroke rate by 4 percentage points to 16% (number needed to treat = 25).

Use of different summary statistics (risk ratio, odds ratio and risk difference) will demonstrate different relationships with baseline risk. Summary statistics that show close to no relationship with baseline risk are generally preferred for use in meta-analysis (see Section 9.4.4.4).

Investigating any relationship between effect estimates and the control group risk is also complicated by a technical phenomenon known as regression to the mean. This arises because the control group risk forms an integral part of the effect estimate. A high risk in a control group, observed entirely by chance, will on average give rise to a higher than expected effect estimate, and vice versa. This phenomenon results in a false correlation between effect estimates and control group risks. Methods are available, requiring sophisticated software, that correct for regression to the mean (McIntosh 1996, Thompson 1997). These should be used for such analyses and statistical expertise is recommended.