9.4.8  Meta-analysis of counts and rates

Results may be expressed as count data when each participant may experience an event, and may experience it more than once (see Section 9.2.5). For example, ‘number of strokes’, or ‘number of hospital visits’ are counts. These events may not happen at all, but if they do happen there is no theoretical maximum number of occurrences for an individual.

 

As described in Chapter 7 (Section 7.7.5), count data may be analysed using methods for dichotomous (see Section 9.4.4), continuous (see Section 9.4.5) and time-to-event data (see Section 9.4.9) as well as being analysed as rate data.

 

Rate data occur if counts are measured for each participant along with the time over which they are observed. This is particularly appropriate when the events being counted are rare. For example, a woman may experience two strokes during a follow-up period of two years. Her rate of strokes is one per year of follow-up (or, equivalently 0.083 per month of follow-up). Rates are conventionally summarized at the group level. For example, participants in the control group of a clinical trial may experience 85 strokes during a total of 2836 person-years of follow-up. An underlying assumption associated with the use of rates is that the risk of an event is constant across participants and over time. This assumption should be carefully considered for each situation. For example, in contraception studies, rates have been used (known as Pearl indices) to describe the number of pregnancies per 100 women-years of follow-up. This is now considered inappropriate since couples have different risks of conception, and the risk for each woman changes over time. Pregnancies are now analysed more often using life tables or time-to-event methods that investigate the time elapsing before the first pregnancy.

 

Analysing count data as rates is not always the most appropriate approach and is uncommon in practice. This is because:

  1. the assumption of a constant underlying risk may not be suitable; and

  2. statistical methods are not as well developed as they are for other types of data.

The results of a study may be expressed as a rate ratio, that is the ratio of the rate in the experimental intervention group to the rate in the control group. Suppose EE events occurred during TE participant-years of follow-up in the experimental intervention group, and EC events during TC participant-years in the control intervention group. The rate ratio is

.

 

The (natural) logarithms of the rate ratios may be combined across studies using the generic inverse-variance method (see Section 9.4.3.2). An approximate standard error of the log rate ratio is given by

.

A correction of 0.5 may be added to each count in the case of zero events. Note that the choice of time unit (i.e. patient-months, women-years, etc) is irrelevant since it is cancelled out of the rate ratio and does not figure in the standard error. However the units should still be displayed when presenting the study results. An alternative means of estimating the rate ratio is through the approach of Whitehead and Whitehead (Whitehead 1991).

 

In a randomized trial, rate ratios may often be very similar to relative risks obtained after dichotomizing the participants, since the average period of follow-up should be similar in all intervention groups. Rate ratios and relative risks will differ, however, if an intervention affects the likelihood of some participants experiencing multiple events.

 

It is possible also to focus attention on the rate difference,

.

An approximate standard error for the rate difference is

.

The analysis again requires use of the generic inverse-variance method in RevMan. One of the only discussions of meta-analysis of rates, which is still rather short, is that by Hasselblad and McCrory (Hasselblad 1995).