The methods outlined in this chapter for selecting an adequate sample size have been available for many years, but it is probably not an exaggeration to state that the majority of intervention trials are much too small. Although there is an increasing awareness of the need to enrol a large enough sample, this chapter is concluded by discussing the consequences of choosing a sample size that is too small.
First, suppose that the intervention under study has little or no effect on the outcome of interest. The difference observed in a trial is likely therefore to be non-significant. However, the width of the CI for the effect measure (for example, the relative risk) will depend on the sample size. If the sample is small, the CI will be very wide, and so, even though it will probably include the null value (a zero difference between the groups, or a relative risk of 1), it will extend to include large values of the effect measure. In other words, the trial will have failed to establish that the intervention is unlikely to have an effect of public health or clinical importance. For example, in the mosquito-net trial, suppose only 50 children were included in each group, and suppose the observed spleen rates in the two groups were identical at 40%, giving an estimated relative risk of R =1. The approximate 95% CI for R would extend from 0.62 to 1.62 (Section 3.1). A relative risk of 0.62 would imply a very substantial effect, i.e. a reduction in spleen rate from 40% to 25%, and this small trial would be unable to exclude such an effect as being very unlikely. If the sample size in each group were increased to 500, the 95% CI would extend only from 0.86 to 1.16, a much narrower interval.
Suppose that the intervention does have an appreciable effect. A trial that is too small will have low power, i.e. it will have little chance of giving a statistically significant difference. In other words, there is little chance to demonstrate that the intervention has an effect. In the example, if the true effect of the intervention is to reduce the spleen rate from 40% to 25%, a sample size of 50 in each group would give a power of only 36%. A total of 205 children would be needed in each group to give 90% power (Table 5.2). Even if a significant difference is found, the CI on the effect will still be very wide, so there will be uncertainty at the end of the trial whether the effect of the intervention is small and unimportant, or very large and of major importance.
The conduct of trials that are too small has consequences extending beyond the results of the specific trial. There is considerable evidence that trials showing large effects are more likely to be published than those showing little or no effect. Suppose a number of small trials of a specific intervention are conducted. Because of the large sampling error implied by small sample sizes, a few of these trials will produce estimates of the effect of the intervention that are much larger than the true effect. These trials are more likely to be published, and the result is that the findings in the literature are likely to overestimate considerably the true effects of interventions. This publication bias is much smaller for larger trials, because a large trial showing little or no effect is more likely to be published than a small trial with a similar difference.