determine the e¤ect of a new agent: for example, on the prevention of a toxic-
ity. The primary endpoint may be measured on a continuous scale. In other
trials, a pharmacologic- or biologic-to-outcome correlative objective may be
the target.
12.5.1 Continuous Endpoints
When the primary outcome of a trial is measured on a continuous scale, the
focus is on the mean. Because of this focus, the planning of sample size can be
approached in terms of controlling the width of a desired confidence interval
for the parameter of interest, the (population) mean. The sample size determi-
nation is similar to the case when the focus is the response rate. That is, for the
confidence interval to be useful, it must be short enough to pinpoint the value
of the parameter, the mean, reasonably well with a high degree of confidence,
say 95%. If a study is unplanned or poorly planned, there is a real possibility
that the resulting confidence interval will be too long to be of any use to the
researcher. In this case, we may decide to have an estimate error not exceeding
d, an upper bound for the margin of error. With a given level of the maximum
tolerated errord, the minimum required sample size is given by
n¼ð 1 : 96 Þ^2 s^2
d^2(rounded up to the next integer). This required sample size is also a¤ected by
three factors:
- The coe‰cient 1.96. As mentioned previously, a di¤erent coe‰cient is
used for a di¤erent degree of confidence, which is set arbitrarily by the
investigator; 95% is a conventional choice. - The maximum tolerated errord, which is also set arbitrarily by the
investigator. - The variability of the population measurements, the variance. This seems
like a circular problem. We want to find the size of a sample so as to
estimate the mean accurately, and to do that, we need to know the vari-
ance before we have the data! Of course, the exact value of the variance is
also unknown. However, we can use information from similar studies,
past studies, or some reasonable upper bound. If nothing else is available,
we may need to run a preliminary or pilot study. One-fourth of the range
may serve as a rough estimate for the standard deviation.
12.5.2 Correlation Endpoints
When the parameter is a coe‰cient of correlation, the planning of sample size
is approached di¤erently because it is very di‰cult to come up with a mean-
454 STUDY DESIGNS