For continuous and group sequential analysis based on monitoring Poisson data conditioned on matched
historical Poisson data, the power, expected time to signal, expected sample size and alpha spending impplied by user-specified thresholds are calculated with
Performance.Threshold.CondPoisson. The user can select one between two scales to enter with the
threshold, the Conditional Maximized Sequential
Probability Ratio Test statistic (CMaxSPRT) scale (Li and Kulldorff, 2010), or the surveillance versus historical person-time ratio (Silva et al., 2019a).
For the CMaxSRT scale, the input is CV.upper. This can be entered as a vector for group sequential analysis. For example, for a three-group sequential test,
the i-th entry represents the critical value for the i-th test, with i=1, 2, 3. If a single number is informed in CV.upper, then
a flat critical value for all tests is used for both continuous or group sequential fashions. The number of tests is defined with the input GroupSizes,
as shall be detailed here after the desciption of Person_timeRatioH0.
An alternative way to inform the threshold is by using Person_timeRatioH0, which is in the scale of the ratio between the person-time
in the surveillance period and the
overall person-time of the historical period. Using the notation by Silva et al. (2019a) and Silva et al. (2019b), let \(V\) denote the
total person-time from the historical data, where cc events were observed, and let \(P_{k(i)}\) denote the the cummulative
person-time from the surveillance data at the i-th test with a cummulative \(k(i)\) events. With Person_timeRatioH0,
the entries must have increasing numbers, from the first to the last. For example,
for a three-group sequential plan with sample sizes of 20, 15, 25, a hypothetical choice is
Person_timeRatioH0=c(0.1, 0.5, 1). This way, H0 is rejected if: \(P_20/V\) <= 0.1 in the first test,
or \(P_35/V\) <= 0.5 in the second test, or \(P_60/V\) <= 1 in the third test.
Note: only one of the inputs CV.upper or Person_timeRatioH0 is to be used.
With GroupSizes the user informs the sample size of each test in the scale of the
number of events in the surveillance period. Therefore, only positive
numbers are accepted in GroupSizes. For irregular group sizes, a vector must be informed
with each test-specific number of events between two looks at the data, therefore the entries of
GroupSizes must sums up K. For regular group sizes, a single number can be informed
for the constant sample size of each test. For example, for continuous sequential analysis,
GroupSizes=1. For ten-group sequential analysis with K=50, GroupSizes=5.
For RR the user must specify the target relative risks for calculation of statistical performance measures.
It can be a vector of positive numbers or a single number.
For details on the calculation of signaling thresholds and alpha spending for Poisson data conditioned to historical data,
see the papers by Silva et al. (2019a) and Silva et al. (2019b), respectively.