Sequential (version 1.1)

Performance.G.Poisson: Power, Expected Signal Time and Expected Length of Serveillance for the Poisson Group MaxSPRT.

Description

The Performance.G.Poisson function calculates several performance metrics for the continuous Poisson based MaxSPRT. The user specifies the upper limit on the sample size (SampleSize), the upper boundary critical value (cv), the maximum number of tests to be perfomed (Looks), the minimum number of events required before rejecting the null hypothesis (M) and a relative risk (RR). The metrics calculated are the statistical power, the expected time to signal when the null hypothesis is rejected and the expected sample size at the end of the analysis whether the null hypothesis was rejected or not. If the user wants to calculate the statistical significance level alpha, that can be done by setting RR=1, in which case the power output value is the alpha level.

Usage

Performance.G.Poisson(SampleSize,cv,Looks=1,M=1,RR=2)

Arguments

SampleSize

The upper limit on the sample size (length of surveillance) expressed in terms of the expected number of events under the null hypothesis. "SampleSize" must be greater than 0. To avoid very large computation times, we suggest not using values greater th

cv

the critical value for a group sequential MaxSPRT test (see CV.G.Poisson).

Looks

The maximum number of tests to be performed, which is, the number of equally spaced looks at the data if the null hypothesis is never rejected. The value must be an integer greater or equal to 1. The default value is 'Looks=1'.

M

The minimum number of events needed before the null hypothesis can be rejected. The default value is 'M=1'.

RR

the relative risk (>=1) to calculate the power and the expected time to have a signal. The default value is 'RR=2'.

Value

• Power
  the statistical power for a given flat upper boundary (CV).
• Expected time to signal
  the expected time to have a signal.
• Expected length of surveillance
  the expected length of surveillance.

See also

CV.Poisson, SampleSize.Poisson, CV.G.Poisson, Performance.Poisson, poisson.test

Details

The function Performance.G.Poisson calculates the power, the expected time to have a signal and the expected time of surveillance by using the group sequential MaxSPRT for poisson data, given a flat boundary, an upper limit on the number "SampleSize" of expected events under the null, and a delayed start in the vigilance given by "M". It is important to point out that large values of "SampleSize", as "SampleSize>1000", for example, leads to a high computational effort. The times when each test will be performed is defined by using regular time intervals that are referenced by constant expected number of adverse events between looks at the accumulated data. In another words, the MaxSPRT statistic is compared against cv whenever the time is a multiple of $SampleSize/Looks$.

References

Ivair R. Silva, Martin Kulldorff. (2012). Continuous versus Group Sequential Analysis for Vaccine and Drug Safety Surveillance. Manuscript, to be submitted. Jennison, V. and Turnbull, B. (1999), Group Sequential Methods with Applications to Clinical Trials, no. ISBN 0-8493-0316-8, London: Chapman and Hall/CRC. Martin Kulldorff, Ivair R. Silva. (2012). Continuous Sequential Analysis with a Delayed Start. Munuscript, under review. Martin Kulldorff, Robert L. Davis, Margarette Kolczak, Edwin Lewis, Tracy Lieu, and Richard Platt. (2011). A Maximized Sequential Probability Ratio Test for Drug and Safety Surveillance. Sequential Analysis, 30: 58--78.

Examples

## Critical value for a significance level of 0.05:

cvt<- CV.G.Poisson(SampleSize=30,alpha=0.05,Looks=5,M=1)

# Power, expected signal time and expected surveillance time for a relative risk equal
# to 2:

#Performance.G.Poisson(SampleSize=30,cvt,Looks=5,M=1,RR=1.5)