Sequential (version 1.1)

Performance.Poisson: Power, Expected Signal Time and Sample Size for Continuous Sequential Analysis with Poisson Data.

Description

The Performance.Poisson function calculates several performance metrics for the continuous Poisson based MaxSPRT. The user specifies the upper limit on the sample size (SampleSize), the delayed start of analysis (D), the minimujm number of events required before rejecting the null hypothesis (M), the upper boundary critical value (cv) 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.Poisson(SampleSize, D = 0, M = 1, cv, RR = 2)

Arguments

SampleSize

The upper limit on the sample size (length of surveillance) expressed in terms of the epected 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 tha

D

The expected number of events under the null hypothesis before the first look at the data. The default is "D=0", which is also the best choice. This means that there is no delay in the start of the sequential analyses. It is required that 'D

M

The minimum number of events needed before the null hypothesis can be rejected. The default is 'M=1', which means that even a single event can reject the null hypothesis if it occurs sufficiently early. A good rule of thumb is to set 'M=4' (Kulldorff a

cv

The critical value constituting the upper rejection boundary. This can be calculated using the CV.Poisson) function.

RR

The relative risk (>=1) for which statistical power, expected signal time and expected length of surveillance is calculated. The default is RR=2.

Value

• Power
  The statistical power.
• SignalTime
  The expected time to signal given that the null hypothesis is rejected.
• SurveillanceTime
  The expected sample size when the analysis ends (length of surveillance) whether the null hypothesis was rejected or not.

See also

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

Details

For the continuous Poisson based MaxSPRT, the Performance.Poisson function calculates the statistical power, the expected time to signal when the null hypothesis is rejected and the expected sample size until the analysis ends whether the null is rejected or not. Large values of "SampleSize", such as "SampleSize>1000", leads to a long comcputing times.

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 an upper limit on the sample size equal to 10 and a significance 
# level equal to 0.05:

cvt<- CV.Poisson(SampleSize=10,D=0,M=1,alpha=0.05)

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

#Performance.Poisson(SampleSize=10,D=0,M=3,cvt,RR=2)