SampleSize.Poisson: Sample Size Calculation for Continuous Sequential Analysis with Poisson Data.

Description

The function SampleSize.poisson obtains the maximum sample size (length of surveillance) needed to guarantee a desired statistical power when applying the MaxSPRT test with a Wald type upper boundary, which is flat with respect to the log-likelihood ratio.

Usage

SampleSize.Poisson(alpha=0.05,power=0.9,M=1,D=0,RR=2,precision=0.000001)

Arguments

alpha

The significance level. The default value is 'alpha=0.05'. To avoid numerical complications on the calculation of the critical value for values of alpha close to zero or one, 'alpha' must be in the range (0,0.5].

power

The target overall power to detect an increased risk of the relative risk (RR). The default value is 'power=0.90'.

The minimum number of events needed before the null hypothesis can be rejected. The default value 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' (Kulld

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

A target relative risk to be detected with the requested statistical power. The default value is 'RR=2'

precision

The tolerance for how much larger is the allowed power with respect to the target one. The default value is 'precision=0.000001'.

Value

SampleSizeThe upper limit on the sample size (length of surveillance) needed by the continuous Poisson based MaxSPRT in order to achive ethe desired statistical "power" for the user specified relative risk "RR".

Details

The function SampleSize.Poisson calculates the upper limit on the sample size (length of surveillance) that needs to be set for the continuous Poisson based MaxSPRT in order to provide the user specified statistical power for the user specified relative risk (RR). The solution is exact using iterative numerical calculations. For details, see Kulldorff et al. (2011).

References

Ivair R. Silva, Martin Kulldorff. (2012). Continuous versus Group Sequential Analysis for Vaccine and Drug Safety Surveillance. Manuscript, to be submitted. 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

Run this code

#  Upper limit on the sample size required to obtain a power of 90%, for a relati-
#  ve risk of 3, no delay for starting the surveillance (D=0), and the null hypothe-
#  sis can be rejected with only one event (M=1).

# SampleSize.Poisson(alpha=0.05,power=0.8,M=1,D=0,RR=3)

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