*! version 1.02 7Aug2014
help sampsi_fleming

Title

Exact sample size calculation for single-stage designs

Syntax

sampsi_fleming
[, options]

Main
p0(#) specifies the null proportion.

p1(#) specifies the alternative proportion.

alpha(#) specifies the type I error, the default is 0.05.

power(#) specifies the power, the default is 0.9.

start(#) specifies the starting sample size of the search.

n(#) specifies the sample size of the trial.

r(#) specifies the number of responders to reject the null hypothesis.

check specifies that p0. p1, n and r are fixed and will calculate the power and type 1 error of the design.

Description

A single stage design requires all n patients to receive and experimental treatment.
Within a specified time period they will be observed to have responded (success) or not (failure).
The probability of a success in the trial is p and this is compared to a fixed value p0, which is the
probability of a success under the null hypothesis, this could represent no treatment or standard treatment.
The trial therefore tests the null hypothesis H0:p=p0 against the alternative hypothesis H1:p>p0.
A particular value p1 (p1>p0) is considered to be the desired probability of success.

The number of successes, S, will follow a Binomial distribution with parameters n and p. A
sample size is found by using a search such that P(S>=u|p0)<=alpha and P(S>=u|p1)>=power. The design
is therefore characterised by the sample size n and the critical value u, the null hypothesis is
rejected if there are u or more successes in a trial of size n.

Latest Version

The latest version is always kept on the SSC website. To install the latest version click
on the following link

ssc install sampsi_fleming, replace.

Options

Main

p0(#) specifies the null proportion.

p1(#) specifies the alternative proportion.

alpha(#) specifies the type I error, the default is 0.05.

power(#) specifies the power, the default is 0.9.

Start(#) specifies the starting sample size for the search.

n(#) specifies the sample size of the trial.

r(#) specifies the number of responders to reject the null hypothesis.

check specifies that p0. p1, n and r are fixed and will calculate the power and type 1 error of the design.

Examples

The default sample size calculation

sampsi_fleming

The default design has a sample size of 47 and a critical value of 15, the type I error is 0.0366 and power is 0.9012.

sampsi_fleming, p0(0.45) p1(0.5) s(800)

A sample size of 861 and a critical value of 412 gives a type I error of 0.0499 and a power of 0.9024.

sampsi_fleming, a(0.01) p(0.8)

A sample size of 52 and a critical value of 18 gives a type I error of 0.0099 and a power of 0.8245.

sampsi_fleming, p0(0.1) p1(0.35) a(0.01) p(0.8)

A sample size of 25 and a critical value of 7 gives a type I error of 0.0095 and a power of 0.8266.

sampsi_fleming, p0(0.1) p1(0.2) start(84) power(0.8) a(0.05)

Start searching for the above design at a sample size of 84, note there is a better design than this!

sampsi_fleming, p0(0.1) p1(0.2) n(84) r(13) check

Shows that the selected design has a 0.0741 chance of a type I error and 88.22% power.

Author

Adrian Mander, MRC Biostatistics Unit, Cambridge, UK.

Email adrian.mander@mrc-bsu.cam.ac.uk

References

R.P.A'Hern (2001) Sample size tables for exact single-stage phase II designs. Statistics in Medicine 20:859-866.

J.Whitehead (2008) Bayesian sample size for exploratory clinical trials incorporating historical data. Statistics in Medicine 27:2307-2327.

T.R. Fleming (1982) One-sample multiple testing procedure for phase II clinical trials. Biometrics 38:143-151.

Also see

Related commands

HELP FILES SSC installation links Description

samplesize (if installed) (ssc install samplesize) Sample Size graphics

sampsi_reg (if installed) (ssc install sampsi_reg) Sample Size for linear regression

sampsi_mcc (if installed) (ssc install sampsi_mcc) Sample Size for matched case/control studies

sampsi_rho (if installed) (ssc install sampsi_rho) Sample Size for Pearson correlation