```help sampsi_fleming
-------------------------------------------------------------------------------

Title

Exact sample size calculation for single-stage designs

Syntax

sampsi_fleming [, options]

options               Description
-------------------------------------------------------------------------
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 start sample size in the initial
sample size search, the default is 1.
end(#)               specifies the largest sample size in the initial
sample size search, the default is 40.
-------------------------------------------------------------------------

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.

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

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 start sample size in the initialgrid search, the
default is 1.

end(#) specifies the largest sample size in the initial grid search, the
default is 40.

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.

Author

Adrian Mander, MRC Biostatistics Unit, Cambridge, 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

```