help simon2stage-------------------------------------------------------------------------------

Title

Finding Simon two stage designs with extensions

Syntax

simon2stage[,options]

optionsDescription ------------------------------------------------------------------------- Mainp0(#) specifies the null proportion, the default is 0.1.p1(#) specifies the alternative proportion, the default is 0.4.alpha(#) specifies the type I error, the default is 0.05.beta(#) specifies the type 2 error, the default is 0.2.minn(#) specifies the start sample size in the initial grid search, the default is 1.maxn(#) specifies the largest sample size in the initial grid search, the default is 35.optimalspecifies that the interest is in the optimal design rather than the minimax.optp(#) specifies the true proportion to optimize the design for, the default is p0.effspecifies that the design can stop for efficacy as well as futility.deltaminimaxspecifies that the delta-minimax design is found.admissspecifies that the set of admissible designs should be found. -------------------------------------------------------------------------

DescriptionThe Simon two stage design is a single arm study with an interim analysis. The main purpose of this design is to investigate whether an intervention works or not and to stop the study early for futility. Under the null hypothesis the probability of a success is

p0, this is usually taken as the probability of success for the current standard treatment. The probability of a success in this study,p, is tested using the null hypothesisH0:p=p0versus the alternative hypothesisH1:p>=p1. The probability of success for the alternative hypothesis is fixed to be a pre-specified valuep1, wherep1>p0.The Simon two stage design consists of studying

n1participants in a first stage and the study stops if there arer1or fewer responders to the intervention. If there are more thanr1responders in the first stage then the study continues untilnparticipants in total are studied. Then the null hypothesis is not rejected if there areror fewer responders. Each design must satisfy the type 1 (alpha) and type 2 (beta) errors.The probability of not rejecting

H0can be calculated conditional on anypand let this function beR(p). The design must therefore satisfy the constraintsR(p0)>=1-alphaandR(p1)<=beta. The minimax design is one that satisfies these constraints with the smallest total sample sizenand the smallest expected sample size underH0. The alternative is to find the "optimal" design which is the design with the smallest expected sample size conditional on the true proportion being specified by theoptp()option. The default is optimising the design under the null proportionp0and this is the classical Simon two stage design, however this command allows greater flexibility.The Simon two stage design has been extended here to allow for stopping for efficacy. The design can be indexed by 5 numbers

(r1 r2/n1, r/n). Now the study stops for futility if there arer1or fewer responders OR stops for efficacy if there are more thanr2responders in the first stage. If the study continues to the second stage then the null hypothesis is no rejected if there areror fewer responders. Again the type 1 and type 2 errors must be satisfied for a design to be considered.There are two additional designs that are of interest firstly the delta-minimax design as described in Shuster 2002 and secondly the set of admissible designs as described by Mander et al. (2010). The set of admissible designs are displayed by using a novel figure to help with decision making.

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

ssc install simon2stage, replace.

Options+------+ ----+ Main +-------------------------------------------------------------

p0(#)specifies the null proportion, the default is 0.1.

p1(#)specifies the alternative proportion, the default is 0.4.

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

beta(#)specifies the type II error, the default is 0.2.

minn(#)specifies the start total sample size in the initial grid search, the default is 1.

maxn(#)specifies the largest total sample size in the initial grid search, the default is 35.

optimalspecifies that the interest is in the optimal design rather than the minimax.

optp(#)specifies the true proportion to optimize the design for, the default is p0.

effspecifies that the design can stop for efficacy as well as futility.

deltaminimaxspecifies that the delta-minimax design is found.

admissspecifies that the set of admissible designs should be found.

Examplessimon2stage

The minimax design is

{1/8 3/13}, if there are no responders or one responder out of the first 8 participants then the study stops and the null hypothesis is not rejected. If the study proceeds to the second stage then the null hypothesis is rejected if there are more than 3 responders. Under the null hypothesis there is a 0.813 chance that the study stops at the first stage and hence the average sample size is 8*0.813+13*(1-0.813) = 8.934.simon2stage, optimal

The optimal design is

{1/7 3/15}, this is similar to the previous design but there is now a 0.85 chance that the study finishes at stage 1 and the average sample size under the null hypothesis is 8.198 which is slightly smaller than the minimax desgin.simon2stage, optimal optp(0.2)

The optimal design is still

{1/7 3/15}but the average sample size is much greater at 10.386 as a direct result of a smaller chance 0.577 of early termination.simon2stage, optimal optp(0.2) eff

The optimal design is

{(1 2)/7 3/15}the expected sample size, 9.202, is smaller than the previous design because of a greater chance of an early termination 0.725.simon2stage,optimal eff deltaminimax

The delta-minimax design is

{(1 2)/7 3/15}the expected sample size, 9.550, is larger than the previous designs because this is themaximumexpected sample size.

simon2stage, optp(0.2)

The minimax design optimised at a true response of

0.2is{1/8 3/13}. The expected sample size, 10.483, much greater than when calculating the expected sample size at the null value. This has not altered the minimax design.simon2stage,optimal eff admiss maxn(16)

The set of admissible designs is plotted. Setting the maximum to be

16means that the set of admissible designs are found by fixing the maximum sample size to be 16 or lower (this limits the designs to search through). Interestingly the design{(1 2)/7 3/15}is only good if there is little weight given to the overall sample size.

AuthorAdrian Mander, MRC Biostatistics Unit, Cambridge, UK. Email adrian.mander@mrc-bsu.cam.ac.uk

ReferencesR.P.A'Hern (2001) Sample size tables for exact single-stage phase II designs.

Statistics in Medicine20:859-866.T.R. Fleming (1982) One-sample multiple testing procedure for phase II clinical trials.

Biometrics38:143-151.Richard Simon (1989) Optimal two-stage designs for phase II clinical trials.

Controlled Clinical Trials10:1-10.A.P. Mander and S.G. Thompson (2010) Two-stage designs optimal under the alternative hypothesis for phase II cancer trials.

Contemporary ClinicalTrials31(6):572-578.A.P. Mander, J.M. Wason, M.J. Sweeting and S.G. Thompson (2010) Admissible two-stage designs for phase II cancer clinical trials.

(Submitted)

Also seeRelated commands

HELP FILES SSC installation links Description

samplesize (if installed) (ssc install samplesize) Sample Size graphics sampsi_fleming (if installed) (ssc install sampsi_fleming) Sample Size for Fleming design 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