CT_Normal: SSR for adaptive multi-arm design with normal outcomes

In cherryyan/MASSR: Sample Size Re-Estimation for Two-Stage Flexible Multi-Arm Trials with Treatment Selection

Description

Function to calculate conditional power and perform SSR for adaptive multi-arm designs with normal outcomes. The adaptive design is either based on inverse normal combination function or Fisher's combination function.

Usage

CT_Normal(combF, a, sel_rule, n1 = NULL, N2 = NULL, initialSS = 2, r21,
  rmax, alpha = 0.025, ushape = "obf", lfix = 0, theta, sigma, x0_1, x1,
  beta, ConditionalPower, ssr, delta = NULL, side = "upper")

Arguments

combF	Combination function, either "Inverse Normal" or "Fisher".
a	Number of experimental treatments (a = 2 or 3)
sel_rule	Treatment selection rule at interim analysis. There are four treatment selection rule, 1) sel_tr = 1, select the best treatment; 2) sel_tr = 2, keep all promising treatments that do not cross either efficacy boundaries or futility boundaries; 3) sel_tr = 3, select the best treatment only if the mean difference (treatment - control if side = "upper", control - treatment if side = "lower") is above a threshold delta; 4) sel_tr = 4, keep all promising treatments where the mean difference is above delta.
n1	First stage sample size per arm (default is NULL).
N2	Total sample size per arm at the end of the trial (default is NULL).
initialSS	Whether initial sample size needs to be calculated. If initial sample size does not need to be calculated, then n1 and N2 have to be provided and initialSS is set to 0. If initial sample size need to be calculated, then initialSS can take numeric value 1 (initial sample size will be calculated using the method for traditional fixed two-arm design) or 2 (initial sample size will be calculated using the method for group sequential two-arm design).
r21	Allocation ratio of N2 to n1 (r21 = N2/n1). If initialSS = NULL, then it should also be NULL. If initialSS = 1 or 2, then it should be a numeric value that is larger than 1.
rmax	The ratio of the maximum sample size allowed per arm (N2_max) to N2 (rmax = N2_max/N2). It should be a numeric value that is larger than 1.
alpha	One sided familywise error rate (default is 0.025).
ushape	The shape of the efficacy boundaries (default is "obf"). Either a function specifying the shape or one of "pocock", "obf" (the default), "triangular" and "fixed".
lfix	Fixed lower boundary on z-scale (default is 0). lfix must be smaller than Phi(1-alpha)/2 to ensure that it is smaller than the upper boundary.
theta	Planned absolute mean difference of experimental treatment to control. It is used for initial sample size caculation and SSR based on the planned treatment effect.
sigma	Known standard deviation of normal distribution.
x0_1	First stage sample mean of control arm. It has to be a one column matrix with the same number of rows as x1.
x1	First stage sample mean of experimental treatment arms. It has to be a matrix with each row represents one trial, and the number of colum should be equal to a.
beta	Type II error. 1-beta is used as the desired power and conditional power.
ConditionalPower	Methods for conditional power. If ConditionalPower = "planned", then conditional power will be calculated using the planned treatment effect (theta). If ConditionalPower = "observed", then conditional power will be calcuated using the maximum observed treatment effect at interim analysis.
ssr	Whether sample size re-estimation should be performed. If ssr = 0, sample size re-estimation will not be performed. If ssr = 1, sample size will be performed if conditional power is lower than 1-beta.
delta	The minimum treatment effect that is of interest. The default is NULL, but when sel_rule = 3 or 4, a numeric value has to be specified.
side	Side for conditional power (default is "upper"). Either "upper" or "lower".

Details

This function calculates conditional power and perform sample size re-estimation (SSR) based on the conditional power approach for two-stage adaptive multi-arm design with normal outcomes. It is assumed that sample size is equally allocated among arms and the observations from each arm follow a normal distribution with a common known variance. At interim analysis, a trial will be stopped if any treatments cross the efficacy boundaries, and any treatments cross the futility boundary will be dropped. Conditional power is calculated under the global alternative hypothesis where it is assumed all the treatment effects are equal to planned treatment effect (theta) or maximum observed treatment effect. If a trial stops at interim analysis, conditional power(CP), new second stage sample size per arm (n2new) and new conditional power(cp_new) will not be calculated and will all be returned as NA. If a trial can continue to the second stage and conditional power is larger than 1-beta, then n2new and cp_new will not be calculated and will be returned as NA. Multiple trials can be assessed at the same time.

Value

A list containing the following components:

EfficacyBound	The efficacy boundaries for both interim analysis and final analysis.
FutilityBound	The futility boundaries for both interim analysis and final analysis.
stop_efficacy	A matrix indicating which arms are stopped for efficacy. 1 indicates stopping for efficacy and 0 otherwise.
stop_futility	A matrix indicating which arms are stopped for futility. 1 indicates stopping for efficacy and 0 otherwise.
sel_tr	A matrix indicating which experimental treatments can continue to the second stage.
cp	Conditional power at interim analysis. If a trial stops at interim analysis, conditional power will not be calculated and returned as NA.
n1	First stage sample size per arm.
n2new	New second stage sample size per arm.
cp_new	Conditional power based on the new second stage sample size.

References

Bauer P, Kohne K: Evaluation of experiments with adaptive interim analyses. Biometrics 1994, 50(4):1029-1041.

Bretz F, Koenig F, Brannath W, Glimm E, Posch M: Adaptive designs for confirmatory clinical trials. Statistics in Medicine 2009, 28(8):1181-1217.

Examples

 # two-stage three experiments versus control design, initial sample size was given and all the promising treatments are selected at the interim analysis
CT_Normal(combF = "Inverse Normal", a = 3, sel_rule = 2, n1=72, N2=144, initialSS = 1, r21 = NULL, rmax= 1.5, alpha = 0.025, ushape = "obf" ,lfix=0, theta=2, sigma = 6, x0_1=matrix(2.2,nrow=2,ncol=1), x1=matrix(c(2,2.2,3.1,3.7,3.5,2.5),nrow=2,ncol=3), beta=0.2,ConditionalPower = "observed",ssr = 1,delta = NULL)

cherryyan/MASSR documentation built on May 13, 2019, 3:54 p.m.