ynegbinompowersim: Two-sample sample size calculation for negative binomial...

In NBDesign: Design and Monitoring of Clinical Trials with Negative Binomial Endpoint

Description

This will calculate the power for the negative binomial distribution for the 2-sample case under different follow-up scenarios: 1: fixed follow-up, 2: fixed follow-up with drop-out, 3: variable follow-up with a minimum fu and a maximum fu, 4: variable follow-up with a minimum fu and a maximum fu and drop-out.

Usage

ynegbinompowersim(nsize=200,r0=1.0,r1=0.5,shape0=1,shape1=shape0,pi1=0.5,
   alpha=0.05,twosided=1,fixedfu=1,type=1,u=c(0.5,0.5,1),ut=c(0.5,1.0,1.5),
   tfix=ut[length(ut)]+0.5,maxfu=10.0,tchange=c(0,0.5,1),
   ratec1=c(0.15,0.15,0.15),ratec0=ratec1,rn=10000)

Arguments

nsize	total number of subjects in two groups
r0	event rate for the control
r1	event rate for the treatment
shape0	dispersion parameter for the control
shape1	dispersion parameter for the treatment
pi1	allocation prob for the treatment
alpha	type-1 error
twosided	1: two-side, others: one-sided
fixedfu	fixed follow-up time for each patient
type	follow-up time type, type=1: fixed fu with fu time fixedfu; type=2: same as 1 but subject to censoring; type=3: depending on entry time, minimum fu is fixedfu and maximum fu is maxfu; type=4: same as 3 but subject to censoring
u	recruitment rate
ut	recruitment interval, must have the same length as u
tfix	fixed study duration, often equals to recruitment time plus minimum follow-up
maxfu	maximum follow-up time, should not be greater than tfix
tchange	a strictly increasing sequence of time points starting from zero at which the drop-out rate changes. The first element of tchange must be zero. The above rates and tchange must have the same length.
ratec1	piecewise constant drop-out rate for the treatment
ratec0	piecewise constant drop-out rate for the control
rn	Number of repetitions

Details

Let τ_{min} and τ_{max} correspond to the minimum follow-up time fixedfu and the maximum follow-up time maxfu. Let T_f, C, E and R be the follow-up time, the drop-out time, the study entry time and the total recruitment period(R is the last element of ut). For type 1 follow-up, T_f=τ_{min}. For type 2 follow-up T_f=min(C,τ_{min}). For type 3 follow-up, T_f=min(R+τ_{min}-E,τ_{max}). For type 4 follow-up, T_f=min(R+τ_{min}-E,τ_{max},C). Let f be the density of T_f. Suppose that Y_i is the number of event obsevred in follow-up time t_i for patient i with treatment assignment Z_i, i=1,…,n. Suppose that Y_i follows a negative binomial distribution such that

P(Y_i=y\mid Z_i=j)=\frac{Γ(y+1/k_j)}{Γ(y+1)Γ(1/k_j)}\Bigg(\frac{k_ju_i}{1+k_ju_i}\Bigg)^y\Bigg(\frac{1}{1+k_ju_i}\Bigg)^{1/k_j},

where k_j, j=0,1 are the dispersion parameters for control j=0 and treatment j=1 and

\log(u_i)=\log(t_i)+β_0+β_1 Z_i.

The data will be gnerated according to the above model. Note that the piecewise exponential distribution and the piecewise uniform distribution are genrated using R package PWEALL functions "rpwe" and "rpwu", respectively.

The parameters in the model are estimated by MLE using the R package MASS function "glm.nb".

Value

power

simulation power (in percentage)

Author(s)

Xiaodong Luo

Examples

##calculating the sample sizes
abc=ynegbinompowersim(nsize=200,r0=1.0,r1=0.5,shape0=1,
        pi1=0.5,alpha=0.05,twosided=1,fixedfu=1,
        type=4,u=c(0.5,0.5,1),ut=c(0.5,1.0,1.5),
        tchange=c(0,0.5,1),
        ratec1=c(0.15,0.15,0.15),rn=10)
###Power
abc$power

NBDesign documentation built on Sept. 13, 2020, 5:14 p.m.