# 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

 1 2 3 4 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)

Xiaodong Luo

## Examples

 1 2 3 4 5 6 7 8 ##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 May 2, 2019, 2:09 a.m.