# nsurvival: Sample size calculation in clinical trials with one primary... In coprimary: Sample Size Calculation for Two Primary Time-to-Event Endpoints in Clinical Trials

## Description

nsurvival() is used to determine the sample size for one time to event endpoint, such as Overall Survival (OS), Progression Free Survival or the health related quality of life (HRQoL). If it is HRQoL, several HRQoL dimension can be considered.

## Usage

 `1` ```nsurvival(design,Survhyp,alpha,duraccrual,durstudy,power,pe,look,fup,dropout,dqol) ```

## Arguments

 `design` Superiority=c(1,sided)[with sided=1 if 1-sided and 2 if 2-sided]; Non inferiority=c(2); Equivalence=c(3) `Survhyp` For Superiority=c(thyp,t,hype,Sc); for Non inferiority=c(thyp,t,hype,Sc,hypeA); for Equivalence=c(t,delta,Sc): parameters at time t if thyp=1 then hype is survival rate in experimental arm under the null hypothesis and hypeA is the survival rate in the experimental arm under the alternative hypothesis; if thyp=2 then hype is the hazard ratio under the null hypothesis and hypeA is the hazard ratio under the alternative hypothesis; Sc is survival rate in the control arm; delta is the log hazard ratio equivalence margin. When endpoint is HRQoL, the survival rate is replaced by the rate of patients without HRQoL deterioration. `alpha` Type I error, for Non inferiority, Equivalence and 1-sided superiority is a vector of length one. For 2-sided superiority is a vector to length two c(alpha.low, alpha.up). `duraccrual` Accrual duration, expressed in number of days, months or years `durstudy` Study duration, expressed in number of days, months or years `power` 1- Probability of a type II error. Default value=0.80. `pe` Proportion (ratio) of patients assigned to the experimental arm (with 0

## Details

The nsurvival function computes the sample size for one time to event endpoint, such as OS, PFS or HRQoL. HRQoL has become increasingly important in clinical trials over the past two decades.

## Value

Event: number of events estimated

Total: number of patients

Ne: number for experimental arm for each endpoint

Nc: number for control arm for each endpoint

HR: Hazard ratio for each endpoint

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40``` ```############################################################# ############### Design superiority:one-sided ############### ############################################################# ## 7-year survival rates Se=0.57 and Sc=0.53, alpha=0.05, accrual duration of 4 years, ## study duration of 8 years and default values i.e power=0.80, pe=0.5, look=1, fup=0, ## dropout=0, dqol=0 ns1 <- nsurvival(design=c(1,1),Survhyp=c(1,7,0.57,0.53),alpha=0.05,duraccrual=4,durstudy=8) ############################################################ ############### Design superiority:two-sided ############### ############################################################ ## 5-year rate without HRQoL deterioration Se=0.75 and Sc=0.65, alpha=c(0.04,0.01), accrual ## duration of 2 years, study duration of 6 years, power=0.90, pe=0.55, follow-up 5 years, ## 3 target variables for health related quality of life and default values i.e look=1, dropout=0 ns2 <- nsurvival(design=c(1,2),Survhyp=c(1,5,0.75,0.65),alpha=c(0.04,0.01),duraccrual=2, durstudy=6,power=0.90,pe=0.55,fup=c(1,5),dqol=3) ########################################################### ############### Design non-inferiority ################## ########################################################### ## 5-year survival rates are equal under the alternative hypothesis, i.e Se=0.60 and Sc=SeA=0.70, ## with alpha=0.05, accrual duration of 4 years, study duration of 8 years, two interim analysis ## after the occurence 1/3 and 2/3 of the events and default values i.e power=0.80, pe=0.5, fup=0, ## dropout=0, dqol=0 ns3 <- nsurvival(design=c(2),Survhyp=c(1,5,0.60,0.70, 0.70),alpha=0.05,duraccrual=4, durstudy=8,look=c(3,c(1,1),c(1/3,2/3))) ########################################################## ############### Design superiority ################## ########################################################## ## 3-year rate without HRQoL deterioration Sc=0.80 and log hazard equivalence margin delta=0.1 ## with alpha=0.10, accrual duration of 3 years, study duration of 5 years, drop out hazard rate ## of 0.05 per arm, 2 target variables for health related quality of life and default values i.e ## power=0.80, pe=0.5, look=1, fup=0 ns4 <- nsurvival(design=c(3),Survhyp=c(3,0.10,0.80),alpha=0.10,duraccrual=3,durstudy=5, dropout=c(1,0.05,0.05),dqol=2) ```

coprimary documentation built on May 1, 2019, 10:10 p.m.