Package 'NPHMC' reference manual

Title:	Sample Size Calculation for the Proportional Hazards Mixture Cure Model
Description:	An R-package for calculating sample size of a survival trial with or without cure fractions.
Authors:	Chao Cai, Songfeng Wang, Wenbin Lu, Jiajia Zhang
Maintainer:	Chao Cai <[email protected]>
License:	GPL-2
Version:	2.3
Built:	2024-11-29 08:46:01 UTC
Source:	CRAN

An R-package for Estimating Sample Size of Proportional Hazards Mixture Cure Model

Description

Estimating sample size for survival trial with or without cure fractions

Details

Package:	NPHMC
Type:	Package
Version:	2.2
Date:	2013-09-23
License:	GPL-2
LazyLoad:	yes

Author(s)

Chao Cai, Songfeng Wang, Wenbin Lu, Jiajia Zhang

Maintainer: Chao Cai <[email protected]>

References

S. Wang, J. Zhang, and W. Lu. Sample size calculation for the proportional hazards cure model. Statistics in medicine, 31:3959-3971, 2012

C. Cai, et al., smcure: An R-Package for estimating semiparametric mixture cure models. Computer Methods and Programs in Biomedicine, 108(3):1255-60, 2012

Eastern Cooperative Oncology Group (ECOG) Data

Description

Example data of nonparametric estimation approach with treatment as only covariate

Usage

data(e1684szdata)data(e1684szdata)

Format

A data frame with 285 observations on the following 3 variables:

Time: observed relapse-free time
Status: censoring indicator (1 = event of interest happens, and 0 = censoring)
X: arm indicator (1 = treatment and 0 = control)

Examples

data(e1684szdata)
data(e1684szdata)

Function One

Description

The first integrate function

Usage

f1(t, survdist, k, lambda0)
f1(t, survdist, k, lambda0)

Arguments

`t`	time variable
`survdist`	survival distribution of uncured patients. It can be "`exp`" or "`weib`".
`k`	if `survdist` = "`weib`", the shape parameter `k` needs to be specified. By default `k` = 1, which refers to the exponential distribution.
`lambda0`	the scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm. The density function of Weibull distribution with shape parameter `k` and scale parameter $\lambda_{0}$ is given by $f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),$ for $t > 0$ , and the corresponding survival distribution is $S(t)=\exp(-(\lambda_0 t)^k).$

Function Two

Description

The second integrate function

Usage

f2(t, accrualtime, followuptime, accrualdist, survdist, k, lambda0)
f2(t, accrualtime, followuptime, accrualdist, survdist, k, lambda0)

Arguments

`t`	time variable
`accrualtime`	length of accrual period.
`followuptime`	length of follow-up time.
`accrualdist`	accrual pattern. It can be "`uniform`", "`increasing`" or "`decreasing`".
`survdist`	survival distribution of uncured patients. It can be "`exp`" or "`weib`".
`k`	if `survdist` = "`weib`", the shape parameter `k` needs to be specified. By default `k` = 1, which refers to the exponential distribution.
`lambda0`	the scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm. The density function of Weibull distribution with shape parameter `k` and scale parameter $\lambda_0$ is given by $f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),$ for $t > 0$ , and the corresponding survival distribution is $S(t)=\exp(-(\lambda_0 t)^k).$

Function Three

Description

The third integrate function

Usage

f3(t, beta0, gamma0, pi0, survdist, k, lambda0)
f3(t, beta0, gamma0, pi0, survdist, k, lambda0)

Arguments

`t`	time variable
`beta0`	log hazard ratio of uncured patients
`gamma0`	log odds ratio of cure rates between two arms
`pi0`	cure rate for the control arm, which is between 0 and 1.
`survdist`	survival distribution of uncured patients. It can be "`exp`" or "`weib`".
`k`	if `survdist` = "`weib`", the shape parameter `k` needs to be specified. By default `k` = 1, which refers to the exponential distribution.
`lambda0`	the scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm. The density function of Weibull distribution with shape parameter `k` and scale parameter $\lambda_0$ is given by $f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),$ for $t > 0$ , and the corresponding survival distribution is $S(t)=\exp(-(\lambda_0 t)^k).$

Function Four

Description

The fourth integrate function

Usage

f4(t, accrualtime, followuptime, accrualdist, beta0, gamma0, pi0, survdist,
 k, lambda0)
f4(t, accrualtime, followuptime, accrualdist, beta0, gamma0, pi0, survdist,
 k, lambda0)

Arguments

`t`	time variable
`accrualtime`	length of accrual period.
`followuptime`	length of follow-up time.
`accrualdist`	accrual pattern. It can be "`uniform`", "`increasing`" or "`decreasing`".
`beta0`	log hazard ratio of uncured patients
`gamma0`	log odds ratio of cure rates between the two arms
`pi0`	cure rate for the control arm, which is between 0 and 1.
`survdist`	survival distribution of uncured patients. It can be "`exp`" or "`weib`".
`k`	if `survdist` = "`weib`", the shape parameter `k` needs to be specified. By default `k` = 1, which refers to the exponential distribution.
`lambda0`	the scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm. The density function of Weibull distribution with shape parameter `k` and scale parameter $\lambda_0$ is given by $f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),$ for $t > 0$ , and the corresponding survival distribution is $S(t)=\exp(-(\lambda_0 t)^k).$

Cumulative hazard function

Description

Cumulative Hazard Function for Exponential and Weibull Distributions

Usage

H0(t, survdist, k, lambda0)
H0(t, survdist, k, lambda0)

Arguments

`t`	time variable
`survdist`	survival distribution of uncured patients. It can be "`exp`" or "`weib`".
`k`	if `survdist` = "`weib`", the shape parameter `k` needs to be specified. By default `k` = 1, which refers to the exponential distribution.
`lambda0`	the scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm. The density function of Weibull distribution with shape parameter `k` and scale parameter $\lambda_0$ is given by $f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),$ for $t > 0$ , and the corresponding survival distribution is $S(t)=\exp(-(\lambda_0 t)^k).$

M Function

Description

M integrate function

Usage

m(t, beta0, gamma0, pi0, survdist, k, lambda0)
m(t, beta0, gamma0, pi0, survdist, k, lambda0)

Arguments

`t`	time variable
`beta0`	log hazard ratio of uncured patients
`gamma0`	log odds ratio of cure rates between two arms
`pi0`	cure rate for the control arm, which is between 0 and 1.
`survdist`	survival distribution of uncured patients. It can be "`exp`" or "`weib`".
`k`	if `survdist` = "`weib`", the shape parameter `k` needs to be specified. By default `k` = 1, which refers to the exponential distribution.
`lambda0`	the scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm. The density function of Weibull distribution with shape parameter `k` and scale parameter $\lambda_0$ is given by $f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),$ for $t > 0$ , and the corresponding survival distribution is $S(t)=\exp(-(\lambda_0 t)^k).$

Title

Description

Title

Usage

NPHMC(
  n = NULL,
  power = 0.8,
  alpha = 0.05,
  accrualtime = NULL,
  followuptime = NULL,
  p = 0.5,
  accrualdist = c("uniform", "increasing", "decreasing"),
  hazardratio = NULL,
  oddsratio = NULL,
  pi0 = NULL,
  survdist = c("exp", "weib"),
  k = 1,
  lambda0 = NULL,
  data = NULL
)
NPHMC(
  n = NULL,
  power = 0.8,
  alpha = 0.05,
  accrualtime = NULL,
  followuptime = NULL,
  p = 0.5,
  accrualdist = c("uniform", "increasing", "decreasing"),
  hazardratio = NULL,
  oddsratio = NULL,
  pi0 = NULL,
  survdist = c("exp", "weib"),
  k = 1,
  lambda0 = NULL,
  data = NULL
)

Arguments

`n`	sample size needed for power calculation
`power`	powered needed for sample size calculation
`alpha`	level of significance of statistical test (default is 0.05)
`accrualtime`	level of accrual period
`followuptime`	length of follow up time
`p`	proportion of subjects in treatment arm (default is 0.5)
`accrualdist`	accrual pattern (uniform, decreasing, increasing)
`hazardratio`	hazard ratio of uncured patients between two arms (must be greater than 0)
`oddsratio`	odds ratio of cured patients between two arms. It must be greater than 0. If it is 0, the model is reduced to standard proportional hazards model.
`pi0`	cure rate for the control arm (between 0 and 1)
`survdist`	distribution of uncured patients (`exp` or `weib`)
`k`	shape parameter if survdist = 'weib' (By default, it is 1 referrring to exponential distribution)
`lambda0`	scale parameter of exponential or Weibull distribution for survival times of uncured patients in the control arm.
`data`	observed or historical data if available

Value

a NPHMC object

Examples

NPHMC(power=0.90,alpha=0.05,accrualtime=3,followuptime=4,p=0.5,accrualdist="uniform",
hazardratio=2/2.5,oddsratio=2.25,pi0=0.1,survdist="exp",k=1,lambda0=0.5)
data(e1684szdata)
NPHMC(power=0.80,alpha=0.05,accrualtime=4,followuptime=3,p=0.5,accrualdist="uniform",
     data=e1684szdata)
n=seq(100, 500, by=50)
NPHMC(n=n, alpha=0.05,accrualtime=3,followuptime=4,p=0.5,
     accrualdist="uniform", hazardratio=2/2.5,oddsratio=2.25,pi0=0.1,survdist="exp",
     k=1,lambda0=0.5)
n=seq(100, 500, by=50)
NPHMC(n=n,alpha=0.05,accrualtime=4,followuptime=3,p=0.5,
     accrualdist="uniform",data=e1684szdata)
NPHMC(power=0.90,alpha=0.05,accrualtime=3,followuptime=4,p=0.5,accrualdist="uniform",
hazardratio=2/2.5,oddsratio=2.25,pi0=0.1,survdist="exp",k=1,lambda0=0.5)
data(e1684szdata)
NPHMC(power=0.80,alpha=0.05,accrualtime=4,followuptime=3,p=0.5,accrualdist="uniform",
     data=e1684szdata)
n=seq(100, 500, by=50)
NPHMC(n=n, alpha=0.05,accrualtime=3,followuptime=4,p=0.5,
     accrualdist="uniform", hazardratio=2/2.5,oddsratio=2.25,pi0=0.1,survdist="exp",
     k=1,lambda0=0.5)
n=seq(100, 500, by=50)
NPHMC(n=n,alpha=0.05,accrualtime=4,followuptime=3,p=0.5,
     accrualdist="uniform",data=e1684szdata)

S0 Function

Description

Baseline survival function for mixture cure model

Usage

S0(t, pi0, survdist, k, lambda0)
S0(t, pi0, survdist, k, lambda0)

Arguments

`t`	time variable
`pi0`	cure rate for the control arm, which is between 0 and 1.
`survdist`	survival distribution of uncured patients. It can be "`exp`" or "`weib`".
`k`	if `survdist` = "`weib`", the shape parameter `k` needs to be specified. By default `k` = 1, which refers to the exponential distribution.
`lambda0`	scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm. The density function of Weibull distribution with shape parameter `k` and scale parameter $\lambda_0$ is given by $f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),$ for $t > 0$ , and the corresponding survival distribution is $S(t)=\exp(-(\lambda_0 t)^k).$

Sc Function

Description

Survival distribution of censoring times

Usage

Sc(t, accrualtime, followuptime, accrualdist)
Sc(t, accrualtime, followuptime, accrualdist)

Arguments

`t`	time variable
`accrualtime`	length of accrual period.
`followuptime`	length of follow-up time.
`accrualdist`	accrual pattern. It can be "`uniform`", "`increasing`" or "`decreasing`".

Package 'NPHMC'

Help Index

An R-package for Estimating Sample Size of Proportional Hazards Mixture Cure Model

Description

Details

Author(s)

References

See Also

Eastern Cooperative Oncology Group (ECOG) Data

Description

Usage

Format

Examples

Function One

Description

Usage

Arguments

Function Two

Description

Usage

Arguments

Function Three

Description

Usage

Arguments

Function Four

Description

Usage

Arguments

Cumulative hazard function

Description

Usage

Arguments

M Function

Description

Usage

Arguments

Title

Description

Usage

Arguments

Value

Examples

S0 Function

Description

Usage

Arguments

Sc Function

Description

Usage

Arguments