| Title: | Flexible Parametric Accelerated Hazards Models |
|---|---|
| Description: | Flexible parametric Accelerated Hazards (AH) regression models in overall and relative survival frameworks with 13 distinct Baseline Distributions. The AH Model can also be applied to lifetime data with crossed survival curves. Any user-defined parametric distribution can be fitted, given at least an R function defining the cumulative hazard and hazard rate functions. See Chen and Wang (2000) <doi:10.1080/01621459.2000.10474236>, and Lee (2015) <doi:10.1007/s10985-015-9349-5> for more details. |
| Authors: | Authors@R. c(person("Abdisalam", "Hassan","Muse" email="[email protected]", role=c("aut", "ctb","cre")), person("Samuel", "Mwalili", role=c("ctb")), person("Oscar", "Ngesa", role=c("ctb")), person("Mutua", "Kilai", role = c("ctb")) ) |
| Maintainer: | Abdisalam Hassan Muse <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2024-11-12 03:40:46 UTC |
| Source: | https://github.com/cran/AHSurv |
The flexible parametric accelerated excess hazards (AEH) model's maximum likelihood estimation, log-likelihood, and information criterion. Baseline hazards:NGLL, GLL, KW,EW, MLL, PGW, GG, MKW, Log-logistic, Weibull, Log-normal, Burr-XII, and Gamma
AEHMLE( init, time, delta, n, basehaz, z, hp.obs, method = "Nelder-Mead", maxit = 1000, log = FALSE )AEHMLE( init, time, delta, n, basehaz, z, hp.obs, method = "Nelder-Mead", maxit = 1000, log = FALSE )
init |
: initial points for optimisation |
time |
: survival times |
delta |
: vital indicator (0-alive,1 - dead) |
n |
: The number of the observations of the data set |
basehaz |
: baseline hazard structure including baseline (NGLLAEH,GLLAEH,EWAEH,KWAEH,MLLAEH, PGWAEH,GGAEH,MKWAEH,LLAEH,WAEH,GAEH, LNAEH,BXIIAEEH) |
z |
: design matrix for covariates (p x n), p >= 1 |
hp.obs |
: population hazards (for uncensored individuals) |
method |
:"nlminb" or a method from "optim" |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
By default the function calculates the following values:
AIC: Akaike Information Criterion;
CAIC: Consistent Akaikes Information Criterion;
BIC: Bayesian Information Criterion;
BCAIC: Bozdogan’s Consistent Akaike Information Criterion;
HQIC: Hannan-Quinn information criterion;
par: maximum likelihood estimates;
Value: value of the likelihood function;
Convergence: 0 indicates successful completion and 1 indicates that the iteration limit maxit.
a list containing the output of the optimisation (OPT) and the information criterion including (AIC, BIC, CAIC, BCAIC, and HQIC).
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT AEHMLE(init = c(1.0,0.5,1.0,0.5),time = time,delta = delta,n=nrow(z), basehaz = "GLLAEH",z = z,hp.obs=0.6,method = "Nelder-Mead", maxit = 1000)data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT AEHMLE(init = c(1.0,0.5,1.0,0.5),time = time,delta = delta,n=nrow(z), basehaz = "GLLAEH",z = z,hp.obs=0.6,method = "Nelder-Mead", maxit = 1000)
The flexible parametric accelerated hazards (AH) model's maximum likelihood estimation, log-likelihood, and information criterion. Baseline hazards: NGLL, GLL,KW, EW, MLL, PGW, GG, MKW, Log-logistic, Weibull, Log-normal, Burr-XII, and Gamma
AHMLE( init, time, delta, n, basehaz, z, method = "Nelder-Mead", maxit = 1000, log = FALSE )AHMLE( init, time, delta, n, basehaz, z, method = "Nelder-Mead", maxit = 1000, log = FALSE )
init |
: initial points for optimisation |
time |
: survival times |
delta |
: vital indicator (0-alive,1 - dead,) |
n |
: The number of the observations of the data set |
basehaz |
: baseline hazard structure including baseline (NGLLAH,GLLAH,EWAH,KWAH,MLLAH,PGWAH,GGAH, MKWAH,LLAH,WAH,GAH,LNAH,BXIIAH) |
z |
: design matrix for covariates (p x n), p >= 1 |
method |
:"nlminb" or a method from "optim" |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
By default the function calculates the following values:
AIC: Akaike Information Criterion;
CAIC: Consistent Akaikes Information Criterion;
BIC: Bayesian Information Criterion;
BCAIC: Bozdogan’s Consistent Akaike Information Criterion;
HQIC: Hannan-Quinn information criterion;
par: maximum likelihood estimates;
Value: value of the likelihood function;
Convergence: 0 indicates successful completion and 1 indicates that the iteration limit maxit.
The function AHMLE returns MLE estimates and information criterion.
a list containing the output of the optimisation (OPT) and the information criterion including (AIC, BIC, CAIC, BCAIC, and HQIC).
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
#Example #1 data(ipass) time<-ipass$time delta<-ipass$status z<-ipass$arm AHMLE(init = c(1.0,1.0,1.0,0.5),time = time,delta = delta,n=nrow(z), basehaz = "GLLAH",z = z,method = "Nelder-Mead", maxit = 1000) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT AHMLE(init = c(1.0,1.0,1.0,0.5),time = time,delta = delta,n=nrow(z), basehaz = "GLLAH",z = z,method = "Nelder-Mead", maxit = 1000) #Example #3 data("e1684") time<-e1684$FAILTIME delta<-e1684$FAILCENS TRT<-e1684$TRT AGE<-e1684$TRT z<-as.matrix(cbind(scale(TRT), scale(AGE) )) AHMLE(init = c(1.0,1.0,1.0,0.5,0.75),time = time,delta = delta,n=nrow(z), basehaz = "GLLAH",z = z,method = "Nelder-Mead",maxit = 1000) #Example #4 data("LeukSurv") time<-LeukSurv$time delta<-LeukSurv$cens age<-LeukSurv$age wbc<-LeukSurv$wbc tpi<-LeukSurv$tpi z<-as.matrix(cbind(scale(age), scale(tpi),scale(wbc) )) AHMLE(init = c(1.0,1.0,1.0,1.0,0.5,0.65,0.85),time = time,delta = delta,n=nrow(z), basehaz = "NGLLAH",z = z,method = "Nelder-Mead",maxit = 1000)#Example #1 data(ipass) time<-ipass$time delta<-ipass$status z<-ipass$arm AHMLE(init = c(1.0,1.0,1.0,0.5),time = time,delta = delta,n=nrow(z), basehaz = "GLLAH",z = z,method = "Nelder-Mead", maxit = 1000) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT AHMLE(init = c(1.0,1.0,1.0,0.5),time = time,delta = delta,n=nrow(z), basehaz = "GLLAH",z = z,method = "Nelder-Mead", maxit = 1000) #Example #3 data("e1684") time<-e1684$FAILTIME delta<-e1684$FAILCENS TRT<-e1684$TRT AGE<-e1684$TRT z<-as.matrix(cbind(scale(TRT), scale(AGE) )) AHMLE(init = c(1.0,1.0,1.0,0.5,0.75),time = time,delta = delta,n=nrow(z), basehaz = "GLLAH",z = z,method = "Nelder-Mead",maxit = 1000) #Example #4 data("LeukSurv") time<-LeukSurv$time delta<-LeukSurv$cens age<-LeukSurv$age wbc<-LeukSurv$wbc tpi<-LeukSurv$tpi z<-as.matrix(cbind(scale(age), scale(tpi),scale(wbc) )) AHMLE(init = c(1.0,1.0,1.0,1.0,0.5,0.65,0.85),time = time,delta = delta,n=nrow(z), basehaz = "NGLLAH",z = z,method = "Nelder-Mead",maxit = 1000)
Bone marrow transplant study which is widely used in the hazard-based regression models
There were 46 patients in the allogeneic treatment and 44 patients in the autologous treatment group
Time: time to event
Status: censor indicator, 0 for censored and 1 for uncensored
TRT: 1 for autologous treatment group; 0 for allogeneic treatment group
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Robertson, V. M., Dickson, L. G., Romond, E. H., & Ash, R. C. (1987). Positive antiglobulin tests due to intravenous immunoglobulin in patients who received bone marrow transplant. Transfusion, 27(1), 28-31.
Burr-XII (BXII) Cumulative Hazard Function.
CHBXII(t, kappa, alpha)CHBXII(t, kappa, alpha)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
the value of the BXII cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) CHBXII(t=t, kappa=0.5, alpha=0.35)t=runif(10,min=0,max=1) CHBXII(t=t, kappa=0.5, alpha=0.35)
Exponentiated Weibull (EW) Cumulative Hazard Function.
CHEW(t, lambda, kappa, alpha)CHEW(t, lambda, kappa, alpha)
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
the value of the EW cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Rubio, F. J., Remontet, L., Jewell, N. P., & Belot, A. (2019). On a general structure for hazard-based regression models: an application to population-based cancer research. Statistical methods in medical research, 28(8), 2404-2417.
t=runif(10,min=0,max=1) CHEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75)t=runif(10,min=0,max=1) CHEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75)
Gamma (G) Cumulative Hazard Function.
CHG(t, shape, scale)CHG(t, shape, scale)
t |
: positive argument |
shape |
: shape parameter |
scale |
: scale parameter |
the value of the G cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) CHG(t=t, shape=0.85, scale=0.5)t=runif(10,min=0,max=1) CHG(t=t, shape=0.85, scale=0.5)
Generalised Gamma (GG) Cumulative Hazard Function.
CHGG(t, kappa, alpha, eta)CHGG(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the GG cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) CHGG(t=t, kappa=0.5, alpha=0.35, eta=0.9)t=runif(10,min=0,max=1) CHGG(t=t, kappa=0.5, alpha=0.35, eta=0.9)
Generalized Log-logistic (GLL) cumulative hazard function.
CHGLL(t, kappa, alpha, eta)CHGLL(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the GLL cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Muse, A. H., Mwalili, S., Ngesa, O., Almalki, S. J., & Abd-Elmougod, G. A. (2021). Bayesian and classical inference for the generalized log-logistic distribution with applications to survival data. Computational intelligence and neuroscience, 2021.
t=runif(10,min=0,max=1) CHGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)t=runif(10,min=0,max=1) CHGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)
Kumaraswamy Weibull (KW) Cumulative Hazard Function.
CHKW(t, alpha, kappa, eta, zeta)CHKW(t, alpha, kappa, eta, zeta)
t |
: positive argument |
alpha |
: scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
the value of the KW cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) CHKW(t=t, alpha=0.35, kappa=0.5, eta=1.20, zeta=1.5)t=runif(10,min=0,max=1) CHKW(t=t, alpha=0.35, kappa=0.5, eta=1.20, zeta=1.5)
Log-logistic (LL) Cumulative Hazard Function.
CHLL(t, kappa, alpha)CHLL(t, kappa, alpha)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
the value of the LL cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) CHLL(t=t, kappa=0.5, alpha=0.35)t=runif(10,min=0,max=1) CHLL(t=t, kappa=0.5, alpha=0.35)
Lognormal (LN) Cumulative Hazard Function.
CHLN(t, kappa, alpha)CHLN(t, kappa, alpha)
t |
: positive argument |
kappa |
: meanlog parameter |
alpha |
: sdlog parameter |
the value of the LN cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) CHLN(t=t, kappa=0.75, alpha=0.95)t=runif(10,min=0,max=1) CHLN(t=t, kappa=0.75, alpha=0.95)
Modified Kumaraswamy Weibull (MKW) Cumulative Hazard Function.
CHMKW(t, alpha, kappa, eta)CHMKW(t, alpha, kappa, eta)
t |
: positive argument |
alpha |
: Inverse scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
the value of the MKW cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) CHMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)t=runif(10,min=0,max=1) CHMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)
Modified Log-logistic (MLL) cumulative hazard function.
CHMLL(t, kappa, alpha, eta)CHMLL(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the MLL cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Kayid, M. (2022). Applications of Bladder Cancer Data Using a Modified Log-Logistic Model. Applied Bionics and Biomechanics, 2022.
t=runif(10,min=0,max=1) CHMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)t=runif(10,min=0,max=1) CHMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)
New Generalized Log-logistic (GLL) cumulative hazard function.
CHNGLL(t, kappa, alpha, eta, zeta)CHNGLL(t, kappa, alpha, eta, zeta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
the value of the NGLL cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Hassan Muse, A. A new generalized log-logistic distribution with increasing, decreasing, unimodal and bathtub-shaped hazard rates: properties and applications, in Proceedings of the Symmetry 2021 - The 3rd International Conference on Symmetry, 8–13 August 2021, MDPI: Basel, Switzerland, doi:10.3390/Symmetry2021-10765.
t=runif(10,min=0,max=1) CHNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)t=runif(10,min=0,max=1) CHNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)
Power Generalised Weibull (PGW) cumulative hazard function.
CHPGW(t, kappa, alpha, eta)CHPGW(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the PGW cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Alvares, D., & Rubio, F. J. (2021). A tractable Bayesian joint model for longitudinal and survival data. Statistics in Medicine, 40(19), 4213-4229.
t=runif(10,min=0,max=1) CHPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)t=runif(10,min=0,max=1) CHPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)
Weibull (W) Cumulative Hazard Function.
CHW(t, kappa, alpha)CHW(t, kappa, alpha)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
the value of the W cumulative hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) CHW(t=t, kappa=0.75, alpha=0.5)t=runif(10,min=0,max=1) CHW(t=t, kappa=0.75, alpha=0.5)
Exponentiated Weibull (EW) Probability Density Function.
dexpweibull(t, lambda, kappa, alpha, log = FALSE)dexpweibull(t, lambda, kappa, alpha, log = FALSE)
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the EW probability density function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) dexpweibull(t=t, lambda=0.6,kappa=0.5, alpha=0.45, log=FALSE)t=runif(10,min=0,max=1) dexpweibull(t=t, lambda=0.6,kappa=0.5, alpha=0.45, log=FALSE)
Generalised Gamma (GG) Probability Density Function.
dggamma(t, kappa, alpha, eta, log = FALSE)dggamma(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the GG probability density function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) dggamma(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)t=runif(10,min=0,max=1) dggamma(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)
Eastern Cooperative Oncology Group (ECOG) data used for modeling hazard-based regression models
A data frame with 284 observations on the following 5 variables.
TRT: 0=control group, 1=IFN treatment group
FAILTIME: observed relapse-free time
FAILCENS: relapse-free censor indicator
AGE:continuous variable, which is centered to the mean
SEX: 0 for male, 1 fopr female
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Kirkwood, J. M., Manola, J., Ibrahim, J., Sondak, V., Ernstoff, M. S., & Rao, U. (2004). A pooled analysis of eastern cooperative oncology group and intergroup trials of adjuvant high-dose interferon for melanoma. Clinical Cancer Research, 10(5), 1670-1677.
Burr-XII (BXII) Hazard Function.
hBXII(t, kappa, alpha, log = FALSE)hBXII(t, kappa, alpha, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the BXII hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) hBXII(t=t, kappa=0.85, alpha=0.45,log=FALSE)t=runif(10,min=0,max=1) hBXII(t=t, kappa=0.85, alpha=0.45,log=FALSE)
Exponentiated Weibull (EW) Hazard Function.
hEW(t, lambda, kappa, alpha, log = FALSE)hEW(t, lambda, kappa, alpha, log = FALSE)
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the EW hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Khan, S. A. (2018). Exponentiated Weibull regression for time-to-event data. Lifetime data analysis, 24(2), 328-354.
t=runif(10,min=0,max=1) hEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75, log=FALSE)t=runif(10,min=0,max=1) hEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75, log=FALSE)
Gamma (G) Hazard Function.
hG(t, shape, scale, log = FALSE)hG(t, shape, scale, log = FALSE)
t |
: positive argument |
shape |
: shape parameter |
scale |
: scale parameter |
log |
:log scale (TRUE or FALSE) |
the value of the G hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) hG(t=t, shape=0.5, scale=0.85,log=FALSE)t=runif(10,min=0,max=1) hG(t=t, shape=0.5, scale=0.85,log=FALSE)
Generalised Gamma (GG) Hazard Function.
hGG(t, kappa, alpha, eta, log = FALSE)hGG(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the GG hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Agarwal, S. K., & Kalla, S. L. (1996). A generalized gamma distribution and its application in reliabilty. Communications in Statistics-Theory and Methods, 25(1), 201-210.
t=runif(10,min=0,max=1) hGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)t=runif(10,min=0,max=1) hGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)
Generalized Log-logistic (GLL) hazard function.
hGLL(t, kappa, alpha, eta, log = FALSE)hGLL(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the GLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Muse, A. H., Mwalili, S., Ngesa, O., Alshanbari, H. M., Khosa, S. K., & Hussam, E. (2022). Bayesian and frequentist approach for the generalized log-logistic accelerated failure time model with applications to larynx-cancer patients. Alexandria Engineering Journal, 61(10), 7953-7978.
t=runif(10,min=0,max=1) hGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, log=FALSE)t=runif(10,min=0,max=1) hGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, log=FALSE)
Kumaraswamy Weibull (KW) Hazard Function.
hKW(t, alpha, kappa, eta, zeta, log = FALSE)hKW(t, alpha, kappa, eta, zeta, log = FALSE)
t |
: positive argument |
alpha |
: scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the KW hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Cordeiro, G. M., Ortega, E. M., & Nadarajah, S. (2010). The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347(8), 1399-1429.
t=runif(10,min=0,max=1) hKW(t=t, alpha=0.35, kappa=0.5, eta=1.20, zeta=1.5, log=FALSE)t=runif(10,min=0,max=1) hKW(t=t, alpha=0.35, kappa=0.5, eta=1.20, zeta=1.5, log=FALSE)
Log-logistic (LL) Hazard Function.
hLL(t, kappa, alpha, log = FALSE)hLL(t, kappa, alpha, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the LL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) hLL(t=t, kappa=0.5, alpha=0.35,log=FALSE)t=runif(10,min=0,max=1) hLL(t=t, kappa=0.5, alpha=0.35,log=FALSE)
Lognormal (LN) Hazard Function.
hLN(t, kappa, alpha, log = FALSE)hLN(t, kappa, alpha, log = FALSE)
t |
: positive argument |
kappa |
: meanlog parameter |
alpha |
: sdlog parameter |
log |
:log scale (TRUE or FALSE) |
the value of the LN hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) hLN(t=t, kappa=0.5, alpha=0.75,log=FALSE)t=runif(10,min=0,max=1) hLN(t=t, kappa=0.5, alpha=0.75,log=FALSE)
Modified Kumaraswamy Weibull (MKW) Hazard Function.
hMKW(t, alpha, kappa, eta, log = FALSE)hMKW(t, alpha, kappa, eta, log = FALSE)
t |
: positive argument |
alpha |
: inverse scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the MKW hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Khosa, S. K. (2019). Parametric Proportional Hazard Models with Applications in Survival analysis (Doctoral dissertation, University of Saskatchewan).
t=runif(10,min=0,max=1) hMKW(t=t, alpha=0.35, kappa=0.7, eta=1.4, log=FALSE)t=runif(10,min=0,max=1) hMKW(t=t, alpha=0.35, kappa=0.7, eta=1.4, log=FALSE)
Modified Log-logistic (MLL) hazard function.
hMLL(t, kappa, alpha, eta, log = FALSE)hMLL(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the MLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) hMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9,log=FALSE)t=runif(10,min=0,max=1) hMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9,log=FALSE)
New Generalized Log-logistic (GLL) hazard function.
hNGLL(t, kappa, alpha, eta, zeta, log = FALSE)hNGLL(t, kappa, alpha, eta, zeta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the NGLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) hNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4, log=FALSE)t=runif(10,min=0,max=1) hNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4, log=FALSE)
Power Generalised Weibull (PGW) hazard function.
hPGW(t, kappa, alpha, eta, log = FALSE)hPGW(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the PGW hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) hPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6,log=FALSE)t=runif(10,min=0,max=1) hPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6,log=FALSE)
Weibull (W) Hazard Function.
hW(t, kappa, alpha, log = FALSE)hW(t, kappa, alpha, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the w hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) hW(t=t, kappa=0.75, alpha=0.5,log=FALSE)t=runif(10,min=0,max=1) hW(t=t, kappa=0.75, alpha=0.5,log=FALSE)
Argyropoulos and Unruh (2015) published reconstructed IPASS clinical trial data. Despite being reconstructed, this data set retains all of the features shown in references, as well as full access to the observations from this clinical trial.The database spans the months of March 2006 to April 2008.The study's main goal is to compare gefitinib to carboplatin/paclitaxel doublet chemotherapy as first-line treatment in terms of progression-free survival (in months) in selected non-small-cell lung cancer (NSCLC) patients.
A data frame with 1217 rows and 3 variables:
time: progression free survival (in months)
status: failure indicator (1 - failure; 0 - otherwise)
arm: (1 - gefitinib; 0 - carboplatin/paclitaxel doublet chemotherapy)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Argyropoulos, C. and Unruh, M. L. (2015). Analysis of time to event outcomes in randomized controlled trials by generalized additive models. PLOS One 10, 1-33.
A dataset on the survival of acute myeloid leukemia in 1,043 pateietns, first analyzed by Henderson et al. (2002). It is of interest to investigate possible spatial variation in survival after accounting for known subject-specific prognostic factors, which include age, sex, white blood cell count (wbc) at diagnosis, and the Townsend score (tpi) for which higher values indicates less affluent areas. Both exact residential locations of all patients and their administrative districts (24 districts that make up the whole region) are available.
A data frame with 1043 rows and 9 variables:
time: survival time in days
cens: right censoring status 0=censored, 1=dead
xcoord: coordinates in x-axis of residence
ycoord: coordinates in y-axis of residence
age: age in years
sex:male=1 female=0
wbc:white blood cell count at diagnosis, truncated at 500
tpi: the Townsend score for which higher values indicates less affluent areas
district:administrative district of residence
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
Henderson, R., Shimakura, S., and Gorst, D. (2002), Modeling spatial variation in leukemia survival data, Journal of the American Statistical Association, 97(460), 965-972.
Exponentiated Weibull (EW) Cumulative Distribution Function.
pexpweibull(t, lambda, kappa, alpha, log.p = FALSE)pexpweibull(t, lambda, kappa, alpha, log.p = FALSE)
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
the value of the EW cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) pexpweibull(t=t, lambda=0.65,kappa=0.45, alpha=0.25, log.p=FALSE)t=runif(10,min=0,max=1) pexpweibull(t=t, lambda=0.65,kappa=0.45, alpha=0.25, log.p=FALSE)
Generalised Gamma (GG) Cumulative Distribution Function.
pggamma(t, kappa, alpha, eta, log.p = FALSE)pggamma(t, kappa, alpha, eta, log.p = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
the value of the GG cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) pggamma(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)t=runif(10,min=0,max=1) pggamma(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)
Generalised Gamma (GG) Survival Function.
sggamma(t, kappa, alpha, eta, log.p = FALSE)sggamma(t, kappa, alpha, eta, log.p = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
the value of the GG survival function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Mutua Kilai, [email protected]
t=runif(10,min=0,max=1) sggamma(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)t=runif(10,min=0,max=1) sggamma(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)