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AmoudSurv: R Package For Tractable Parametric Odds-Based Regression Models
AmoudSurv: R Package For Tractable Parametric Odds-Based Regression Models
Abdisalam Hassan Muse2022, CRAN
Fits tractable fully parametric odds-based regression models for survival data, including proportional odds (PO), accelerated failure time (AFT), accelerated odds (AO), and General Odds (GO) models in overall survival frameworks. Given at least an R function specifying the survivor, hazard rate and cumulative distribution functions, any user-defined parametric distribution can be fitted. We applied and evaluated a minimum of seventeen (17) various baseline distributions that can handle different failure rate shapes for each of the four different proposed odds-based regression models. For more information see Bennet et al., (1983) <doi:10.1002/sim.4780020223>, and Muse et al., (2022) <doi:10.1016/j.aej.2022.01.033>.
Related Papers
2022 •
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.
Accelerated life testing (ALT) is used to obtain failure data of products in a short time period in order to extrapolate the reliability and lifetime of the products under normal conditions. Estimation of the reliability and lifetime is based on models, which can be classified as parametric and non-parametric models. Non-parametric models are commonly used because of the distribution-free property. Proportional hazard model (PHM) and proportional odds model (POM) are two widely used non-parametric models for reliability prediction based on ALT data. These two models perform well if the underlying distributions are Weibull and log-logistic respectively. However, in some situations the failure time data may be obtained from a mixed population and using PHM or POM will result in inaccurate estimates of the reliability at normal operating conditions. In this paper, we develop a proportional hazard-proportional odds (PH-PO) model in order to obtain more accurate estimation for both mixed...
Axioms
Amoud Class for Hazard-Based and Odds-Based Regression Models: Application to Oncology Studies2022 •
The purpose of this study is to propose a novel, general, tractable, fully parametric class for hazard-based and odds-based models of survival regression for the analysis of censored lifetime data, named as the “Amoud class (AM)” of models. This generality was attained using a structure resembling the general class of hazard-based regression models, with the addition that the baseline odds function is multiplied by a link function. The class is broad enough to cover a number of widely used models, including the proportional hazard model, the general hazard model, the proportional odds model, the general odds model, the accelerated hazards model, the accelerated odds model, and the accelerated failure time model, as well as combinations of these. The proposed class incorporates the analysis of crossing survival curves. Based on a versatile parametric distribution (generalized log-logistic) for the baseline hazard, we introduced a technique for applying these various hazard-based and odds-based regression models. This distribution allows us to cover the most common hazard rate shapes in practice (decreasing, constant, increasing, unimodal, and reversible unimodal), and various common survival distributions (Weibull, Burr-XII, log-logistic, exponential) are its special cases. The proposed model has good inferential features, and it performs well when different information criteria and likelihood ratio tests are used to select hazard-based and odds-based regression models. The proposed model’s utility is demonstrated by an application to a right-censored lifetime dataset with crossing survival curves.
Mathematics
Parametric Distributions for Survival and Reliability Analyses, a Review and Historical SketchDuring its 330 years of history, parametric distributions have been useful for survival and reliability analyses. In this paper, we comprehensively review the historical backgrounds and statistical properties of a number of parametric distributions used in survival and reliability analyses. We provide encyclopedic coverage of the important parametric distributions, which is more extensive than the existing textbooks on survival and reliability analyses. We also explain how these distributions have been adopted in survival and reliability analyses with original and state-of-the-art references. We cover the exponential, Weibull, Rayleigh, lognormal, log-logistic, gamma, generalized gamma, Pareto (types I, II, and IV), Hjorth, Burr (types III and XII), Dagum, exponential power, Gompertz, Birnbaum-Saunders, exponential-logarithmic, piecewise exponential, generalized exponential, exponentiated Weibull, generalized modified Weibull, and spline distributions. We analyze a real dataset for ...
Journal of Statistical Planning and Inference
Applied survival analysis: regression modeling of time to event data2000 •
Statistics in Medicine
A general framework for parametric survival analysis2014 •
Parametric survival models are being increasingly used as an alternative to the Cox model in biomedical research. Through direct modelling of the baseline hazard function, we can gain greater understanding of the risk profile of patients over time, obtaining absolute measures of risk. Commonly used parametric survival models, such as the Weibull, make restrictive assumptions of the baseline hazard function, such as monotonicity, which is often violated in clinical datasets. In this article, we extend the general framework of parametric survival models proposed by Crowther and Lambert (Journal of Statistical Software 53:12, 2013), to incorporate relative survival, and robust and cluster robust standard errors. We describe the general framework through three applications to clinical datasets, in particular, illustrating the use of restricted cubic splines, modelled on the log hazard scale, to provide a highly flexible survival modelling framework. Through the use of restricted cubic splines, we can derive the cumulative hazard function analytically beyond the boundary knots, resulting in a combined analytic/numerical approach, which substantially improves the estimation process compared with only using numerical integration. User-friendly Stata software is provided, which significantly extends parametric survival models available in standard software. Copyright © 2014 John Wiley & Sons, Ltd.
2010 •
Time to event data arise in several fields including biostatistics, demography, economics, engineering and sociology. The terms duration analysis, event-history analysis, failure-time analysis, reliability analysis, and transition analysis refer essentially to the same group of techniques although the emphases in certain modeling aspects could differ across disciplines. SAS® procedures LIFETEST, LIFEREG, PHREG, RELIABILITY, and QLIM have different capabilities for analyzing duration data. Methods include Kaplan-Meier estimation, accelerated life-testing models, and the ubiquitous Cox model. Recent developments in SAS extend their reach to include analyses of multiple failure times, recurrent events, frailty models, Markov models and use of Bayesian methods. We present an overview of these methods with examples illustrating their application in the appropriate context.
2022 •
In this study, we consider a general, flexible, parametric hazard-based regression model for censored lifetime data with covariates and term it the “general hazard (GH)” regression model. Some well-known models, such as the accelerated failure time (AFT), and the proportional hazard (PH) models, as well as the accelerated hazard (AH) model accounting for crossed survival curves, are sub-classes of this general hazard model. In the proposed class of hazard-based regression models, a covariate’s effect is identified as having two distinct components, namely a relative hazard ratio and a time-scale change on hazard progression. The new approach is more adaptive to modelling lifetime data and could give more accurate survival forecasts. The nested structure that includes the AFT, AH, and PH models in the general hazard model may offer a numerical tool for identifying which of them is most appropriate for a certain dataset. In this study, we propose a method for applying these various parametric hazard-based regression models that is based on a tractable parametric distribution for the baseline hazard, known as the generalized log-logistic (GLL) distribution. This distribution is closed under all the PH, AH, and AFT frameworks and can incorporate all of the basic hazard rate shapes of interest in practice, such as decreasing, constant, increasing, V-shaped, unimodal, and J-shaped hazard rates. The Bayesian and frequentist approaches were used to estimate the model parameters. Comprehensive simulation studies were used to evaluate the performance of the proposed model’s estimators and its nested structure. A right-censored cancer dataset is used to illustrate the application of the proposed approach. The proposed model performs well on both real and simulation datasets, demonstrating the importance of developing a flexible parametric general class of hazard-based regression models with both time-independent and time-dependent covariates for evaluating the hazard function and hazard ratio over time.
Mathematical and Computational Applications
Flexible Parametric Accelerated Hazard Model: Simulation and Application to Censored Lifetime Data with Crossing Survival Curves2022 •
This study aims to propose a flexible, fully parametric hazard-based regression model for censored time-to-event data with crossing survival curves. We call it the accelerated hazard (AH) model. The AH model can be written with or without a baseline distribution for lifetimes. The former assumption results in parametric regression models, whereas the latter results in semi-parametric regression models, which are by far the most commonly used in time-to-event analysis. However, under certain conditions, a parametric hazard-based regression model may produce more efficient estimates than a semi-parametric model. The parametric AH model, on the other hand, is inappropriate when the baseline distribution is exponential because it is constant over time; similarly, when the baseline distribution is the Weibull distribution, the AH model coincides with the accelerated failure time (AFT) and proportional hazard (PH) models. The use of a versatile parametric baseline distribution (generalized log-logistic distribution) for modeling the baseline hazard rate function is investigated. For the parameters of the proposed AH model, the classical (via maximum likelihood estimation) and Bayesian approaches using noninformative priors are discussed. A comprehensive simulation study was conducted to assess the performance of the proposed model’s estimators. A real-life right-censored gastric cancer dataset with crossover survival curves is used to demonstrate the tractability and utility of the proposed fully parametric AH model. The study concluded that the parametric AH model is effective and could be useful for assessing a variety of survival data types with crossover survival curves.
Package ‘AmoudSurv’
September 8, 2022
Type Package
Title Tractable Parametric Odds-Based Regression Models
Version 0.1.0
Maintainer Abdisalam Hassan Muse <abdisalam.h.muse@gmail.com>
Description Fits tractable fully parametric odds-based regression models for survival data, including proportional odds (PO), accelerated failure time (AFT), accelerated odds (AO), and General Odds (GO) models in overall survival frameworks. Given at least an R function specifying the survivor, hazard rate and cumulative distribution functions, any user-defined parametric distribution can be fitted. We applied and evaluated a minimum of seventeen (17) various baseline distributions that can handle different failure rate shapes for each of the four different proposed odds-based regression models. For more information see Bennet et al., (1983) <doi:10.1002/sim.4780020223>, and Muse et al., (2022) <doi:10.1016/j.aej.2022.01.033>.
License GPL-3
Encoding UTF-8
LazyData true
Imports AHSurv, flexsurv, pracma, stats, stats4
Depends R (>= 2.10)
RoxygenNote 7.2.1
NeedsCompilation no
Author Abdisalam Hassan Muse [aut, cre]
(<https://orcid.org/0000-0003-4905-0044>),
Samuel Mwalili [aut, ctb],
Oscar Ngesa [aut, ctb],
Christophe Chesneau [aut, ctb]
Repository CRAN
Date/Publication 2022-09-08 09:12:56 UTC
R topics documented:
alloauto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
bmt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
3
4
R topics documented:
2
gastric . .
larynx . .
MLEAFT
MLEAO .
MLEGO .
MLEPO .
pASLL .
pATLL . .
pCLL . .
pdGG . .
pEW . . .
pG . . . .
pGG . . .
pGLL . .
pLL . . .
pLN . . .
pMKW .
pMLL . .
pNGLL .
pPGW . .
pSCLL . .
pSLL . .
pTLL . .
pW . . . .
rASLL . .
rATLL . .
rCLL . .
rEW . . .
rG . . . .
rGG . . .
rGLL . .
rLL . . .
rLN . . .
rMKW . .
rMLL . .
rNGLL .
rPGW . .
rSCLL . .
rSLL . . .
rTLL . . .
rW . . . .
sASLL . .
sATLL . .
sCLL . .
sEW . . .
sG . . . .
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3
alloauto
sLL . .
sLN . .
sMKW .
sMLL .
SNGLL
sPGW .
sSCLL .
sSLL . .
sTLL .
sW . . .
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48
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56
alloauto
Leukemia data set
Description
The alloauto data frame has 101 rows and 3 columns.
Format
This data frame contains the following columns:
• time: Time to death or relapse, months
• type :Type of transplant (1=allogeneic, 2=autologous)
• delta:Leukemia-free survival indicator (0=alive without relapse, 1=dead or relapse)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa,Christophe Chesneau, <abdisalam.hassan@amoud.edu.so>
Source
Klein and Moeschberger (1997) Survival Analysis Techniques for Censored and truncated data,
Springer. Kardaun Stat. Nederlandica 37 (1983), 103-126.
Examples
{
data(alloauto)
str(alloauto)
}
4
gastric
Bone Marrow Transplant (bmt) data set
bmt
Description
Bone marrow transplant study which is widely used in the hazard-based regression models
Format
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
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, <abdisalam.hassan@amoud.edu.so>
References
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.
gastric
Gastric data set
Description
The gastric data frame has 90 rows and variables.It is a data set from a clinical trial conducted by the
Gastrointestinal Tumor Study Group (GTSG) in 1982. The data set refers to the survival times of
patients with locally nonresectable gastric cancer. Patients were either treated with chemotherapy
combined with radiation or chemotherapy alone.
Format
This data frame contains the following columns:
• time: survival times in days
• trt :treatments (1=chemotherapy + radiation; 0=chemotherapy alone)
• status:failure indicator (1=failure, 0=otherwise)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa,Christophe Chesneau, <abdisalam.hassan@amoud.edu.so>
5
larynx
Source
Gastrointestinal Tumor Study Group. (1982) A Comparison of Combination Chemotherapy and
Combined Modality Therapy for Locally Advanced Gastric Carcinoma. Cancer 49:1771-7.
Examples
{
data(gastric)
str(gastric);head(gastric)
}
larynx
Larynx Cancer-Patients data set
Description
Larynx Cancer-Patients data set which is widely used in the survival regression models
Format
The data frame contains 90 rows and 5 columns:
• time: time to event, in months
• delta: Censor indicator, 0 alive and 1 for dead
• stage: Stage of disease (1=stage 1, 2=stage2, 3=stage 3, 4=stage 4)
• diagyr: Year of diagnosis of larynx cancer
• age: Age at diagnosis of larynx cancer
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, <abdisalam.hassan@amoud.edu.so>
References
Klein and Moeschberger (1997) Survival Analysis Techniques for Censored and truncated data,
Springer. Kardaun Stat. Nederlandica 37 (1983), 103-126.
6
MLEAFT
Accelerated Failure Time (AFT) Model.
MLEAFT
Description
Tractable Parametric accelerated failure time (AFT) model’s maximum likelihood estimation, loglikelihood, and information criterion. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW,
LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
Usage
MLEAFT(
init,
times,
status,
n,
basehaz,
z,
method = "BFGS",
hessian = TRUE,
conf.int = 0.95,
maxit = 1000,
log = FALSE
)
Arguments
init
: initial points for optimisation
times
: survival times
status
: vital status (1 - dead, 0 - alive)
n
: The number of the data set
basehaz
: baseline hazard structure including baseline (New generalized log-logistic accelerated failure time "NGLLAFT" model, generalized log-logisitic accelerated
failure time "GLLAFT" model, modified log-logistic accelerated failure time
"MLLAFT" model, exponentiated Weibull accelerated failure time "EWAFT"
model, power generalized weibull accelerated failure time "PGWAFT" model,
generalized gamma accelerated failure time "GGAFT" model, modified kumaraswamy
Weibull proportional odds "MKWAFT" model, log-logistic accelerated failure
time "LLAFT" model, tangent-log-logistic accelerated failure time "TLLAFT"
model, sine-log-logistic accelerated failure time "SLLAFT" model, cosine loglogistic accelerated failure time "CLLAFT" model, secant-log-logistic accelerated failure time "SCLLAFT" model, arcsine-log-logistic accelerated failure
time "ASLLAFT" model, arctangent-log-logistic accelerated failure time "ATLLAFT" model, Weibull accelerated failure time "WAFT" model, gamma accelerated failure time "GAFT", and log-normal accelerated failure time "LNAFT")
7
MLEAFT
z
: design matrix for covariates (p x n), p >= 1
method
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent".
hessian
:A function to return (as a matrix) the hessian for those methods that can use this
information.
conf.int
: confidence level
maxit
:The maximum number of iterations. Defaults to 1000
log
:log scale (TRUE or FALSE)
Value
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
#Example #1
data(alloauto)
time<-alloauto$time
delta<-alloauto$delta
z<-alloauto$type
MLEAFT(init = c(1.0,0.20,0.05),times = time,status = delta,n=nrow(z),
basehaz = "WAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #2
data(bmt)
time<-bmt$Time
delta<-bmt$Status
z<-bmt$TRT
MLEAFT(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z),
basehaz = "LNAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #3
data("gastric")
time<-gastric$time
delta<-gastric$status
z<-gastric$trt
MLEAFT(init = c(1.0,0.50,0.5),times = time,status = delta,n=nrow(z),
basehaz = "LLAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #4
data("larynx")
time<-larynx$time
delta<-larynx$delta
8
MLEAO
larynx$age<-as.numeric(scale(larynx$age))
larynx$diagyr<-as.numeric(scale(larynx$diagyr))
larynx$stage<-as.factor(larynx$stage)
z<-model.matrix(~ stage+age+diagyr, data = larynx)
MLEAFT(init = c(1.0,0.5,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "LNAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
Accelerated Odds (AO) Model.
MLEAO
Description
A Tractable Parametric Accelerated Odds (AO) model’s maximum likelihood estimates,log-likelihood,
and Information Criterion values. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL,
TLL, SLL,CLL,SCLL,ATLL, and ASLL
Usage
MLEAO(
init,
times,
status,
n,
basehaz,
z,
method = "BFGS",
hessian = TRUE,
conf.int = 0.95,
maxit = 1000,
log = FALSE
)
Arguments
init
: Initial parameters to maximize the likelihood function;
times
: survival times
status
: vital status (1 - dead, 0 - alive)
n
: The number of the data set
basehaz
: baseline hazard structure including baseline (New generalized log-logistic accelerated odds "NGLLAO" model, generalized log-logisitic accelerated odds
"GLLAO" model, modified log-logistic accelerated odds "MLLAO" model,exponentiated
Weibull accelerated odds "EWAO" model, power generalized weibull accelerated odds "PGWAO" model, generalized gamma accelerated odds "GGAO"
model, modified kumaraswamy Weibull accelerated odds "MKWAO" model,
9
MLEAO
log-logistic accelerated odds "LLAO" model, tangent-log-logistic accelerated
odds "TLLAO" model, sine-log-logistic accelerated odds "SLLAO" model, cosine log-logistic accelerated odds "CLLAO" model,secant-log-logistic accelerated odds "SCLLAO" model, arcsine-log-logistic accelerated odds "ASLLAO"
model,arctangent-log-logistic accelerated odds "ATLLAO" model, Weibull accelerated odds "WAO" model, gamma accelerated odds "WAO" model, and lognormal accelerated odds "ATLNAO" model.)
z
: design matrix for covariates (p x n), p >= 1
method
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent".
hessian
:A function to return (as a matrix) the hessian for those methods that can use this
information.
conf.int
: confidence level
maxit
:The maximum number of iterations. Defaults to 1000
log
:log scale (TRUE or FALSE)
Value
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
#Example #1
data(alloauto)
time<-alloauto$time
delta<-alloauto$delta
z<-alloauto$type
MLEAO(init = c(1.0,0.40,0.50,0.50),times = time,status = delta,n=nrow(z),
basehaz = "GLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #2
data(bmt)
time<-bmt$Time
delta<-bmt$Status
z<-bmt$TRT
MLEAO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z),
basehaz = "CLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #3
data("gastric")
time<-gastric$time
delta<-gastric$status
z<-gastric$trt
10
MLEGO
MLEAO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z),
basehaz = "LNAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #4
data("larynx")
time<-larynx$time
delta<-larynx$delta
larynx$age<-as.numeric(scale(larynx$age))
larynx$diagyr<-as.numeric(scale(larynx$diagyr))
larynx$stage<-as.factor(larynx$stage)
z<-model.matrix(~ stage+age+diagyr, data = larynx)
MLEAO(init = c(1.0,1.0,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "ASLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
General Odds (GO) Model.
MLEGO
Description
A Tractable Parametric General Odds (GO) model’s Log-likelihood, MLE and information criterion
values. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL,
and ASLL
Usage
MLEGO(
init,
times,
status,
n,
basehaz,
z,
zt,
method = "BFGS",
hessian = TRUE,
conf.int = 0.95,
maxit = 1000,
log = FALSE
)
Arguments
init
: initial points for optimisation
times
: survival times
status
: vital status (1 - dead, 0 - alive)
n
: The number of the data set
11
MLEGO
basehaz
: baseline hazard structure including baseline (New generalized log-logistic general odds "NGLLGO" model, generalized log-logisitic general odds "GLLGO"
model, modified log-logistic general odds "MLLGO" model,exponentiated Weibull
general odds "EWGO" model, power generalized weibull general odds "PGWGO" model, generalized gamma general odds "GGGO" model, modified kumaraswamy Weibull general odds "MKWGO" model, log-logistic general odds
"LLGO" model, tangent-log-logistic general odds "TLLGO" model, sine-loglogistic general odds "SLLGO" model, cosine log-logistic general odds "CLLGO"
model,secant-log-logistic general odds "SCLLGO" model, arcsine-log-logistic
general odds "ASLLGO" model, arctangent-log-logistic general odds "ATLLGO"
model, Weibull general odds "WGO" model, gamma general odds "WGO" model,
and log-normal general odds "ATLNGO" model.)
z
: design matrix for odds-level effects (p x n), p >= 1
zt
: design matrix for time-dependent effects (q x n), q >= 1
method
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent".
hessian
:A function to return (as a matrix) the hessian for those methods that can use this
information.
conf.int
: confidence level
maxit
:The maximum number of iterations. Defaults to 1000
log
:log scale (TRUE or FALSE)
Value
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
#Example #1
data(alloauto)
time<-alloauto$time
delta<-alloauto$delta
z<-alloauto$type
MLEGO(init = c(1.0,0.50,0.50,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "PGWGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #2
data(bmt)
time<-bmt$Time
delta<-bmt$Status
z<-bmt$TRT
MLEGO(init = c(1.0,0.50,0.45,0.5),times = time,status = delta,n=nrow(z),
basehaz = "TLLGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
12
MLEPO
log=FALSE)
#Example #3
data("gastric")
time<-gastric$time
delta<-gastric$status
z<-gastric$trt
MLEGO(init = c(1.0,1.0,0.50,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "GLLGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
Proportional Odds (PO) model.
MLEPO
Description
Tractable Parametric Proportional Odds (PO) model’s maximum likelihood estimation, log-likelihood,
and information criterion. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL,
SLL,CLL,SCLL,ATLL, and ASLL
Usage
MLEPO(
init,
times,
status,
n,
basehaz,
z,
method = "BFGS",
hessian = TRUE,
conf.int = 0.95,
maxit = 1000,
log = FALSE
)
Arguments
init
: initial points for optimisation
times
: survival times
status
: vital status (1 - dead, 0 - alive)
n
: The number of the data set
basehaz
: baseline hazard structure including baseline (New generalized log-logistic proportional odds "NGLLPO" model, generalized log-logisitic proportional odds
"GLLPO" model, modified log-logistic proportional odds "MLLPO" model,
exponentiated Weibull proportional odds "EWPO" model, power generalized
13
MLEPO
weibull proportional odds "PGWPO" model, generalized gamma proportional
odds "GGPO" model, modified kumaraswamy Weibull proportional odds "MKWPO" model, log-logistic proportional odds "PO" model, tangent-log-logistic
proportional odds "TLLPO" model, sine-log-logistic proportional odds "SLLPO"
model, cosine log-logistic proportional odds "CLLPO" model, secant-log-logistic
proportional odds "SCLLPO" model, arcsine-log-logistic proportional odds "ASLLPO"
model, and arctangent-log-logistic proportional odds "ATLLPO" model, Weibull
proportional odds "WPO" model, gamma proportional odds "GPO" model, and
log-normal proportional odds "LNPO" model.)
z
: design matrix for covariates (p x n), p >= 1
method
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent".
hessian
:A function to return (as a matrix) the hessian for those methods that can use this
information.
conf.int
: confidence level
maxit
:The maximum number of iterations. Defaults to 1000
log
:log scale (TRUE or FALSE)
Value
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
#Example #1
data(alloauto)
time<-alloauto$time
delta<-alloauto$delta
z<-alloauto$type
MLEPO(init = c(1.0,0.40,1.0,0.50),times = time,status = delta,n=nrow(z),
basehaz = "GLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #2
data(bmt)
time<-bmt$Time
delta<-bmt$Status
z<-bmt$TRT
MLEPO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z),
basehaz = "SLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #3
data("gastric")
time<-gastric$time
delta<-gastric$status
14
pASLL
z<-gastric$trt
MLEPO(init = c(1.0,0.50,1.0,0.75),times = time,status = delta,n=nrow(z),
basehaz = "PGWPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #4
data("larynx")
time<-larynx$time
delta<-larynx$delta
larynx$age<-as.numeric(scale(larynx$age))
larynx$diagyr<-as.numeric(scale(larynx$diagyr))
larynx$stage<-as.factor(larynx$stage)
z<-model.matrix(~ stage+age+diagyr, data = larynx)
MLEPO(init = c(1.0,1.0,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "ATLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
Arcsine-Log-logistic (ASLL) Cumulative Distribution Function.
pASLL
Description
Arcsine-Log-logistic (ASLL) Cumulative Distribution Function.
Usage
pASLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the ASLL Cumulative Distribution Function.
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with
Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
15
pATLL
Examples
t=runif(10,min=0,max=1)
pASLL(t=t, alpha=0.7, beta=0.5)
Arctangent-Log-logistic (ATLL) Cumulative Distribution Function.
pATLL
Description
Arctangent-Log-logistic (ATLL) Cumulative Distribution Function.
Usage
pATLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the ATLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Alkhairy, I., Nagy, M., Muse, A. H., & Hussam, E. (2021). The Arctan-X family of distributions:
Properties, simulation, and applications to actuarial sciences. Complexity, 2021.
Examples
t=runif(10,min=0,max=1)
pATLL(t=t, alpha=0.7, beta=0.5)
16
pCLL
Cosine-Log-logistic (SLL) Cumulative Distribution Function.
pCLL
Description
Cosine-Log-logistic (SLL) Cumulative Distribution Function.
Usage
pCLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the CLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Souza, L., Junior, W. R. D. O., de Brito, C. C. R., Ferreira, T. A., & Soares, L. G. (2019). General
properties for the Cos-G class of distributions with applications. Eurasian Bulletin of Mathematics
(ISSN: 2687-5632), 63-79.
Examples
t=runif(10,min=0,max=1)
pCLL(t=t, alpha=0.7, beta=0.5)
17
pdGG
pdGG
Generalised Gamma (GG) Probability Density Function.
Description
Generalised Gamma (GG) Probability Density Function.
Usage
pdGG(t, kappa, alpha, eta, log = FALSE)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the GG probability density function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
pdGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)
pEW
Exponentiated Weibull (EW) Cumulative Distribution Function.
Description
Exponentiated Weibull (EW) Cumulative Distribution Function.
Usage
pEW(t, lambda, kappa, alpha, log.p = FALSE)
18
pG
Arguments
t
: positive argument
lambda
: scale parameter
kappa
: shape parameter
alpha
: shape parameter
log.p
:log scale (TRUE or FALSE)
Value
the value of the EW cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
pEW(t=t, lambda=0.65,kappa=0.45, alpha=0.25, log.p=FALSE)
Gamma (G) Cumulative Distribution Function.
pG
Description
Gamma (G) Cumulative Distribution Function.
Usage
pG(t, shape, scale)
Arguments
t
: positive argument
shape
: shape parameter
scale
: scale parameter
Value
the value of the G Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
19
pGG
Examples
t=runif(10,min=0,max=1)
pG(t=t, shape=0.85, scale=0.5)
pGG
Generalised Gamma (GG) Cumulative Distribution Function.
Description
Generalised Gamma (GG) Cumulative Distribution Function.
Usage
pGG(t, kappa, alpha, eta, log.p = FALSE)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
log.p
:log scale (TRUE or FALSE)
Value
the value of the GG cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
pGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)
20
pGLL
pGLL
Generalized Log-logistic (GLL) cumulative distribution function.
Description
Generalized Log-logistic (GLL) cumulative distribution function.
Usage
pGLL(t, kappa, alpha, eta)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
Value
the value of the GLL cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
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.
Examples
t=runif(10,min=0,max=1)
pGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)
21
pLL
Log-logistic (LL) Cumulative Distribution Function.
pLL
Description
Log-logistic (LL) Cumulative Distribution Function.
Usage
pLL(t, kappa, alpha)
Arguments
t
kappa
alpha
: positive argument
: scale parameter
: shape parameter
Value
the value of the LL cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
pLL(t=t, kappa=0.5, alpha=0.35)
Lognormal (LN) Cumulative Distribution Function.
pLN
Description
Lognormal (LN) Cumulative Distribution Function.
Usage
pLN(t, kappa, alpha)
Arguments
t
kappa
alpha
: positive argument
: meanlog parameter
: sdlog parameter
22
pMKW
Value
the value of the LN cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
pLN(t=t, kappa=0.75, alpha=0.95)
pMKW
Modified Kumaraswamy Weibull (MKW) Cumulative Distribution
Function.
Description
Modified Kumaraswamy Weibull (MKW) Cumulative Distribution Function.
Usage
pMKW(t, alpha, kappa, eta)
Arguments
t
: positive argument
alpha
: Inverse scale parameter
kappa
: shape parameter
eta
: shape parameter
Value
the value of the MKW cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
pMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)
23
pMLL
pMLL
Modified Log-logistic (MLL) cumulative distribution function.
Description
Modified Log-logistic (MLL) cumulative distribution function.
Usage
pMLL(t, kappa, alpha, eta)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
Value
the value of the MLL cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Kayid, M. (2022). Applications of Bladder Cancer Data Using a Modified Log-Logistic Model.
Applied Bionics and Biomechanics, 2022.
Examples
t=runif(10,min=0,max=1)
pMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)
24
pNGLL
pNGLL
New Generalized Log-logistic (NGLL) cumulative distribution function.
Description
New Generalized Log-logistic (NGLL) cumulative distribution function.
Usage
pNGLL(t, kappa, alpha, eta, zeta)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
zeta
: shape parameter
Value
the value of the NGLL cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
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.
Examples
t=runif(10,min=0,max=1)
pNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)
25
pPGW
pPGW
Power Generalised Weibull (PGW) cumulative distribution function.
Description
Power Generalised Weibull (PGW) cumulative distribution function.
Usage
pPGW(t, kappa, alpha, eta)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
Value
the value of the PGW cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Alvares, D., & Rubio, F. J. (2021). A tractable Bayesian joint model for longitudinal and survival
data. Statistics in Medicine, 40(19), 4213-4229.
Examples
t=runif(10,min=0,max=1)
pPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)
26
pSCLL
Secant-log-logistic (SCLL) Cumulative Distribution Function.
pSCLL
Description
Secant-log-logistic (SCLL) Cumulative Distribution Function.
Usage
pSCLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the SCLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Souza, L., de Oliveira, W. R., de Brito, C. C. R., Chesneau, C., Fernandes, R., & Ferreira, T. A.
(2022). Sec-G class of distributions: Properties and applications. Symmetry, 14(2), 299.
Examples
t=runif(10,min=0,max=1)
pSCLL(t=t, alpha=0.7, beta=0.5)
27
pSLL
Sine-Log-logistic (SLL) Cumulative Distribution Function.
pSLL
Description
Sine-Log-logistic (SLL) Cumulative Distribution Function.
Usage
pSLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the SLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Souza, L., Junior, W., De Brito, C., Chesneau, C., Ferreira, T., & Soares, L. (2019). On the SinG class of distributions: theory, model and application. Journal of Mathematical Modeling, 7(3),
357-379.
Examples
t=runif(10,min=0,max=1)
pSLL(t=t, alpha=0.7, beta=0.5)
28
pW
Tangent-Log-logistic (TLL) Cumulative Distribution Function.
pTLL
Description
Tangent-Log-logistic (TLL) Cumulative Distribution Function.
Usage
pTLL(t, alpha, beta)
Arguments
t
alpha
beta
: positive argument
: scale parameter
: shape parameter
Value
the value of the TLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
pTLL(t=t, alpha=0.7, beta=0.5)
Weibull (W) Cumulative Distribution Function.
pW
Description
Weibull (W) Cumulative Distribution Function.
Usage
pW(t, kappa, alpha)
Arguments
t
kappa
alpha
: positive argument
: scale parameter
: shape parameter
29
rASLL
Value
the value of the W Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
pW(t=t, kappa=0.75, alpha=0.5)
rASLL
Arcsine-Log-logistic (ASLL) Hazard Rate Function.
Description
Arcsine-Log-logistic (ASLL) Hazard Rate Function.
Usage
rASLL(t, alpha, beta, log = FALSE)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the ASLL Hazard Rate Function.
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rSLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
30
rCLL
rATLL
Arctangent-Log-logistic (ATLL) Hazard Function.
Description
Arctangent-Log-logistic (ATLL) Hazard Function.
Usage
rATLL(t, alpha, beta, log = FALSE)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the ATLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rATLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
rCLL
Cosine-Log-logistic (CLL) Hazard Function.
Description
Cosine-Log-logistic (CLL) Hazard Function.
Usage
rCLL(t, alpha, beta, log = FALSE)
31
rEW
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the CLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Souza, L., Junior, W. R. D. O., de Brito, C. C. R., Ferreira, T. A., & Soares, L. G. (2019). General
properties for the Cos-G class of distributions with applications. Eurasian Bulletin of Mathematics
(ISSN: 2687-5632), 63-79.
Examples
t=runif(10,min=0,max=1)
rCLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
rEW
Exponentiated Weibull (EW) Hazard Function.
Description
Exponentiated Weibull (EW) Hazard Function.
Usage
rEW(t, lambda, kappa, alpha, log = FALSE)
Arguments
t
: positive argument
lambda
: scale parameter
kappa
: shape parameter
alpha
: shape parameter
log
:log scale (TRUE or FALSE)
32
rG
Value
the value of the EW hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Khan, S. A. (2018). Exponentiated Weibull regression for time-to-event data. Lifetime data analysis, 24(2), 328-354.
Examples
t=runif(10,min=0,max=1)
rEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75, log=FALSE)
rG
Gamma (G) Hazard Function.
Description
Gamma (G) Hazard Function.
Usage
rG(t, shape, scale, log = FALSE)
Arguments
t
shape
scale
log
: positive argument
: shape parameter
: scale parameter
:log scale (TRUE or FALSE)
Value
the value of the G hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rG(t=t, shape=0.5, scale=0.85,log=FALSE)
33
rGG
rGG
Generalised Gamma (GG) Hazard Function.
Description
Generalised Gamma (GG) Hazard Function.
Usage
rGG(t, kappa, alpha, eta, log = FALSE)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the GG hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
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.
Examples
t=runif(10,min=0,max=1)
rGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)
34
rGLL
rGLL
Generalized Log-logistic (GLL) hazard function.
Description
Generalized Log-logistic (GLL) hazard function.
Usage
rGLL(t, kappa, alpha, eta, log = FALSE)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the GLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
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.
Examples
t=runif(10,min=0,max=1)
rGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, log=FALSE)
35
rLL
rLL
Log-logistic (LL) Hazard Function.
Description
Log-logistic (LL) Hazard Function.
Usage
rLL(t, kappa, alpha, log = FALSE)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the LL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rLL(t=t, kappa=0.5, alpha=0.35,log=FALSE)
rLN
Lognormal (LN) Hazard Function.
Description
Lognormal (LN) Hazard Function.
Usage
rLN(t, kappa, alpha, log = FALSE)
36
rMKW
Arguments
t
: positive argument
kappa
: meanlog parameter
alpha
: sdlog parameter
log
:log scale (TRUE or FALSE)
Value
the value of the LN hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rLN(t=t, kappa=0.5, alpha=0.75,log=FALSE)
rMKW
Modified Kumaraswamy Weibull (MKW) Hazard Function.
Description
Modified Kumaraswamy Weibull (MKW) Hazard Function.
Usage
rMKW(t, alpha, kappa, eta, log = FALSE)
Arguments
t
: positive argument
alpha
: inverse scale parameter
kappa
: shape parameter
eta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the MKW hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
37
rMLL
References
Khosa, S. K. (2019). Parametric Proportional Hazard Models with Applications in Survival analysis
(Doctoral dissertation, University of Saskatchewan).
Examples
t=runif(10,min=0,max=1)
rMKW(t=t, alpha=0.35, kappa=0.7, eta=1.4, log=FALSE)
rMLL
Modified Log-logistic (MLL) hazard function.
Description
Modified Log-logistic (MLL) hazard function.
Usage
rMLL(t, kappa, alpha, eta, log = FALSE)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the MLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9,log=FALSE)
38
rPGW
rNGLL
New Generalized Log-logistic (NGLL) hazard function.
Description
New Generalized Log-logistic (NGLL) hazard function.
Usage
rNGLL(t, kappa, alpha, eta, zeta, log = FALSE)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
zeta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the NGLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4, log=FALSE)
rPGW
Power Generalised Weibull (PGW) hazard function.
Description
Power Generalised Weibull (PGW) hazard function.
Usage
rPGW(t, kappa, alpha, eta, log = FALSE)
39
rSCLL
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the PGW hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6,log=FALSE)
rSCLL
Secant-log-logistic (SCLL) Hazard Function.
Description
Secant-log-logistic (SCLL) Hazard Function.
Usage
rSCLL(t, alpha, beta, log = FALSE)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the SCLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
40
rSLL
References
Souza, L., de Oliveira, W. R., de Brito, C. C. R., Chesneau, C., Fernandes, R., & Ferreira, T. A.
(2022). Sec-G class of distributions: Properties and applications. Symmetry, 14(2), 299.
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with
Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
Examples
t=runif(10,min=0,max=1)
rSCLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
rSLL
Sine-Log-logistic (SLL) Hazard Function.
Description
Sine-Log-logistic (SLL) Hazard Function.
Usage
rSLL(t, alpha, beta, log = FALSE)
Arguments
t
alpha
beta
log
: positive argument
: scale parameter
: shape parameter
:log scale (TRUE or FALSE)
Value
the value of the SLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Souza, L. (2015). New trigonometric classes of probabilistic distributions. esis, Universidade Federal Rural de Pernambuco, Brazil.
Examples
t=runif(10,min=0,max=1)
rSLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
41
rTLL
rTLL
Tangent-Log-logistic (TLL) Hazard Function.
Description
Tangent-Log-logistic (TLL) Hazard Function.
Usage
rTLL(t, alpha, beta, log = FALSE)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the TLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Muse, A. H., Tolba, A. H., Fayad, E., Abu Ali, O. A., Nagy, M., & Yusuf, M. (2021). Modelling the
COVID-19 mortality rate with a new versatile modification of the log-logistic distribution. Computational Intelligence and Neuroscience, 2021.
Examples
t=runif(10,min=0,max=1)
rTLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
42
sASLL
Weibull (W) Hazard Function.
rW
Description
Weibull (W) Hazard Function.
Usage
rW(t, kappa, alpha, log = FALSE)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
log
:log scale (TRUE or FALSE)
Value
the value of the w hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
rW(t=t, kappa=0.75, alpha=0.5,log=FALSE)
sASLL
Arcsine-Log-logistic (ASLL) Survival Function.
Description
Arcsine-Log-logistic (ASLL) Survival Function.
Usage
sASLL(t, alpha, beta)
43
sATLL
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the ASLL Survival Function.
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with
Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
Examples
t=runif(10,min=0,max=1)
sASLL(t=t, alpha=0.7, beta=0.5)
Arctangent-Log-logistic (ATLL) Survivor Function.
sATLL
Description
Arctangent-Log-logistic (ATLL) Survivor Function.
Usage
sATLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the ATLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
44
sCLL
References
Alkhairy, I., Nagy, M., Muse, A. H., & Hussam, E. (2021). The Arctan-X family of distributions:
Properties, simulation, and applications to actuarial sciences. Complexity, 2021.
Examples
t=runif(10,min=0,max=1)
sATLL(t=t, alpha=0.7, beta=0.5)
Cosine-Log-logistic (CLL) Survivor Function.
sCLL
Description
Cosine-Log-logistic (CLL) Survivor Function.
Usage
sCLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the CLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Mahmood, Z., M Jawa, T., Sayed-Ahmed, N., Khalil, E. M., Muse, A. H., & Tolba, A. H. (2022).
An Extended Cosine Generalized Family of Distributions for Reliability Modeling: Characteristics
and Applications with Simulation Study. Mathematical Problems in Engineering, 2022.
Examples
t=runif(10,min=0,max=1)
sCLL(t=t, alpha=0.7, beta=0.5)
45
sEW
sEW
Exponentiated Weibull (EW) Survivor Function.
Description
Exponentiated Weibull (EW) Survivor Function.
Usage
sEW(t, lambda, kappa, alpha)
Arguments
t
: positive argument
lambda
: scale parameter
kappa
: shape parameter
alpha
: shape parameter
Value
the value of the EW survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Rubio, F. J., Remontet, L., Jewell, N. P., & Belot, A. (2019). On a general structure for hazardbased regression models: an application to population-based cancer research. Statistical methods
in medical research, 28(8), 2404-2417.
Examples
t=runif(10,min=0,max=1)
sEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75)
46
sGG
Gamma (G) Survivor Function.
sG
Description
Gamma (G) Survivor Function.
Usage
sG(t, shape, scale)
Arguments
t
: positive argument
shape
: shape parameter
scale
: scale parameter
Value
the value of the G Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
sG(t=t, shape=0.85, scale=0.5)
sGG
Generalised Gamma (GG) Survival Function.
Description
Generalised Gamma (GG) Survival Function.
Usage
sGG(t, kappa, alpha, eta, log.p = FALSE)
47
sGLL
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
log.p
:log scale (TRUE or FALSE)
Value
the value of the GG survival function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
sGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)
sGLL
Generalized Log-logistic (GLL) survivor function.
Description
Generalized Log-logistic (GLL) survivor function.
Usage
sGLL(t, kappa, alpha, eta)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
Value
the value of the GLL survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
48
sLL
References
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.
Examples
t=runif(10,min=0,max=1)
sGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)
Log-logistic (LL) Survivor Function.
sLL
Description
Log-logistic (LL) Survivor Function.
Usage
sLL(t, kappa, alpha)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
Value
the value of the LL survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
sLL(t=t, kappa=0.5, alpha=0.35)
49
sLN
Lognormal (LN) Survivor Hazard Function.
sLN
Description
Lognormal (LN) Survivor Hazard Function.
Usage
sLN(t, kappa, alpha)
Arguments
t
: positive argument
kappa
: meanlog parameter
alpha
: sdlog parameter
Value
the value of the LN Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
sLN(t=t, kappa=0.75, alpha=0.95)
sMKW
Modified Kumaraswamy Weibull (MKW) Survivor Function.
Description
Modified Kumaraswamy Weibull (MKW) Survivor Function.
Usage
sMKW(t, alpha, kappa, eta)
50
sMLL
Arguments
t
: positive argument
alpha
: Inverse scale parameter
kappa
: shape parameter
eta
: shape parameter
Value
the value of the MKW survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
sMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)
sMLL
Modified Log-logistic (MLL) survivor function.
Description
Modified Log-logistic (MLL) survivor function.
Usage
sMLL(t, kappa, alpha, eta)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
Value
the value of the MLL survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
51
SNGLL
References
Kayid, M. (2022). Applications of Bladder Cancer Data Using a Modified Log-Logistic Model.
Applied Bionics and Biomechanics, 2022.
Examples
t=runif(10,min=0,max=1)
sMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)
New Generalized Log-logistic (NGLL) survivor function.
SNGLL
Description
New Generalized Log-logistic (NGLL) survivor function.
Usage
SNGLL(t, kappa, alpha, eta, zeta)
Arguments
t
kappa
alpha
eta
zeta
:
:
:
:
:
positive argument
scale parameter
shape parameter
shape parameter
shape parameter
Value
the value of the NGLL survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
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.
Examples
t=runif(10,min=0,max=1)
SNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)
52
sPGW
sPGW
Power Generalised Weibull (PGW) survivor function.
Description
Power Generalised Weibull (PGW) survivor function.
Usage
sPGW(t, kappa, alpha, eta)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
eta
: shape parameter
Value
the value of the PGW survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Alvares, D., & Rubio, F. J. (2021). A tractable Bayesian joint model for longitudinal and survival
data. Statistics in Medicine, 40(19), 4213-4229.
Examples
t=runif(10,min=0,max=1)
sPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)
53
sSCLL
Secant-log-logistic (SCLL) Survivor Function.
sSCLL
Description
Secant-log-logistic (SCLL) Survivor Function.
Usage
sSCLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the SCLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
sSCLL(t=t, alpha=0.7, beta=0.5)
Sine-Log-logistic (SLL) Survivor Function.
sSLL
Description
Sine-Log-logistic (SLL) Survivor Function.
Usage
sSLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
54
sTLL
Value
the value of the SLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
References
Souza, L., Junior, W., De Brito, C., Chesneau, C., Ferreira, T., & Soares, L. (2019). On the SinG class of distributions: theory, model and application. Journal of Mathematical Modeling, 7(3),
357-379.
Examples
t=runif(10,min=0,max=1)
sSLL(t=t, alpha=0.7, beta=0.5)
Tangent-Log-logistic (TLL) Survivor Function.
sTLL
Description
Tangent-Log-logistic (TLL) Survivor Function.
Usage
sTLL(t, alpha, beta)
Arguments
t
: positive argument
alpha
: scale parameter
beta
: shape parameter
Value
the value of the TLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
sTLL(t=t, alpha=0.7, beta=0.5)
55
sW
Weibull (W) Survivor Function.
sW
Description
Weibull (W) Survivor Function.
Usage
sW(t, kappa, alpha)
Arguments
t
: positive argument
kappa
: scale parameter
alpha
: shape parameter
Value
the value of the W Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau <abdisalam.hassan@amoud.edu.so>
Examples
t=runif(10,min=0,max=1)
sW(t=t, kappa=0.75, alpha=0.5)
Index
∗ datasets
alloauto, 3
bmt, 4
gastric, 4
larynx, 5
rEW, 31
rG, 32
rGG, 33
rGLL, 34
rLL, 35
rLN, 35
rMKW, 36
rMLL, 37
rNGLL, 38
rPGW, 38
rSCLL, 39
rSLL, 40
rTLL, 41
rW, 42
alloauto, 3
bmt, 4
gastric, 4
larynx, 5
MLEAFT, 6
MLEAO, 8
MLEGO, 10
MLEPO, 12
sASLL, 42
sATLL, 43
sCLL, 44
sEW, 45
sG, 46
sGG, 46
sGLL, 47
sLL, 48
sLN, 49
sMKW, 49
sMLL, 50
SNGLL, 51
sPGW, 52
sSCLL, 53
sSLL, 53
sTLL, 54
sW, 55
pASLL, 14
pATLL, 15
pCLL, 16
pdGG, 17
pEW, 17
pG, 18
pGG, 19
pGLL, 20
pLL, 21
pLN, 21
pMKW, 22
pMLL, 23
pNGLL, 24
pPGW, 25
pSCLL, 26
pSLL, 27
pTLL, 28
pW, 28
rASLL, 29
rATLL, 30
rCLL, 30
56
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