# Proportional Odds (PO) model. 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 ```r 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 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) ## Returns a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik) ## Examples ```r #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 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) ``` ## Author(s) Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so

MLEPO function