# Mable fit of proportional odds rate regression model Maximum approximate Bernstein/Beta likelihood estimation in general proportional odds regression model based on interal censored event time data. ```r mable.po( formula, data, M, g = NULL, tau, x0 = NULL, controls = mable.ctrl(), progress = TRUE ) ``` ## Arguments - `formula`: regression formula. Response must be `cbind`. See 'Details'. - `data`: a data frame containing variables in `formula`. - `M`: a positive integer or a vector `(m0, m1)`. If `M = m` or `m0 = m1 = m`, then `m` is a preselected degree. If `m03`. - `g`: an initial guess of $d$-vector of regression coefficients. See 'Details'. - `tau`: right endpoint of support $[0, \tau]$ must be greater than or equal to the maximum observed time - `x0`: a data frame specifying working baseline covariates on the right-hand-side of `formula`. See 'Details'. - `controls`: Object of class `mable.ctrl()` specifying iteration limit and other control options. Default is `mable.ctrl`. - `progress`: if `TRUE` a text progressbar is displayed ## Returns A list with components * `m` the selected/preselected optimal degree `m` * `p` the estimate of $p = (p_0, \dots, p_m)$, the coefficients of Bernstein polynomial of degree `m` * `coefficients` the estimated regression coefficients of the PO model * `SE` the standard errors of the estimated regression coefficients * `z` the z-scores of the estimated regression coefficients * `mloglik` the maximum log-likelihood at an optimal degree `m` * `tau.n` maximum observed time $\tau_n$ * `tau` right endpoint of support $[0, \tau]$ * `x0` the working baseline covariates * `egx0` the value of $e^{\gamma'x_0}$ * `convergence` an integer code, 1 indicates either the EM-like iteration for finding maximum likelihood reached the maximum iteration for at least one `m` or the search of an optimal degree using change-point method reached the maximum candidate degree, 2 indicates both occured, and 0 indicates a successful completion. * `delta` the final `delta` if `m0 = m1` or the final `pval` of the change-point for searching the optimal degree `m`; and, if `m0u u[veteran$status==0]<-Inf veteran1<-data.frame(l=l, u=u, karno=veteran$karno, celltype=veteran$celltype, trt=veteran$trt, age=veteran$age, prior=veteran$prior>0) fit.sp<-ic_sp(cbind(l,u) ~ karno+celltype, data = veteran1, model="po") x0<-data.frame(karno=100, celltype="squamous") tau<-2000 res<-mable.po(cbind(l,u) ~ karno+celltype, data = veteran1, M=c(1,35), g=-fit.sp$coefficients, x0=x0, tau=tau) op<-par(mfrow=c(2,2)) plot(res, which = "likelihood") plot(res, which = "change-point") plot(res, y=data.frame(karno=20, celltype="squamous"), which="survival", add=FALSE, type="l", xlab="Days", main=expression(paste("Survival: ", bold(x)==0))) plot(res, y=data.frame(karno=80, celltype="smallcell"), which="survival", add=FALSE, type="l", xlab="Days", main=expression(paste("Survival: ", bold(x)==bold(x)[0]))) par(op) ``` ## References Guan, Z. Maximum Likelihood Estimation in Proportional Odds Regression Model Based on Interval-Censored Event-time Data ## See Also `maple.ph` ## Author(s) Zhong Guan

mable.po function