Getting Started with survivalMPL • survivalMPL

Overview

survivalMPL fits Cox proportional hazards models by maximum penalised likelihood (MPL). Unlike partial likelihood, MPL estimates the baseline hazard $h_0$ jointly with the regression coefficients $\boldsymbol{\beta}$ , by expanding it in a basis of non-negative functions

$h_0(t) = \sum_{u=1}^{m} \theta_u \psi_u(t), \qquad \boldsymbol{\theta} \geq \mathbf{0},$

and penalising the roughness of the result. Because $h_0$ is estimated rather than profiled out, fits yield absolute hazard, cumulative hazard and survival estimates, and the method extends naturally to censoring schemes the partial likelihood cannot handle.

Supported data:

right censoring, including left truncation (delayed entry)
left censoring
interval censoring
any mixture of the above, together with exact event times

Installation

From CRAN:

install.packages("survivalMPL")

The development version:

# install.packages("remotes")
remotes::install_github("survivalMPL/survivalMPL")

Then attach it alongside survival, which provides the Surv() response constructor:

library(survivalMPL)
#> Loading required package: survival
#> Loading required package: MASS
library(survival)

The main function

coxph_mpl() is the entry point. Its interface follows survival::coxph():

coxph_mpl(formula, data, subset, na.action, entry, control, ...)

Argument	Purpose
`formula`	A model formula whose response is a `Surv()` object
`data`	Data frame containing the variables in `formula`
`entry`	Optional left-truncation (delayed entry) times
`control`	A list from `coxph_mpl.control()`

The response tells coxph_mpl() which censoring scheme applies. Right-censored data can use the familiar two-argument form; everything else uses type = "interval2", where NA marks an unobserved endpoint:

Data	Response
Right censored	`Surv(time, status)`
Left censored	`Surv(NA, t_R, type = "interval2")`
Interval censored	`Surv(t_L, t_R, type = "interval2")`
Exact event	`Surv(t, t, type = "interval2")`

Tuning the fit

Every fit runs with sensible defaults, so control can be omitted entirely. When it is supplied, coxph_mpl.control() collects everything governing the baseline hazard and the optimiser. The arguments most often changed are:

Argument	Meaning
`basis`	Basis for $h_0$ : `"uniform"`, `"msplines"`, `"gaussian"`, `"epanechikov"`
`n.knots`	Length-2 vector: numbers of quantile and equally spaced internal knots
`smooth`	Smoothing value $\lambda$ ; `NULL` selects it automatically by marginal likelihood, `0` fits by plain maximum likelihood
`n.obs`	Number of exact events, used to set default knot counts
`max.iter`	Iteration limits for the three optimisation stages
`tol`	Convergence tolerance; `1e-5` is used throughout the book

The registered bases are:

"uniform" (alias "u") - piecewise-constant step functions
"msplines" (alias "m") - M-splines of order $o$ , cubic by default
"gaussian" (alias "g") - truncated Gaussian kernels
"epanechikov" (aliases "e", "epanechnikov") - Epanechnikov kernels

Control Parameters works through these arguments one at a time, and Basis Functions for the Baseline Hazard gives the mathematical definition of each basis.

Methods

A fitted coxph_mpl object supports the usual generics:

Call	Returns
`summary(fit)`	Coefficients, standard errors, and $\boldsymbol{\theta}$
`coef(fit)`	Regression coefficients
`predict(fit, type = "risk")`	Estimated hazard $\hat h(t)$
`predict(fit, type = "survival")`	Estimated survival $\hat S(t)$
`plot(fit)`	Baseline hazard and survival with confidence bands
`residuals(fit)`	Martingale and Cox-Snell residuals

Where to go next

The tutorials work through one censoring scheme at a time (Right Censoring, Interval Censoring, Left Truncation), each with a complete worked example. Three further articles cover the modelling choices: Control Parameters on tuning a fit, Basis Functions for the Baseline Hazard, and Comparing coxph() and coxph_mpl() on the same data.

See ?coxph_mpl and ?coxph_mpl.control for the full argument lists.