Fit Cox Proportional Hazards Regression Model Via MPL

Simultaneously estimate the regression coefficients and the baseline hazard function of proportional hazard Cox models using maximum penalised likelihood (MPL).

Usage

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

# S3 method for class 'coxph_mpl'
print(x, ...)

Arguments

formula: A survival formula with the response on the left-hand side and covariates on the right. The response must be built with [survival::Surv()] using type = "interval2" for interval-censored data (right-censored responses are converted internally).
data: Optional data frame in which to evaluate formula.
subset: Optional expression specifying a subset of observations to use.
na.action: Optional missing-data filter function applied to the model frame; defaults to options()\$na.action.
control: Optional list returned by [coxph_mpl.control()] specifying basis choice, smoothing value, iteration limits, and related options. When missing, defaults are built from ....
entry: Optional numeric vector (or a column reference evaluated in data) giving each subject's left-truncation (delayed entry) time. Every value must be strictly less than that subject's event/interval lower bound; violations raise an error. Left-truncated and non-left-truncated subjects may be mixed in the same call. Requires basis = "uniform"; any other basis is replaced by "uniform" with a warning. Defaults to NULL (no truncation), which reproduces prior behaviour exactly.
...: Additional arguments passed to [coxph_mpl.control()].
x: An object of class "coxph_mpl".

Value

An object of class "coxph_mpl"; see [coxph_mpl.object] for components.

Invisibly returns x.

Details

coxph_mpl fits a Cox proportional hazards model allowing right, left, and interval censoring by maximising a penalised likelihood in which a penalty term smooths the baseline hazard estimate. Optimisation combines a Newton step for regression coefficients with a multiplicative step for the baseline hazard parameters while enforcing non-negativity constraints (see Ma, Couturier, Heritier and Marschner (2021)). The covariate matrix is centred during optimisation; baseline estimates and covariance matrices are corrected afterwards using a delta-method adjustment.

Limitations

entry is only supported for basis = "uniform"; another basis is downgraded to it with a warning. Also, [residuals.coxph_mpl()] and [predict.coxph_mpl()] do not yet account for entry — they compute cumulative hazard and survival from time 0 rather than from each subject's entry time. Both are known follow-ups, not yet implemented.

Examples

if (FALSE) { # \dontrun{
## Right-censored example: survival::lung
data(lung, package = "survival")
fit_mpl <- coxph_mpl(Surv(time, status == 2) ~ age + sex + ph.karno +
 wt.loss, data = lung, tol = 1e-05)
summary(fit_mpl)

## Interval-censored example: bcos2
data(bcos2)
fit_mpl <- coxph_mpl(Surv(left, right, type = "interval2") ~ treatment,
                     data = bcos2, basis = "m")
summary(fit_mpl)
} # }