Coxph {tram}

Cox Proportional Hazards Model

Description

Cox model with fully parameterised baseline hazard function

Usage

Coxph(formula, data, subset, weights, offset, cluster, na.action = na.omit, ...)

Arguments

formula

an object of class "formula": a symbolic description of the model structure to be fitted. The details of model specification are given under tram and in the package vignette.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula).

subset

an optional vector specifying a subset of observations to be used in the fitting process.

weights

an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. If present, the weighted log-likelihood is maximised.

offset

this can be used to specify an _a priori_ known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases.

cluster

optional factor with a cluster ID employed for computing clustered covariances.

na.action

a function which indicates what should happen when the data contain NAs. The default is set to na.omit.

...

additional arguments to tram.

Details

The original implementation of Cox models via the partial likelihood, treating the baseline hazard function as a nuisance parameter, is available in coxph. This function allows simultaneous estimation of the log-hazard ratios and the log-cumulative baseline hazard, the latter parameterised by a Bernstein polynomial. The model can be fitted under stratification (time-varying coefficients), all types of random censoring and trunction. An early reference to this parameterisation is McLain and Ghosh (2013).

The response is bounded (bounds = c(0, Inf)) when specified as a Surv object. Otherwise, bounds can be specified via ....

Parameters are log-hazard ratios comparing treatment (or a one unit increase in a numeric variable) with a reference.

Value

An object of class Coxph, with corresponding coef, vcov, logLik, estfun, summary, print, plot and predict methods.

References

Alexander C. McLain and Sujit K. Ghosh (2013). Efficient Sieve Maximum Likelihood Estimation of Time-Transformation Models, Journal of Statistical Theory and Practice, 7(2), 285–303, doi:10.1080/15598608.2013.772835.

Torsten Hothorn, Lisa Moest, Peter Buehlmann (2018), Most Likely Transformations, Scandinavian Journal of Statistics, 45(1), 110–134, doi:10.1111/sjos.12291.

Examples

  data("GBSG2", package = "TH.data")

  library("survival")
  (m1 <- coxph(Surv(time, cens) ~ horTh, data = GBSG2))

  (m2 <- Coxph(Surv(time, cens) ~ horTh, data = GBSG2))

  ### McLain & Ghosh (2013)
  (m3 <- Coxph(Surv(time, cens) ~ horTh, data = GBSG2, 
               frailty = "Gamma"))

  ### Wald intervals
  confint(m1)
  confint(m2)
  ### profile likelihood interval
  confint(profile(m2))
  ### score interval
  confint(score_test(m2))
  ### permutation score interval; uses permutation distribution
  ### see coin::independence_test
  ## Not run: confint(perm_test(m2))