tram (version 1.1-2)

Compris: Competing Risk Regression

Description

An alternative approach to competing risk regression via multivariate transformation models

Usage

Compris(formula, data, subset, weights, na.action, offset, 
        primary = c("Coxph", "Colr", "BoxCox"), 
        competing = switch(primary, Coxph = "weibull", 
                                    Colr = "loglogistic", 
                                    BoxCox = "lognormal"), 
        NPlogLik = FALSE, theta = NULL,
        optim = mltoptim(auglag = list(maxtry = 5)),
        args = list(seed = 1, type = c("MC", "ghalton"), M = 1000),
        scale = FALSE, ...)

Value

An object of class Mmlt, allowing to derive marginal time-to-event distributions for the primary event of interest and all competing events.

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 Details and in the package vignette. The left-hand side must be a Surv object, where "event" is specified by a factor that has levels indicating the independent censoring event, the primary event of interest and then the competing events (in this order).

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

na.action

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

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.

primary

a character defining the marginal model for the primary event of interest, that is, the first status level.

competing

a character defining the marginal models for the remaining competing events.

NPlogLik

logical, optimise nonparametric likelihood defined in terms of multivariate probabilities.

theta

optional starting values.

optim

see Mmlt.

args

a list of arguments for lpmvnorm.

scale

logical defining if variables in the linear predictor shall be scaled. Scaling is internally used for model estimation, rescaled coefficients are reported in model output.

...

addition arguments passed to primary or competing model function.

Details

This is a highly experimental approach to an alternative competing risk regression framework described by Czado and Van Keilegom (2023) and Deresa and Van Keilegom (2023).

References

Claudia Czado and Ingrid Van Keilegom (2023). Dependent Censoring Based on Parametric Copulas. Biometrika, 110(3), 721--738, tools:::Rd_expr_doi("10.1093/biomet/asac067").

Negera Wakgari Deresa and Ingrid Van Keilegom (2023). Copula Based Cox Proportional Hazards Models for Dependent Censoring. Journal of the American Statistical Association, 119(546), 1044--1054, tools:::Rd_expr_doi("10.1080/01621459.2022.2161387").

Examples

  
  if (require("randomForestSRC")) {
    library("survival")
    
    ## Competing risk data set involving follicular cell lymphoma
    ##   (from doi:10.1002/9780470870709)
    data("follic", package = "randomForestSRC")
  
    ## Therapy:
    ### Radiotherapy alone (RT) or Chemotherapy + Radiotherapy (CMTRT)
    follic$ch <- factor(as.character(follic$ch),
      levels = c("N", "Y"), labels = c("RT", "CMTRT")) 
  
    ## Clinical state
    follic$clinstg <- factor(follic$clinstg,
      levels = 2:1, labels = c("II", "I"))
  
    ## Pre-processing as in Deresa & Van Keilegom (2023)
    follic$time <- round(follic$time, digits = 3)
    follic$age <- with(follic, (age - mean(age)) / sd(age)) ## standardised
    follic$hgb <- with(follic, (hgb - mean(hgb)) / sd(hgb)) ## standardised 
    
    ## Setup `Surv' object for fitting Compris():
    ### "status" indicator with levels:
    ###   (1) independent censoring (admin_cens)
    ###   (2) primary event of interest (relapse)
    ###   (3) dependent censoring (death)
    follic$status <- factor(follic$status,
      levels = 0:2, labels = c("admin_cens", "relapse", "death"))
    
    follic$y <- with(follic, Surv(time = time, event = status))
  
    ## Fit a Gaussian Copula-based Cox Proportional Hazards Model with
    ##   a marginal "Coxph" model for the primary event of interest and 
    ##   a Weibull "Survreg" model for dependent censoring
    ## Use very informative starting values to keep CRAN happy
    cf <- c(
            "Event_relapse.Event_relapse.Bs1(Event_relapse)" = -1.89058, 
            "Event_relapse.Event_relapse.Bs2(Event_relapse)" = -1.6566, 
            "Event_relapse.Event_relapse.Bs3(Event_relapse)" = -0.50329, 
            "Event_relapse.Event_relapse.Bs4(Event_relapse)" = -0.50329, 
            "Event_relapse.Event_relapse.Bs5(Event_relapse)" = -0.07402, 
            "Event_relapse.Event_relapse.Bs6(Event_relapse)" = 0.53156, 
            "Event_relapse.Event_relapse.Bs7(Event_relapse)" = 0.67391, 
            "Event_relapse.Event_relapse.chCMTRT" = -0.2861, 
            "Event_relapse.Event_relapse.age" = 0.43178, 
            "Event_relapse.Event_relapse.hgb" = 0.02913, 
            "Event_relapse.Event_relapse.clinstgI" = -0.55601, 
            "Event_death.Event_death.(Intercept)" = -2.20056, 
            "Event_death.Event_death.log(Event_death)" = 0.98102, 
            "Event_death.Event_death.chCMTRT" = 0.25012, 
            "Event_death.Event_death.age" = -0.64826, 
            "Event_death.Event_death.hgb" = -0.02312, 
            "Event_death.Event_death.clinstgI" = 0.57684, 
            "Event_death.Event_relapse.(Intercept)" = -3.48595
           )
    ### gave up after multiple submissions to CRAN resulting
    ### in 5.02 > 5 secs
    # \donttest{
    m <- Compris(y ~ ch + age + hgb + clinstg, data = follic, log_first = TRUE,
                 ### arguments below speed-up example, don't use!
                 theta = cf, 		### informativ starting values
                 optim = mltoptim(),    ### no hessian
                 args  = list(type = "ghalton", 
                              M = 80))	### only 80 MC integration points

    ### log-likelihood
    logLik(m)

    ## Similar to Table 4 of Deresa & Van Keilegom (2023),
    ## but using a Gaussian copula instead of a Gumbel copula.
    ## marginal parameters
    coef(m, type = "marginal")    
    ## Kendall's tau
    coef(m, type = "Kendall")
    # }

  }