wdempsey / markov_survival

Markov Survival Processes Fitting Software

Markov Survival Processes : Fitting Software

Two files, one which contains functions for estimation of parameters under three different markov survival processes (harmonic, gamma, and inverse linear) and another which applies these functions to a particular dataset (Gehan, (1965)).

1. markov_process_fit.R : Contains three functions (har_fit, gamma_fit, and invlin_fit)

• Inputs :
  • times : The observed survival or censoring times for each patient
  • cens : A vector indicating whether the observed time is a censoring or survival time for each patient
  • initial_params (optional) : Initialization of parameters.
  • weights_formula (optional) : The formula for the covariate matrix, W, associated with the weights = exp(W * beta). If missing, weights are set to be identically one for each patient.
  • parameterization (optional) : For the gamma process, choose between either the 'ratio' or 'standard' parameterization.
• Output :
  • par : Maximum likelihood parameter estimates
  • std_err : Standard errors for parameter estimates
  • log_lik : Log-likelihood at the mle
  • conv : Convergence of the parameter estimates (useful when the mle is at a boundary case)
  • cond_dist : Function for the conditional survival distribution at t for a weight given observed times

2. gehan_example.R :

• 6-MP subset of leukemia patients (Gehan, (1965))
  • Fit models under both harmonic and gamma process
  • Produce conditional survival distribution plots (including Kaplan-Meier product limit estimate and the exponential distribution estimate)
• Complete leukemia dataset (Gehan, (1965)) : Treatment and Control Groups
  • Fit models under both inverese linear (limiting harmonic) and gamma process
  • Produce conditional survival distribution plot.