# Assessment of interval-censored survival models

How can I evaluate a survival model made for interval-censored data? I'm building my models in icenReg, which only allows you to check for whether the proporitional hazards assumption is satisfied. What I'm really interested in is the predictive performance.

Harell's C index and Somers' Dxy were my first choices, but I can't find a function in R to calculate it for interval-censored data. I found a package that computes time-varying ROC curves for interval-censored models (intcensROC), from which I could calculate both the C index and Somers' Dxy, but was wondering if there was a more direct method?

• Are your covariate values fixed in time, or are they time-varying?
– EdM
Feb 1, 2023 at 15:11
• My project is a bit of a "special case", I assume that observations are independent of each other but in reality my data represents screening appointments and I'm modelling risk between these appointments to calculate optimal screening intervals... but the way I want to model it, the covariates are fixed in time Feb 2, 2023 at 13:24

One way to assess the relative quality of statistical models is to use the Akaike Information Criterion.

Here is an example of how to compute the AICc of two survival models using a dataset from icenReg and the aicc function available in the GenEst package :

library(GenEst)
library(icenReg)

data("IR_diabetes")

mod_gender <- cpm(formula_l = l ~ gender, formula_s = s ~ gender,
data = IR_diabetes, left = "left", right = "right")

mod_1 <- cpm(formula_l = l ~ 1, formula_s = s ~ 1,
data = IR_diabetes, left = "left", right = "right")

aicc(mod_gender)
aicc(mod_1)


It does not provide information on the absolute fit of the model, but it can help in comparing models to choose which variables to include, or which distribution family to use.

• Thanks! I believe AIC is very close to Harrell's likelihood ratio index so if i wanted to compare similar models i'd go with that. I also think AIC has the same limitation as the likelihood ratio (only reasonable to compare nested models, not much else....). What i'm looking for is something that will allow me to comment on the predictive performance of the model Feb 2, 2023 at 13:27
• @Wojty see this page on AIC. There is admittedly some dispute, but many have no problem in applying it to non-nested models (including Akaike himself). This page examines differences between AIC and AUROC/C-index.
– EdM
Feb 2, 2023 at 14:45