NRI and IDI with differing follow-up time

I am investigating whether the addition of an interaction term between a biomarker and a comorbidity improves a multivariable cox model predicting post-discharge outcomes. In addition to the likelihood ratio χ2 test and C-statiticcs, I would like to perform an NRI/IDI analysis.

My problem however is this: in my dataset, the outcome had a follow-up time 180 days after admission. In order to reflect post-discharge survival time, I have excluded patients that died in hospital and have substracted their time in hospital from total survival time. This has lead to differing follow-up times between patients (as hospital time differs), however to calculate NRI/IDI I have to pick a time point to compare predictions and their classifications.

How do I choose this time-point whilst introducing the least amount of bias and including the most patients? Is this possible at all?

Thanks!

• Exclusions of deaths is a no-no. This creates a serious bias and makes the results not apply prospectively. Consider converting to a "time until successful discharge" goal where deaths are right-censored and counted as not reaching the discharge alive goal. Note that IDI and NDI have many problems. See here for alternatives. If interested in a conditional post-discharge analysis you can instead specify a qualification time and do a landmark analysis to predict survival from the landmark conditional on surviving to the landmark. Jan 18 at 13:27
• Hello Mr. Harrell, thank you for your answer. I understand that exclusions of deaths is a no-no regarding the NRI and IDI, however since I am only looking at outcomes after patients have left the hospital I am allowed to exclude patients that died before discharge no? Is it an issue for the cox models themselves that the follow-up time differs? I thought taking substracting the hospital time from total survival time would solve the exclusion of patients that died in-hospital. Jan 18 at 14:32
• Perhaps relevant: I am using discharge measurements of the biomarker to predict mortality, thus patients who died in the hospital would be excluded by default as they would not have discharge measurements. Jan 18 at 14:42
• The NRI may not be the best approach: see pubmed.ncbi.nlm.nih.gov/26504496 Jan 18 at 15:02
• So you really need a landmark analysis starting with a well-defined qualification (survival) time. The question is whether it is OK not to exclude deaths that occurred right after hospital discharge. Most analysts would start the clock at day of discharge alive, and you'd need the biomarkers to be measured on that day or slightly earlier. Jan 18 at 19:33

the outcome had a follow-up time 180 days after admission...I am only looking at outcomes after patients have left the hospital...(emphasis added)

If your interest is solely in outcomes after discharge from the hospital, then a natural reference for time = 0 is the date of discharge, with covariate values taken at or just before discharge included in your model. There is no need to set time = 0 to the date of admission.

That limits your analysis to those who actually live long enough and are well enough before 180 days to be discharged. That limitation needs to be addressed in your presentation and any application of your model--it wouldn't apply to those who are hospitalized for over 180 days.

Yes, as the length of hospital stay varies among patients there will be different follow-up times among patients relative to their discharge dates. But that's just right censoring of survival-time observations if you are interested in post-discharge survival.

Although NRI/IDI analysis is probably not a good choice, as noted in comments, the issue of choosing survival time points for evaluating models isn't specific to NRI/IDI. For example, the calibrate() function in Frank Harrell's rms package requires such a choice for survival models.

There's no need to restrict yourself to a single time point. Evaluating several time points might be informative in terms of the models' handling of both soon-after-discharge events and later events. If there is some generally accepted evaluation time in your field (for example, re-admission within 30 days of discharge is often of interest), then that should be included among your evaluation times.

Finally, your model comparison is between 2 nested models, one that contains an interaction between 2 predictors and one that doesn't. Thus a likelihood-ratio test between them provides a well established and sensitive comparison, with the related Adequacy Index indicating how much including the interaction improves performance.