Accounting for intra-patient correlation using random effects turns out to not fit correlation patterns very well when data are collected serially. Markov models, where you condition on outcomes in previous time periods as if they were ordinary covariates, works quite well for longitudinal ordinal outcomes. The wake-up call for me was running an example where the efficiency of the treatment effect *increased* as you removed time points from the mixed effect model, whereas for a first-order Markov model the efficiency *decreased* as it should.

The Markov approach is used to do detailed analyses of the ORCHID and VIOLET 2 studies - see the new links for these in https://hbiostat.org/proj/covid19. The case study for VIOLET 2 also contains random effect analyses. You’ll see that the variance of the random effects needed to be huge to allow for a high intra-patient correlation. This makes the model unstable, takes longer to converge, and means that the effective number of parameters in the model is very large.

The generality of the serial ordinal outcome approach is quite impressive IMHO as you can handle the usual time-to-single-event analysis, regular longitudinal analysis of continuous outcomes, and recurrent event analysis within one framework. One design consideration is that you have to measure the ordinal outcomes (those that are not fatal) also at baseline to start the Markov process.

You’ll see in the case studies that the Markov approach uses only standard frequentist or Bayesian models, and if using Bayes it is easy to uncondition on previous outcome states when you’re finished, to get state occupancy probabilities. For the case of a terminating event (absorbing state) such as death, this is equivalent to a cumulative incidence curve. So from Markov models you can get far more than transition probabilities. The ORCHID case study shows how to get a posterior distribution for the mean time that a patient is in either of two states.

I haven’t seen this applied in clinical trials but there are many papers on ordinal longitudinal outcome modeling, for example here.

The video for the talk Ulf mentioned is here.