Practicalities of using Markov Longitudinal Ordinal Models in Cardiovascular Outcome Trials

Cardiovascular outcome trials often have a composite outcome - e.g. Death, Stroke, MI, and Hospitalisation - lumped all together than analysed as time to event.

More recently, the “win ratio” has started to be advocated.

Alternatively, Prof. Harrell’s Markov Longitudinal Ordinal Model [Markov Longitudinal Ordinal Model] has been proposed - and has showed improved power and explainability within COVID trials and others.

If we were to use this approach to cardiovascular outcome trials - what are the thoughts on adapting the ordinal (for the say 4 events above) so it can be practically used?

Death - remains death and an absorbing state.

Presumably - we don’t want to model MI or Stroke as an event that occurs on a single day - but once a patients experiences it - continues to be in this state (but can still climb to even worse states).

We would add in an additional state of having had a stroke and an MI at some point in the past.

How should we deal with hospitalisation - as an type of event like I propose for stroke and MI above - or as a state you can be in that day. Perhaps if the former - we need additional states of hospitalised once, twice, thrice etc…or perhaps we should switch to using it as a daily state so can calculate number of days in hospital (which would be helpful for cost effectively analysis).


Had MI and Stroke
Had Stroke
Had MI
Been hospitalised 3+ times
Been hospitalised 2 times
Been hospitalised 1 times
Alive + Well

Welcome any thoughts or suggestions - or indeed if any empirical data…

Hospitalization is the easy one. Don’t model it as “Been hospitalized 2 times” but rather as a daily/weekly/monthly status variable. Someone needing multiple or long hospitalizations will be counted as worse than someone hospitalized once for one day. This is all automatic.

Stroke is trickier. How long does a stroke last? The easiest way to handle this is to have a functional status/disability measure as part of the scale to capture the sequelae of the stroke. Hospitalization status is a rough way to do this, with worse strokes leading to more days in the hospital or possibly to the absorbing state of death. But better to have a stroke outcome scale that is repeatedly measured.

Many thanks,

Thought as much about hospitalisation - but as it represents a change from current practice good to get your opinion. We have a lot of position papers / consensus documents defining outcome measures (“endpoints”) but never on the analysis of them which is intrinsically linked.

An using an ordinal scale e.g. mRS would be interesting - but would be an expensive addition to a CVOT (would need detailed assessment and adjudication) - and we wouldn’t have for analysis of retrospective trials.

I wonder if anyone has done a head-to-head of survival analysis / win ratio / longitudinal for a CVOT?

I hope someone has. I’ve only done power simulations of Markov ordinal models vs. time to recovery as reported here.

Dear Dr. @f2harrell,

May I ask a small question? Do I cite the Peterson & Harrell (1990) paper for the Markov Longitudinal Partial Proportional Odds model fitted with {VGAM}?


No, the 1990 paper is for the univariate case where time is not involved.

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