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Hello StackEx community,

I am puzzled about a statistical analysis I'm currently performing for a paper. Despite hours of reading on logistic regression (LR) or Cox in the literature or on the forum, I'm still unsure of what's the best way to perform my analysis.

I'm studying a large cohort of +-9000 patients. In those patients, I have :

  • Baseline data at enrollment (which spans a period from 2004 to 2016) : age, gender, BMI, diabetes status, body composition with computed tomography (muscle mass, density, visceral fat, etc.)
  • A follow up time, ranging from 1 day to 14 years
  • Information of death event and/or cardiovascular (CV) event with exact date (knowing that a patient could have a CV event and die day or years after)
  • Information on any CV event history (e.g. before the enrollment)

My scientific question is the following : which are the parameters measured at baseline that are independent predictors of (1) any incident CV event, (2) death event or (3) any adverse event (CV or death)

The aim is to determine whether some body composition characteristics (besides obvious ones such as age) may be useful to stratify "at-risk" patients that could benefit from a close monitoring and/or a therapeutic intervention. I'm thus more interested by whether an event occurs at all than by when it occurs.

What I did so far :

  • I chosed a minimum of 2 years follow-up. I thus removed all patients with less than 2 years follow-up that had no event (i.e. I kept those with <2y follow-up that had either a CV event or died)
  • I computed for all patients a time-to-event metric (time-to-CV event or time-to-death)
  • I removed from consideration any patients that had history of a CV events (as this could predispose to another CV event or death)

I have tried two approaches :

  1. Logistic binary regression (LR) : taking into account all patients (mean follow up of 10 years), what are the parameters independently associated with the occurrence of a CV event, death, or an adverse event (i.e. CV or death) ?

or

  1. Cox proportional hazard : I computed the risk for a CV or death event, using "time-to-event" in the "time" variable

I'm a bit puzzled as some variables are extremely significant in the LR and not in the Cox model.

Alternatively, I was thinking of doing a LR to predict CV or death event (yes/no) at 5 years or 10 years. This would mean that I should remove all patients with less than 5 or 10y follow up and that had no event (i.e. keeping those with an event respectively from follow-up time) and then perform a LR on the resulting cohort, with a "yes or no" CV event outcome. This is an extended version of what I did in my data cleaning (i.e. I already selected those with at least 2y follow-up without event)

In a second time, I would like to compare a LR model that includes all the most signficant variables to some supervised machine learning algorithm (SVM, Random Forest, etc.) to predict CV or death events. I already tested the pipeline in R and it works good. However, in those models, the outcome is a "yes" or "no". Hence, I'm not sure whether I can just do that irrespectively or the follow-up time or whether I should do what I stated above, selecting a minimal follow-up without any event (e.g. 5 or 10 years)

What do you think?

NB : I have detailed information for CV events (type, e.g. myocardial infarction, heart failure, cerebrovascular, etc.) and their respective date. Some patients had multiple CV events: among +-8000 patients, 1300 had at least 1 incident CV event and among those 1300, 280 had 2 events and 70 had more than 2 events. For simplification, I considered them as either 0 (no incident or previous CV event) or 1 (any number of incident CV events). For the time-to-event metric, I considered the date of the first event. I'm pretty sure there might be some sophisticated model to account for this but do not know whether it would have a significant statistical impact.

Many thanks in advance for your inputs..

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2 Answers 2

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What you need is a competing-risks survival model with the possibility of repeated events. Here are problems posed by some of your choices thus far:

I chose a minimum of 2 years follow-up. I thus removed all patients with less than 2 years follow-up that had no event (i.e. I kept those with <2y follow-up that had either a CV event or died).

That introduces a bias toward worse-outcome individuals. You are throwing away all the better-outcome cases with less than 2 years follow-up.

I removed from consideration any patients that had history of a CV events (as this could predispose to another CV event or death).

It would seem that a history of CV events would be a critical baseline predictor for a model.

Logistic binary regression (LR) : taking into account all patients

With different lengths of follow-up, you can't tell whether the lack of an observed event is due to favorable baseline characteristics or short follow-up.

For simplification, I considered them as either 0 (no incident or previous CV event) or 1 (any number of incident CV events). For the time-to-event metric, I considered the date of the first event.

That throws away information about individual propensity to having multiple events.

A competing-risks, multiple-event survival model overcomes these limitations:

  • You use information about all event-free individuals throughout the time that they are observed during your study, so you don't just throw them away.
  • You can include prior CV-event history easily as a baseline covariate, along with any other predictors you choose.
  • The survival analysis directly takes the duration of observation into account in a way that a logistic regression over all patients cannot.
  • You can model CV events and death together in the same model, while allowing for multiple CV events (and, if you wish, to allow CV events that occur during the study to affect the risk of further CV events in that individual).

In summary, a proper survival model would allow you to use all the information available from all individuals in the study.

These methods are implemented, for example, in the R survival package. Cox survival models for "Multiple event types and multiple events per subject" are explained in a section of the main survival vignette. A vignette on multi-state models goes into more detail, and introduces other R packages for such modeling, like the mstate package that might be suitable for your type of data.

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Many many thanks for your input, I immediately jumped onto your suggestions and worked on it for the past few weeks. I now used a competing risk analysis and could successfully account for history of CV events and follow-up duration. Regarding the risk for adverse event or death, so far I created a binary column which is "1" at the first event that occurs between both (not very elegant but did the job..), since my scientific question is "What is the time-to- first adverse event (whether death or CV event).

I did not accounted for multiple events yet (I'm in a hurry to send my thesis) but I will certainly try that as soon as I'll start writing the paper.

All the best

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    $\begingroup$ I hope you read all the suggested documents. Survival analysis is a big field and takes intensive study before proceeding with analysis. $\endgroup$ Aug 31, 2021 at 11:27
  • $\begingroup$ Please provide additional details in your answer. As it's currently written, it's hard to understand your solution. $\endgroup$
    – Community Bot
    Aug 31, 2021 at 12:26

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