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A colleague just told me that he categorises continuous data in survival analysis using "quartiles by event". He essentially uses cut-off points that equally distribute events into four groups.

This strikes me as dubious approach, as you are basing your categories on your data, rather than pre-formed hypotheses. Has anyone heard of this method of categorisation? I couldn't find any references to "quartile by event" anywhere!

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    $\begingroup$ Your intuition has merit. $\endgroup$
    – Alexis
    Commented Jul 11, 2020 at 19:08

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Although categorizing a continuous variable is generally poor practice, as the discussion linked by @Alexis shows, there are some parts of Cox model development in which categorizing a continuous variable into strata can play a role.

In Section 20.1.7 of Regression Modeling Strategies, second edition Harrell says on page 482: "Stratification is useful for checking the PH [proportional hazards] and linearity assumptions for one or more predictors." On page 481, he notes another acceptable use of stratification:

Also, one may know that a certain predictor (either a polytomous one or a continuous one that is grouped) may not satisfy PH and it may be too complex to model the hazard ratio for that predictor as a function of time.

If those are the types of reasons that your colleague is categorizing, then the procedure makes sense. It will provide 4 strata with equal numbers of events.

If the reason is simply to turn the continuous variable into 4 categories for the final model, then your sense is quite correct. Turning the continuous variable into 4 categories uses up degrees of freedom that would better be spent on continuous modeling, say with restricted cubic splines.

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  • $\begingroup$ Thank you for your comprehensive answer, I really appreciate it! Just to clarify, is there little difference in validity between using quartiles to determine cut-offs for strata of your continuous variable and using quartiles "by event" (trying to equally spit the events between groups)? There's no intrinsic bias to using your collected data to determine your cut-offs? $\endgroup$
    – Luke
    Commented Jul 12, 2020 at 7:24
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    $\begingroup$ @Luke there is no inference on a stratification factor in a Cox model, so in that context it's more a question of what ends up best representing the data rather than bias with respect to the stratified variable. Calculations of hazard ratios are based on event times, so I see some point in using the events to split. If there were no censoring, splitting by events or by quartiles of the predictor would give the same result. The problem would be if you used the process to create a 4-level categorical predictor in the model rather than stratifying by it. $\endgroup$
    – EdM
    Commented Jul 12, 2020 at 11:36
  • $\begingroup$ Ahh I see! So to confirm my understanding, this approach is valid to institute a stratification factor (as a way to include the variable in your model when it violates PH assumptions, without providing a HR for the variable). However, it is NOT valid if including the variable as a standard categorical variable in your model associated with an HR. In this context, a better approach would be restricted cubic splines, with a worse alternative being standard quartiles (lower number of df) $\endgroup$
    – Luke
    Commented Jul 12, 2020 at 12:15
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    $\begingroup$ @Luke yes. The "validity" argument has mostly to do with not throwing away useful data and not setting up massive unrealistic breaks by categorizing. You might end up using as many or more df with a spline model, but the spline model would use the data more efficiently. Categorizing by age could mean a massively different prediction for someone who is 49 years and 11 months old versus someone who is 50 years old. Splines avoid that problem, too. $\endgroup$
    – EdM
    Commented Jul 12, 2020 at 12:21
  • $\begingroup$ I think using quartiles (and other forms of binning) is a poor general approach to smoothing regressions. See for example, Buja, A., Hastie, T., and Tibshirani, R. (1989). Linear Smoothers and Additive Models. The Annals of Statistics, 17(2):453–510. $\endgroup$
    – Alexis
    Commented Jul 12, 2020 at 21:47

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