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I have a dataset with 10,000 patients, and for each patient, I have the following information:

  1. Biological sex (male/female)
  2. Baseline age (age at the time the patient joined the study)
  3. Age at the event of interest or age at the end of the follow-up period
  4. An event column (1/0) indicating whether the event occurred or not for each patient.

My task is: create the model that allows to predict individual survival estimates for new pateints based on their sex and current age (it is simlified set up).

My question is: how can I incorporate the current age into the prediction model? (meaning, taking into consideration that new patient do not have an event recorded at the age he/she came for an in-patient visit).

Comment: I would like to use age as a time-scale.

I apologize if this is a basic question, and I appreciate any guidance you can provide. Thank you in advance!

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2 Answers 2

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Using age as the time scale (setting the time = 0 reference point to birth or some fixed age) can sometimes be preferable to evaluating survival in terms of time since study entry. The thing to understand in that case is that your survival data then are left truncated. Someone who enters the study at, say, 55 years of age provides no information about someone who might have already had the event before 55 years of age and never entered the study. That's sometimes called a "delayed entry" study.

Klein and Moeschberger discuss truncation in Section 3.4, providing a similar example of age at death among individuals living in a retirement home. Anyone who didn't live long enough to enter the retirement home obviously isn't included in the study population, so evaluation of survival is conditional upon having lived that long.

Left truncation is handled by the counting process data format for survival times, the same as is used for time-varying covariate values in the R survival package. In your case, the left end of an individual's time interval would be the age at study entry and the right end would be the age at event (or at last follow up if no event yet). Depending on how you are modeling the data, there might be practical problems if there are a few individuals who entered the study at early ages. In that case you might need to restrict analysis further, conditional upon being at some later age at study entry. See Section 4.6 of Klein and Moeschberger.

Also, note this warning from Section 9.4 of that text:

A key assumption for the left-truncated Cox model is that the event time X and the delayed entry time V are independent, given the covariates...

You'll have to apply your understanding of the subject matter to evaluate that assumption.

It sounds like you should be able to accomplish your goals with this approach. For a new patient you could use survival estimates from your data set that are conditional upon someone already having reached that new patient's age.

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  • $\begingroup$ Thank you! The reference by Klein and Moeschberger is precisely what I was looking for. To clarify, it seems that there are two approaches to derive conditional survival probabilities based on age in my case. $\endgroup$
    – nxk056
    Sep 29, 2023 at 1:23
  • $\begingroup$ 1) Treat age as a time-varying covariate: In this approach, I model the survival probabilities while considering baseline age as a covariate that can change over time for each individual. 2) Build separate estimator for each subgroup of patients: Here, I create distinct survival estimators for various patient subgroups. For each subgroup, I select patients who have survived up until a specific age (i.e., i < 0, 1, 2, ..., m, where m is the defined maximum age, e.g., 90) without experiencing the event of interest. Then, for each of these subgroups, I derive a conditional survival function. $\endgroup$
    – nxk056
    Sep 29, 2023 at 1:25
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The patient ageing is by default incorporated in your model, since any survival model has a time component to it (time,status). Since your patients are not getting younger over time,if the event occurs in the future, the patient is obviously older than when they entered the study, and older than patients who were younger when they entered the study.
You should have a column with the time to event, or alternatively if no event happened, time until you stopped following the patient. This will be your "time" instead of the age at which the event happened/at the end of the study. You could also try making a mock variable per age category of your patients and use it as an explanatory variable. Look at this paper for example : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6814612/

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  • $\begingroup$ Thank you for your response! As I understand it, there are several time-scales that can be utilized for constructing the model. You suggest using the "time-on-study time-scale", where we consider years of follow-up as the scale while adjusting for the baseline age. In this scenario, the "current age" of a new patient would serve as the baseline age. However, if I want to specifically use "Age as the time-scale" and incorporate the baseline age through left-truncation (so not as a covariate), how can I utilize the current age of the patient as a predictor? Sorry, if I misunderstood your answer. $\endgroup$
    – nxk056
    Sep 25, 2023 at 19:45
  • $\begingroup$ I do not understand what you mean by "age as the time scale". You include age as a predictor by putting time as a predictor, because time = age. $\endgroup$
    – CaroZ
    Sep 25, 2023 at 20:54

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