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Almost exclusively, I have never seen any references or examples of Survival Analysis being used to estimate Survival Probabilities at the individual patient level. Survival Analysis is almost exclusively used to estimate time dependent survival probabilities at the "cohort" level (i.e. group level):

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For example, in the above graphs - time dependent survival probabilities (for COVID-19) are estimated for groups of patients on different blood thinning medicines ("red" vs "blue"). Based on the above graphs, it would appear that patients in the "red cohort" consistently have better survival probabilities compared to patients in the "blue cohort". However, this is analysis is only at the "cohort level" (i.e. groups of patients).

My Question: Are there any references which explicitly state and justify why Survival Models (e.g. Kaplan-Meier, Cox PH, AFT, ML based Survival Models like Random Survival Forest, etc.) are almost always used to estimate cohort survival probabilities, but are never used to estimate the survival probabilities of individual patients within the cohorts? For example, if a patient named John Smith is in the "blue cohort" - survival probabilities are generally averaged and estimated for all patients within the "blue cohort" : if another patient named Joseph Smith is also in the "blue cohort", regardless of the Survival Model being used, the Survival Model will tell you that John Smith and Joseph Smith have virtually the same survival probability at any future time point.

Is there any reasons why Survival Models are never used to separately estimate the survival probabilities of John Smith and Joseph Smith? Are there any mathematical reasons that explain why this is literally never done in the entire canon of Survival Analysis literature (e.g. just recently some authors have attempted Survival Analysis at the individual level https://era.library.ualberta.ca/items/f83088e6-eda0-4596-b2da-6eec608998ee) ? Perhaps in practice, the variability (i.e. confidence intervals) at the individual level is simply too high for useful estimates?

But are there any standard references which explain why Survival Analysis is almost never used at the individual level?

Thanks!

References:

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    $\begingroup$ Those are not survival forecasts for the cohorts but how many survived. For individuals, it would be a horizontal line at $1$ suddenly dropping to $0$ when that person died. How would you interpret $374$ vertical lines on a chart plus $233$ overlapping horizontal lines which never drop? $\endgroup$
    – Henry
    Nov 19, 2021 at 18:42
  • $\begingroup$ @ Henry: thank you for your reply! You are correct - those are not survival forecasts. I tried to simulate something like that over here: stats.stackexchange.com/questions/552569/… $\endgroup$ Nov 19, 2021 at 18:57
  • $\begingroup$ Not specific to survival curves, but probably what you need: Liu and X.-L. Meng. There is individualized treatment. why not indi- vidualized inference? Annual Review of Statistics and Its Application, 3(1):79–111, 2016. doi: 10.1146/annurev-statistics-010814-020310. URL doi.org/10.1146/annurev-statistics-010814-020310. $\endgroup$ Nov 20, 2021 at 20:11

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Therneau and Grambsch clearly state (page 261):

The building block for all of the expected survival work is the individual expected curve.

What leads to confusion is that the "individual expected curve" $S(t)$ is the complement of a cumulative probability distribution $F(t)$ of event times, $S(t)= 1-F(t)$. It isn't a point estimate of a single survival time, as people sometimes assume. You can calculate point estimates of median or mean survival times and associated errors from survival curves. Most survival curves in practice, however, are so broad that you don't get very precise point estimates.

That doesn't, however, answer your question: "Is there any reasons why Survival Models are never used to separately estimate the survival probabilities of John Smith and Joseph Smith?" when both are in the same cohort. The answer is that "cohorts" in a survival model are defined by shared covariate values. If John and Joseph have the same set of covariate values, then the model does not distinguish their survival probabilities at all. Only if the model incorporates covariates that differ between John and Joseph might they have different survival probabilities.

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