Correct Interpretation of Survival Curves I am interested in learning about how decisions (e.g. prioritization of treatment) can be made in the real world based on Survival Curves (e.g. Kaplan-Meier).
To illustrate my example, I simulated a dataset of survival times for two cohorts ("Blue" : Men, "Pink": Women) using the R programming language. In this dataset (e.g. Years Survived After Liver Surgery) , I purposefully try to show that Men initially have better survival probabilities compared to Women - but as time goes on, Women have better survival probabilities (For the sake of simplicity, I assume that there is no censoring):
library(survival)
library(ranger)
library(ggplot2)
library(dplyr)
library(ggfortify)

#create 4 mini datasets data
times = rnorm(100, 20, 1)
group = 1

data_1 = data.frame(times, group)

times = rnorm(100, 10, 1)
group = 0

data_2 = data.frame(times, group)

times = rnorm(100, 30, 1)
group = 1

data_3 = data.frame(times, group)



times = rnorm(100, 36, 1)
group = 0

data_4 = data.frame(times, group)

#create final dataset
final_data = rbind(data_1, data_2, data_3, data_4)

final_data$status = as.numeric("1")



#cohort level analysis (Kaplan-Meier)
km_trt_fit <- survfit(Surv(times, status) ~ group, data=final_data)


#plot results
autoplot(km_trt_fit)


In this hypothetical example, liver surgery is performed at time = 0.

*

*We can see that after 15 years have passed since the surgery : the average probability of a woman surviving is roughly 50%, whereas the average probability of a man surviving is still at 100%.


*However, after 30 years have passed since the surgery: The average probability of a woman surviving is still roughly at 50%, whereas the average probability of a man surviving is now at 25%.
Simply put, after liver surgery - women are at higher risk of "dying" compared to men, but as the years go on, men are at a higher risk of "dying" compared to women. Furthermore, we can see that confidence intervals generated for Men and Women at different times do not overlap, except for a brief period.
My Question: Based on these survival curves (assuming the data quality is suitable and the data is representative of the real world, negligible measurement errors, etc.), is it "reasonable" ("reasonable" solely based on the data and the results of the model, ignoring "ethical considerations" for the moment) to believe that :

*

*In the first 20 years after liver surgery, "more" healthcare resources should be spent on women.


*Between the 20th and the 30th year after livery surgery, "equal" healthcare resources should be spent on men and women.


*After the 30th year, "more" healthcare resources should be spent on men.
I know that the above questions are very vague and too complicated to have straightforward answers - there is a whole field of "health economics" that studies these problems (e.g. How much is "more"? What about outliers? Cost of misdiagnoses? Benefit of intervention? What about QALY (Quality Adjusted Life Years)? Or perhaps more variables added to the model (e.g. Cox PH) might be able to give more realistic survival curves? Perhaps with more variables, more "precise" cohorts can be defined? Do some of these patients have additional underlying medical conditions that are both severe and undiagnosed that effect survival probability after liver surgery - thus skewing these survival curves? Are certain hereditary and lifestyle related factors influential on survival probabilities but not even recorded and taken into account within the models?  etc.), using the above graphs, could such questions begin to be answered?

*

*Suppose a hospital has a limited budget. And suppose after liver surgery, a patient either comes back to the hospital every year for a checkup or twice a year for a checkup (if considered at higher risk). Each checkup costs the hospital money, but let's assume that checkups have been proven to effectively bring attention to health complications (that arise from liver surgery) which left unaddressed can result in deaths. Could the above survival graphs be used to create and justify a policy that allocates budget for women to get more checkups in the immediate years after surgery, and fewer checkups for women in the later years after surgery?

Does anyone know if survival curves generated from the Kaplan-Meier method are used to make such decisions in the real world? (E.g. I imagine it must be more difficult when there are no clear patterns in the data and the confidence intervals often overlap between cohorts). Or are Survival Curves only used for "statistical inference" (e.g. What is the effect of smoking on survival after liver surgery for men? Is the effect of smoking "statistically significant"? ) ?
Can someone please comment on this?
Thanks!
References:

*

*https://rviews.rstudio.com/2017/09/25/survival-analysis-with-r/
Note 1: I know that "hazard curves" are an integral part of Survival Analysis, and that hazard curves can be estimated by Kaplan-Meier - hazard curves provide valuable information on the "immediate hazard" of experiencing the event. However, explaining the concept of "hazard" to non-technical audiences is at times difficult compared to "survival probabilities" (e.g. survival curves monotonically decrease where as hazard curves can freely fluctuate). This is why I tried to frame my question only in the context of survival curves.
Note 2: I know that this is a hypothetical question I made up, but in the future, someone could also study the "impact of additional checkups on survival probabilities after liver surgery".
(NEW) Note 3: I am just thinking about an example - suppose I have one pot of water boiling on the stove, and another pot of water with sugar. Physics tells us that the pot containing water with sugar boils faster than the pot containing only water. So if I placed equal volumes of both liquids on the stove at the same time, it's more likely that the pot with sugar and water will boil and spill over compared to the pot with only water. One could make the argument that you should be "more attentive" to the pot with sugar/water compared to pot with only water, as the former is "riskier" than the latter. –
The pot with sugar and water likely presents a greater "hazard" than the pot with only water. The pot with sugar and water is likely to "survive for a shorter time without overflowing" compared to the pot with only water. Could the argument be made that I should direct more of my attention to the pot with sugar and water until it boils, and after I have removed it from the stove - then direct more of my attention to the pot only containing water? This kitchen example seems like a fairly reasonable interpretation from a statistics standpoint. –
Without taking into consideration the ethics of health and medicine - from a purely statistical standpoint : what is stopping us from interpreting and making decisions (e.g. prioritizing different cohorts of patients based on time-dependent risk) using the results of Survival Analysis?

The answer is unfortunately no. These curves tell you about the survival profile of men and women under the standard of care. On the other hand, your question is asking about an alternative of care. To understand whether a treatment strategy is effective, we have to understand how patients would respond to the care.
An answer to this question requires causal inference. Let $T_0$ denote the time of death for patients on the standard of care. Let $T_1$ denote the time of death for patients under the care defined by your 20 years/30 years after surgery policy. With this data, we can define an estimands such as
\begin{align*}
 \psi_\mathrm{Male}(t) &= \mathbb{P}[T_1 > t \mid \mathrm{Male}] - \mathbb{P}[T_0 > t \mid \mathrm{Male}] \\
 \psi_\mathrm{Female}(t) &= \mathbb{P}[T_1 > t \mid \mathrm{Female}] - \mathbb{P}[T_0 > t \mid \mathrm{Female}].
\end{align*}
These estimands can be interpreted the expected improvement in survival among males and females after some given time $t$, if we were to implement your policy. If it happens that $\psi_\mathrm{Male}(t)>0$ for all $t$, so that survival is uniformly better among Males under your policy, and likewise $\psi_\mathrm{Female}(t)>0$ for all $t$, then there's a clear argument for using your policy. Males and females would be better off under your policy.
Your data can't be used to answer this question since there's no information about $T_1$, the time of death under your proposed policy. For example, maybe (for whatever reason) additional care would not help females survive in their first 20 years post-surgery.
