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My question is relative to the comparison of a probability of surviving at a fixed point in time with a theorical probability of surviving.

For example, I have a cohort of patients with cancer followed during 3 years (some of them dropped out). I am interested in the probability of being alive at 2 years. This probability is estimated by the method.

I would like to compare this probability with a theorical one (ex: 20%).

Is a chi-squared test an appropriate way to do this?

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    $\begingroup$ Out of curiosity: What is "MD"? $\endgroup$
    – cdalitz
    Commented Jun 23, 2023 at 14:46
  • $\begingroup$ @cdalitz It means a medical doctor, but I have edited out the opening and closing comments. // Kant, the greeting and expressing thanks are polite, but they are considered superfluous on Cross Validated. You might be interested in taking the tour for new users. This in particular addresses what is called "chitchat". $\endgroup$
    – Dave
    Commented Jun 23, 2023 at 18:35

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A Kaplan-Meier estimate of 2-year survival should also come with the option to calculate a confidence interval. Typically, one chooses a 95% confidence interval.

If you have a specific theoretical point estimate of 2-year survival (20% survival in your case) against which to compare the observed 2-year survival, just see whether the point estimate is within or outside the confidence interval at 2 years. If it's within the confidence interval, you can't distinguish the observed survival from the theoretical value. If it's outside, you can distinguish them, at the specified confidence level.

There are a few different ways to calculate the confidence interval. Check your software for the details. The default in the R survfit.formula() function for Kaplan-Meier models is the "log" method, based on the estimated error in the cumulative hazard. So long as you don't use the "plain" method, however, you should be OK. See Section 2.1.2 of Therneau and Grambsch. Just make sure to specify which you chose when you write up your results.

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  • $\begingroup$ How to compute the confidence interval of a theorical point estimate of 2-year survival (20%) as there is no data? $\endgroup$
    – Kant
    Commented Jun 28, 2023 at 11:59
  • $\begingroup$ @Kant if the point estimate is theoretical there is no need to calculate a confidence interval for it. The only thing you need to determine is whether that point estimate is within the confidence interval of the modeled data. $\endgroup$
    – EdM
    Commented Jun 28, 2023 at 21:22

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