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I use the Kaplan-Meier estimator to represent survival functions between two groups. Suppose I have X events at a given time t. How can I predict time t+k to obtain X+i events? As with time series, is there a way to make predictions on survival data?

To give you some details: First: suppose I have 50 events on 12/07/2024 for 500 observations. My goal is to reach 65 events. Is there any way of predicting when these 65 events will be reached (with an IC95%)? Second: assuming I have a Weibull distribution, can I run simulations to predict different forms of the survival function?

Thank you

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    $\begingroup$ Please edit the question to provide more details about the specific situation you are trying to work with and the types of predictions you want to make. You can't extrapolate Kaplan-Meier curves beyond the last event time, but predictions within the range of event times is certainly possible both for Kaplan-Meier and Cox models. With parametric models you can even try to predict beyond the range of event times, provided that you are willing to assume that the parametric form is correct. As it stands, this question is a bit too vague to get a helpful answer. $\endgroup$
    – EdM
    Commented Jul 11 at 17:57

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A Kaplan-Meier curve displays the survival data available to date, but you need to make assumptions to extrapolate. If you are willing to assume a particular parametric distribution, like the Weibull you suggest, you can fit that distribution to the data to date, obtain estimates for the parameters of the distribution, and then extrapolate. The R survival package contains a survreg() function for fitting parametric models to survival data, and associated functions for making predictions.

For example, if you started with 500 individuals at some single specific date, still had information on all 500, and found 50 events by 12/07/2024, then you have 90% survival on that date. To estimate the time for 65 events, if you expect to continue having information on all remaining cases, you could ask the software to use the parameter estimates from the current data to find the time consistent with the corresponding 87% survival.

It would be wise to play with the parameters of the Weibull distribution to see how much that time estimate to reach 65 events would vary, based on the uncertainty in the parameter values. You can use tools in the survival package for simple work, or do more complicated simulations with packages like simsurv.*

You still will be faced with the problem that past experience might not represent future performance. As many illustrious people have noted, including Niels Bohr and the great US philosopher L. P. Berra: predictions are hard, especially about the future.

*Be careful with Weibull and other parametric survival distributions, as parameterizations can differ among packages. See this page among many others.

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  • $\begingroup$ Thank you for your answer. So I'm going to understand how SIMSURV package works. I work with SAS and I already know that the LIFEREG procedure is identical to SURVREG. I will see what I can do with it .. $\endgroup$
    – Guillaume
    Commented Jul 13 at 15:32

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