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I have 32 months of historical data and I am testing forecasting methodologies. I assume that only 12 months of data are available, I forecast months 13-32, and then compare actuals for months 13-32 with my forecasts for months 13-32. The data at hand shows the number of monthly deaths, starting with a fixed population at time 0, and it follows a nice exponential decay curve over time. Plot y-axis shows number of deaths, y-axis shows month elapsed since time 0.

I’ve used traditional time series forecasting and have gotten good results with exponential state space models (ETS function from R package feasts), with results that encompass the variability I’ve seen with this type of data. But I’m exploring other methodologies and am currently studying survival analysis, since I have a lot of variables that correlate with the probability of death and I have data for each study element showing progression stage each month.

So far in survival analysis I see that it is very useful for showing any effect of those variables on death rates (multivariate analysis, etc.), but at this stage I’m only interested in forecasting and simulating future curve paths in the hypothetical scenario of only having a partial curve to work with. Is survival analysis appropriate for forecasting from a partial curve? If so, how does one forecast future curve shape using survival probabilities and hazard rates (ignoring the variates)? Are there other methodologies besides ETS and survival that I should be exploring?

The below images show the survival probabilities plots, and the ETS model forecasts, with this dataset. Basically, is it possible to derive the sort of estimates using survival models that I’ve done with ETS?

Survival probabilities:

enter image description here

Time-series forecasting using ETS:

enter image description here

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  • $\begingroup$ Absolutely not. You could fit a probability based model such as Weibull or Gamma distribution and forecast for unobserved time. $\endgroup$
    – forecaster
    Commented Mar 1, 2023 at 12:11
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    $\begingroup$ @forecaster: I am a bit surprised at "absolutely not", because I think this would definitely be a reasonable approach, in combination with a lot of simulation. For instance, in survival, we know that it will monotonically decrease, be nonnegative and asymptotically approach zero. ETS may have a hard time with the latter two properties, so its longer term forecasts may be off. (It may still be a reasonable simple benchmark, especially for short horizons.) $\endgroup$ Commented Mar 1, 2023 at 12:27
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    $\begingroup$ Exactly @StephanKolassa, in ability of ETS to be non zero and also non decreasing are two reasons why ETS may not work. I’m arguing for a two parameter weibull as a simple benchmark which may be appropriate and more importantly explainable and capture DGP well $\endgroup$
    – forecaster
    Commented Mar 1, 2023 at 12:48
  • $\begingroup$ Thank you for the feedback. I'll work through cumulative hazard and survival functions using Weibull and Gamma distributions. If you know of any online examples of forecasting for unobserved time using Weibull or Gamma distributions, please let me know. Also, when using ETS I use a log transformation in order to avoid < 0 forecasts and scaled logit transformations to limit the possibilities to bands of outcomes. In my work I always deal with curves that monotonically decrease, are nonnegative, and asymptotically approach 0. $\endgroup$ Commented Mar 1, 2023 at 13:39
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    $\begingroup$ I can help you, are the first two survival curves that you have? $\endgroup$
    – forecaster
    Commented Mar 4, 2023 at 14:26

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Here are some links showing the use of survival model with the lung dataset from the survival package: Correctly simulating an extreme value distribution for survival analysis? and How to appropriately model the uncertainty of the exponential distribution model when running survival simulations?

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