# I will survive!

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I have to say I’m not really a massive expert on survival analysis, in the sense that it’s never been my main area of interest/research. But I think the particular case of cost-effectiveness modelling is actually very interesting $-$ the main point is that unlike in a standard trial, where the observed data are used to determine some median estimate of the survival curve (typically across the different treatment arms), in health economic evaluations the target quantity is actually the *mean* survival time(s), because these are then usually used to extrapolate the (limited!) trial data into a full decision-analytic model, often covering a relatively large time horizon. Among many, many others , I think Chris et al make a very good point for this, here.

Anyway, one of the main implications to this is that typically the practitioners are left with the task of fitting a (range of) parametric survival model(s) to their data. Nick Latimer among others have done excellent work in suggesting suitable guidelines. (In fact, both Chris and Nick did come to talk to one of our workshops/seminars, last summer).

Over and above the necessary choice of models, I think there are other interesting issues/challenges for the health economic modeller:

- (Parametric) Survival models are often tricky because there are many different parameterisations, leading to different results presentations. This can be very confusing and without extra care lead to disastrous consequences (because the economic model extrapolates on the wrong survival curves!).
- Even when the parameterisation is taken care of, we are normally interested in characterising the full uncertainty in the joint distribution of the survival model parameters $-$ we need to do this to perform Probabilistic Sensitivity Analysis (PSA), so even in a non-Bayesian model, this is a required output of the analysis. Pragmatically, this means computing a survival curve for a large combination of parameter values and feeding each to the economic model to assess the impact of uncertainty on the final decision-making process.
- Much to my frustration (and, I realise, to the frustration of the people I keep nagging about this!), the economic models are (too) often performed in Excel. This means that while the survival analysis is done externally in a proper statistical software, then the results (usually in tabular form) are copied over the spreadsheet and used to then construct the survival curves (eg via VBA macros).

- formula can be specified using standard R notation, something like Surv(time,event)~as.factor(arm), for MLE analysis or inla.surv(time,event)~as.factor(arm), for INLA. I think I’ve managed to make the function clever enough to recognise which formula should be used depending on what method of inference is specified and also to figure out how to translate this into BUGS language.
- data is shockingly the dataset to be used.
- distr is a (vector) of string(s) indicating which parametric distribution(s) should be fitted to the data, something like distr=c(“exponential”,”weibull”). Again, to make the modellers’ lives easier, I’ve kind of made mine miserable and tried to be very clever in accounting for differences in terminology across the three packages/approaches I cater for.
- method is a string specifying what kind of analysis should be done, with values at “mle”, “inla” or “mcmc”.

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