How to justify your survival curve extrapolation methodology

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Clinical trials are typically of (relatively) short duration, but innovative treatments may impact patient survival over multiple years. Health economists and outcomes researchers often are faced with the challenge of extrapolating clinical trial survival curves to estimate long-term survival gains for the typical patient. These estimates may be done parameterically (e.g., exponential, Weibull, Gompertz, log-logistic, gamma, piecewise), using expert elicitation, or other methods. But a key question is how do researchers justify this choice?

A paper by Lattimer (2013) provides options for justifying extrapolation choice. The first option is visual inspection. This approach just visually checking whether the model

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