[R] defining custom survreg distributions

From: Michael Townsley <uctqmkt_at_ucl.ac.uk>
Date: Sat 23 Apr 2005 - 01:14:37 EST

Dear R Helpers,

I am trying to carry out survival analysis in the presence of long term survivors (immunes/cureds). This involves using a split population model (some call it a mixture model) where the assumption of eventual failure is relaxed. I am following closely the formulation by Maller and Zhou (1996).

Parametric modelling in this situation involves the introduction of a new parameter, p: the proportion of susceptibles. For the Weibull the cumulative distribution function would look like:

F(t) = p*[1 e^(-lambda*t)^scale]

where [...] is the conventional CDF for the Weibull distribution.

I have spent a fair deal of time trying to create a new survreg distribution but have made next to no progress. I understand that there are four 'primary' distributions and any other distribution can be derived from transformations of these. I am unclear how I might 'declare' this new parameter in the newly defined distribution. I am keen to establish how to do this for more than just the Weibull.

Searching R-Help hasn't led me to any obvious solution. The survreg.distribution help page has an example for user-defined distributions but it only looks like a name change.

Can anyone point me in the right direction? It had occurred to me that I could define the likelihood function myself and use mle() but I am uncertain whether this is appropriate for censored data.

Thanks for any advice (and great software......and support),

MT



Michael Townsley
Email: m.townsley@ucl.ac.uk

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