[R] Survreg with gamma distribution

[Prof Brian Ripley]

On Sun, 17 Oct 2004, Kuan-Ta Chen wrote:

> Hi, all:
> 
> I find survreg {survival} has provided many distributions such as weibull,
> lognormal, etc. But I wonder why it doesn't have the support for gamma
> distribution since it should be a good distr. in lifetime analysis. Can
> anybody figure out the reason?

I suspect Dr Therneau had no need of it: it is not commonly a good
distribution in medical applications.  He did however provide a way for
users to specify other distributions: see ?survreg.distributions.

> I've tried to implement the likelihood function of progressively censored
> data for gamma distr. and use optim() to solve the paramemters. The
> log-likelihood function L contains some integrations. I use tryCatch() to

It should not contain numerical integrations: all you need is dgamma and 
pgamma to specify the log-likelihood.

> capture the error when integration lead to divergence and return Inf.
> But if consequent two calls to the objective function return Inf, optim()
> will raise errors:
> 
> Error in optim(c(ga, 1/la), fr, method = "BFGS") :
>         non-finite finite-difference value [1]
> 
> What can I do except for choosing better initial values?

It seems very unlikely that the log-likelihood really is Inf, and so you
need to calculate it more carefully.  Finite-differencing numerical 
integrations is almost bound to be unstable, and you can write down the 
log-likelihood and its first derivative in terms of functions available in 
R.

> The last question, by its name "survreg", survreg does its job by
> regression,
> but why p.75 in Tableman, Kim (2004) said that "We use the S function
> survReg to fit parametric models (with the MLE approach)...". Does survreg
> use regression or MLE approach?

What do you understand by these?  There is no such thing as `regression
approach'.  survreg fits a linear regression model to log survival times,
by maximum likelihood.  Note that `regression' is often used to mean
fitting by OLS, but also often used to mean a linear model for a mean 
effect.

I suggest you find a less confusing text.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595