# Accelerated Failure Time scale parameter excessively large when data is right censored

I am using an accelerated failure time model with the Weibull distribution to predict failure times. My failure times range from 1 - 365, with many (80%) data points that are right censored (no observed failure). Among the observations that did have a failure, the median time to failure was 90 days. When you include the machines that make it all the way through the year, the distribution of failure time is U shaped - lots of mass between 1-90 days, and lots of mass for the machines that last the year.

According to survreg I can get the scale and shape parameters for the Weibull distribution from a survreg fit. The scale parameter is equal to exp(intercept term) from survreg, which in my case is exp(9.3) ~ 11k. This seems excessively large, for example

hist(rweibull(100000, scale = 11000, shape = 0.5))


shows failure times that are extremely large - the median of that histogram is 5000 days, nearly 14 years! I understand that for most of the data we could not observe a failure, so the estimated time until failure would be somewhat large, but this is a bit unreasonable for prediction. Is there anything I can do with the model or the data, or is this phenomenon because 80% of the data is right censored and we don't know any failure times beyond a year?

• If you know things not present in your estimate, it sounds like you are perhaps looking for a more Bayesian approach. – Glen_b Feb 27 '13 at 21:55
• I see, so I should attach a prior on the scale parameter? What would be a good prior for the Weibull? – JCWong Feb 27 '13 at 22:18
• A good prior is one that reflects your prior knowledge. On the other hand, if you're looking for a convenient prior, it looks to me (on a quick glance) like if you had a Weibull prior on the precision (inverse of scale) with the same shape parameter as the data, you could perhaps bring the prior in as pseudo-data, but I didn't follow the algebra through to check that it works. One thing to consider if you have a convenient-but-not-particularly-like-your-actual-prior distribution is the possibility of mixtures of such distributions. – Glen_b Feb 27 '13 at 22:31
• Perhaps this paper may be of some marginal help to you – Glen_b Feb 27 '13 at 22:39