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Re: st: repeat: predict after -streg-

From   Steven Samuels <>
Subject   Re: st: repeat: predict after -streg-
Date   Fri, 13 Jul 2007 12:20:38 -0400


You don't need medians at all, just estimated 30 day readmission rates. I'm not up on this literature, but you might try the following:

1. Fit a survival model with hospital random effects, using -streg-, - stcox-, or -gllamm- with the -frailty- options to define the distributions of the random effects. You can probably improve your predictive model if you add hospital factors as predictors.

2. Rank on the estimated hospital effects. (If you have hospital level factors in your model, add their contribution to the random effect). You can convert the model parameters to estimates of the probabilities of 30 day readmission.

I would start with -streg- and -stcox- because you have already - stset- your data. Try different distributions for survival time and (for -streg-) different frailty distributions. You don't have to believe that these distributions fit beyond 30 days. Rank the estimated hospital effects, adjusted for patient covariates (log survival time scale or log hazard scale). Check on the agreement of the rankings from the different specifications. You may be able to use BIC or some other criterion to choose a "best" model. If so, create predictions of the 30 day readmission rates and CI's from this model. Then show the predictions and CI's on a graph. If you cannot choose between models, you will have to find a way of expressing the uncertainty. One possiblity is to average the 30 day predictions, weighting perhaps on some criterion of model quality. I don't know the literature on model averaging, so I cannot give you a good reference here.

Only -gllamm- will allow interactions of hospital with other factors. And, -gllamm- will produce the empirical Bayes estimates of the readmission rates; estimates for smaller hospitals will be pulled in towards the mean. For estimating the distribution of the hospital re-admission rates, EB will shrink too much: the standard deviation for the "sample" of estimates will be smaller than than that estimated for the assumed distribution of the random effects. Perhaps you can implement a Bayesian ranking scheme which will not overshrink. See: T Louis & W Shen (1999) Innovations in Bayes and empirical Bayes methods: estimating parameters, populations and ranks. Statistics in Medicine 18:17-18, pp 2493-2505.

This all assumes you have lots of hospitals, but not enough observations to estimate a separate curve for each.

The following may also give you some ideas (I haven't read it): Lisa I. Iezzoni. "Risk Adjustment for Measuring Health Care Outcomes", Health Administration Press, 1997, 2nd edition.


On Jul 12, 2007, at 2:33 PM, Jeph Herrin wrote:

Bill, Sam:

This is exactly the insight I was missing. Of course the
predicted median is high, my crude median is high. And
yes, the model is not great, even though all of my covars
are highly (P<0.0001) significant.

Any other thoughts on how to handle this? We are creating
hospital rankings based on 30-day readmission rates; the
problem is that hospitals which discharge patients too
soon may be losing them to mortality before they have a
chance to be readmitted, so I want to account for the
competing risk of death vs readmission. Unfortunately,
we can only follow them for 30 days, during which only
22.5% are readmitted.

The answer seems to be, I can get estimated median time to
readmission for each hospital, adjusted for my covars
(perhaps refined), but these will not translate to 30day
readmission rates because my model does nothing to discriminate
between those readmitted before 30 days and those readmitted
after, it only explains incremental differences in time
to failure.

Steven JH Samuels
18 Cantine's Island
Saugerties, NY 12477
EFax: 208-498-7441

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