[R] Weights using Survreg

[Terry Therneau]

I agree with David that poisson regression would be the simplest thing.
It's a consequence of the poison formulation and an exponential "trick"
  E(#breaks) = breaks per meter * length in meters
             = exp(Xb) * exp(log(length))
             = exp(Xb + log(length))

X = covariates that affect "breaks per meter", b=coefficients 
log(length) appears as an offset, i.e., a covariate that has a known
coefficient of 1.

You could also use log(length) as an offset in a Cox model, for the same
logic.  
  relative risk that a given pipe breaks = length * risk per meter
                                        = exp(Xb + log(length))

You need to decide if such a model is scientifically defensible, e.g.,
if this involved flexing I would expect breakage to go up faster than
linear.
 
Notes: offset has always been a part of coxph and survreg, time to
improve the documentation I guess
   I forgot to include the context in my first reply.

Terry T.


On Tue, 2011-09-06 at 12:19 -0400, David Winsemius wrote:
> I think you are replying to Dr Therneau without including this context:
> >> --- begin----
> >> Survreg produces MLE estimates.
> >>
> >> For your second question, don't know what you are asking.  Can you be
> >> more specific and detailed?
> >>
> >> ---begin included message --
> >> Do you know if the parameters estimators are MLE estimators?
> >>
> >> One more question:
> >> In my case study I have failures that occured on different objects  
> >> that
> >> have different age and length, could I use weight to find the  
> >> estimates of a
> >> weibull law and so to find the probabilty of failure per unit of  
> >> length
> >> for example?
> -----end---------
> 
> On Sep 6, 2011, at 9:50 AM, Boris Beranger wrote:
> 
> > Sorry when we talk about about MLE estimates does that mean WLE?I am  
> > trying
> > to understand if the survreg function is allowing a weight for each  
> > density
> > function when calculating the likelihood.
> >
> > In my second question I was trying to explain that my problem is  
> > that I have
> > pipes of different length and I want to know their probability to  
> > break per
> > metre. My idea was to weight each of my observations to get estimate
> > probabilities per metre.Does that sound realistic?
> 
> I have generally used Poisson regression [ glm(...,  
> family="poisson") ] in that situation. It lets you do two things: a)  
> apply weighting by using offset=log(length_of_pipe) and b) model  
> multiple breaks in a pipe if such an occurrence is possible. (It also  
> produces an MLE estimate if that feature is of some special importance.)
> 
> I respectfully defer to anything Dr Therneau says on this matter and  
> am only really posting in hopes that he will clarify whether there is  
> any value in thinking about the use of offset terms in either   
> parametric or Cox survival models.
> 
> There is an offset argument in glm but I do not see one (any longer?)  
> in survreg or coxph. I have what must be an extremely vague memory of  
> seeing an offset term in coxph formulas, but I do not see such a  
> possibility described in the current help pages. Therenau and Grambsch  
> indicates that CPH models with certain forms of frailty are similar to  
> models with offsets but the help apge for `Surv` specifically warns  
> against the use of "gamma/ml or gaussian/reml [frailty terms] with  
> survreg".
>