# [R] Re : interpretation of coefficients in survreg AND obtaining the hazard function for an individual given a set of predictors

Thomas Lumley tlumley at uw.edu
Tue Nov 16 20:36:06 CET 2010

A coefficient of -0.4 means that survival times are multiplied by
exp(-0.4), that is, people survival only 67% as long.

-thomas

On Wed, Nov 17, 2010 at 4:32 AM, Vincent Vinh-Hung <anhxang at gmail.com> wrote:
> Thanks for sharing the questions and responses!
>
> Is it possible to appreciate how much the coefficients matter in one
> or the other model?
> Say, using Biau's example, using coxph, as.factor(grade2 ==
> "high")TRUE gives hazard ratio 1.27 (rounded).
> As clinician I can grasp this HR as 27% relative increase. I can
> relate with other published results.
> With survreg the Weibull model gives a coefficient -0.4035245: is it
> feasible or meaningful to translate it to HR?
>
>
> Vincent Vinh-Hung
> Geneva University Hospitals
>
> On Sun, Nov 14, 2010 at 6:51 AM, Biau David <djmbiau at yahoo.fr> wrote:
>> Dear R help list,
>>
>> I am modeling some survival data with coxph and survreg (dist='weibull') using
>> package survival. I have 2 problems:
>>
>> 1) I do not understand how to interpret the regression coefficients in the
>> survreg output and it is not clear, for me, from ?survreg.objects how to.
>>
>> Here is an example of the codes that points out my problem:
>> - data is stc1
>> - the factor is dichotomous with 'low' and 'high' categories
>>
>> slr <- Surv(stc1$ti_lr, stc1$ev_lr==1)
>>
>> mwa <- survreg(slr~as.factor(grade2=='high'), data=stc1, dist='weibull',
>> scale=0)
>> mwb <- survreg(slr~as.factor(grade2), data=stc1, dist='weibull', scale=0)
>>
>>> summary(mca)$coef >> coef >> exp(coef) se(coef) z Pr(>|z|) >> as.factor(grade2 == "high")TRUE 0.2416562 1.273356 0.2456232 >> 0.9838494 0.3251896 >> >>> summary(mcb)$coef
>>                                       coef             exp(coef)
>> se(coef)             z                     Pr(>|z|)
>> as.factor(grade2)low -0.2416562 0.7853261     0.2456232     -0.9838494
>> 0.3251896
>>
>>> summary(mwa)$coef >> (Intercept) as.factor(grade2 == "high")TRUE >> 7.9068380 -0.4035245 >> >>> summary(mwb)$coef
>> 7.5033135       0.4035245
>>
>>
>> No problem with the interpretation of the coefs in the cox model. However, i do
>> not understand why
>> a) the coefficients in the survreg model are the opposite (negative when the
>> other is positive) of what I have in the cox model? are these not the log(HR)
>> given the categories of these variable?
>
> No. survreg() fits accelerated failure models, not proportional
> hazards models.   The coefficients are logarithms of ratios of
> survival times, so a positive coefficient means longer survival.
>
>
>> b) how come the intercept coefficient changes (the scale parameter does not
>> change)?
>
> Because you have reversed the order of the factor levels.  The
> coefficient of that variable changes sign and the intercept changes to
> compensate.
>
>
>> 2) My second question relates to the first.
>> a) given a model from survreg, say mwa above, how should i do to extract the
>> base hazard and the hazard of each patient given a set of predictors? With the
>> hazard function for the ith individual in the study given by  h_i(t) =
>> exp(\beta'x_i)*\lambda*\gamma*t^{\gamma-1}, it doesn't look like to me that
>> predict(mwa, type='linear') is \beta'x_i.
>
> No, it's beta'x_i for the accelerated failure parametrization of the
> Weibull.  In terms of the CDF
>
> F_i(t) = F_0( exp((t+beta'x_i)/scale) )
>
> So you need to multiply by the scale parameter and change sign to get
> the log hazard ratios.
>
>
>> b) since I need the coefficient intercept from the model to obtain the scale
>> parameter  to obtain the base hazard function as defined in Collett
>> (h_0(t)=\lambda*\gamma*t^{\gamma-1}), I am concerned that this coefficient
>> intercept changes depending on the reference level of the factor entered in the
>> model. The change is very important when I have more than one predictor in the
>> model.
>
> As Terry Therneau pointed out recently in the context of the Cox
> model, there is no such thing as "the" baseline hazard.  The baseline
> hazard is the hazard when all your covariates are equal to zero, and
> this depends on how you parametrize.  In mwa, zero is grade2="low", in
> mwb, zero is grade2="high", so the hazard at zero has to be different
> in the two cases.
>
>     -thomas
>
> --
> Thomas Lumley
> Professor of Biostatistics
> University of Auckland
>
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>

--
Thomas Lumley
Professor of Biostatistics
University of Auckland