R help - Nov 2010 - interpretation of coefficients in survreg AND obtaining the hazard function for an individual given a set of predictors

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)

mca <- coxph(slr~as.factor(grade2=='high'), data=stc1)
mcb <- coxph(slr~as.factor(grade2), data=stc1)
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
(Intercept)     as.factor(grade2)low 
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?
b) how come the intercept coefficient changes (the scale parameter does not 
change)?

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.
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.

Any help would be greatly appreciated,

David Biau.



      
	[[alternative HTML version deleted]]

On Nov 13, 2010, at 12:51 PM, Biau David 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.
Have you read:

?survreg.distributions  # linked from survreg help
>
> Here is an example of the codes that points out my problem:
> - data is stc1
> - the factor is dichotomous with 'low' and 'high'
categories
Not an unambiguous description for the purposes of answering your many  
questions. Please provide data or at the very least: str(stc1)
>
> slr <- Surv(stc1$ti_lr, stc1$ev_lr==1)
>
> mca <- coxph(slr~as.factor(grade2=='high'), data=stc1)
Not sure what that would be returning since we do not know the  
encoding of grade2. If you want an estimate on a subset wouldn't you  
do the subsetting outside of the formula? (You may be reversing the  
order by offering a logical test for grade2.)
> mcb <- coxph(slr~as.factor(grade2), data=stc1)
You have not provided the data or str(stc1), so it is entirely  
possible that as.factor is superfluous in this call.

> 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
> (Intercept)     as.factor(grade2)low
> 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?
Probably because the order of the factor got reversed when you changed  
the covariate to logical and them back to factor.
> b) how come the intercept coefficient changes (the scale parameter  
> does not
> change)?
>
> 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
Answered by Therneau earlier this week and the next question last month:

https://stat.ethz.ch/pipermail/r-help/2010-November/259570.html

https://stat.ethz.ch/pipermail/r-help/2010-October/257941.html

> 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.
> 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.
>
> Any help would be greatly appreciated,
>
> David Biau.
>

David Winsemius, MD
West Hartford, CT

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)
>
> mca <- coxph(slr~as.factor(grade2=='high'), data=stc1)
> mcb <- coxph(slr~as.factor(grade2), data=stc1)
> 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
> (Intercept) ? ? as.factor(grade2)low
> 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