[R] Problem comparing hazard ratios

[Frank E Harrell Jr]

Ravi Varadhan wrote:
> Frank,
> 
> Is there an article that discusses this idea of bootstrapping the ranks of
> the likelihood ratio chi-square 
> Statistics to assess relative importance of predictors in time-to-event data
> (specifically Cox PH model)? 
> 
> Thanks,
> Ravi.

Do require(rms); ?anova.rms and see related articles:

@Article{hal09usi,
   author = 		 {Hall, Peter and Miller, Hugh},
   title = 		 {Using the bootstrap to quantify the authority of an 
empirical ranking},
   journal = 	 Annals of Stat,
   year = 		 2009,
   volume = 	 37,
   number = 	 {6B},
   pages = 	 {3929-3959},
   annote = 	 {confidence interval for ranks;genomics;high 
dimension;independent component bootstrap;$m$-out-of-$n$ 
bootstrap;ordering;overlap interval;prediction interval;synchronous 
bootstrap;ordinary bootstrap may not provide accurate confidence 
intervals for ranks;may need a different bootstrap if the number of 
parameters being ranked increases with $n$ or is large;estimating $m$ is 
difficult;in their first example, where $m=0.355n$, the ordinary 
bootstrap provided a lower bound to the lengths of more accurate 
confidence intervals of ranks}
}

@Article{xie09con,
   author = 		 {Xie, Minge and Singh, Kesar and Zhang, {Cun-Hui}},
   title = 		 {Confidence intervals for population ranks in the presence 
of ties and near ties},
   journal = 	 JASA,
   year = 		 2009,
   volume = 	 104,
   number = 	 486,
   pages = 	 {775-787},
   annote = 	 {bootstrap ranks;ranking;nonstandard bootstrap 
inference;rank inference;slow convergence rate;smooth ranks in the 
presence of near ties;rank inference for fixed effects risk adjustment 
models}
}

> 
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of Frank E Harrell Jr
> Sent: Tuesday, March 30, 2010 3:57 PM
> To: Michal Figurski
> Cc: r-help at r-project.org
> Subject: Re: [R] Problem comparing hazard ratios
> 
> Michal Figurski wrote:
>> Dear R-Helpers,
>>
>> I am a novice in survival analysis. I have the following code:
>> for (i in 3:12) print(coxph(Surv(time, status)~a[,i], data=a))
>>
>> I used it to fit the Cox Proportional Hazard models separately for every 
>> available parameter (columns 3:12) in my data set - with intention to 
>> compare the Hazard Ratios.
>>
>> However, some of my variables are in range 0.1 to 1.6, others in range 
>> 5000 to 9000. How do I compare HRs between such variables?
>>
>> I have rescaled all the variables to be in 0 to 1 range - is this the 
>> proper way to go? Is there a way to somehow calculate the same HRs (as 
>> for rescaled parameters) from the HRs for original parameters?
>>
>> Many thanks in advance.
>>
> 
> There are a lot of issues related to this that will require a good bit 
> of study, both in survival analysis and in regression.  I would start 
> with bootstrapping the ranks of the likelihood ratio chi-square 
> statistics of the competing biomarkers.
> 
> Frank
> 


-- 
Frank E Harrell Jr   Professor and Chairman        School of Medicine
                      Department of Biostatistics   Vanderbilt University