[R] censored quantile regression

[Ashley Isaac Naimi, Mr]

Hi Allen,

Thanks for your response. Regarding the issue that Portnoy and PH estimators may not compute parameters in the tail, I believe this is dependent on the amount of censoring (e.g., in the extreme case, if all observations are censored in the upper tail, one cannot obtain estimates in the absence of parametric assumptions). Furthermore, it could not explain the problem I encountered, since other fitting methods did not provide what I needed, nor was able to obtain parameter estimates at the desired quantile (0.9th) in the absence of censoring.

Dr Koenker offered a simple solution, which was to replace the last line with:

summary(q2, taus = 1:9/10)

instead of requesting the desired taus in the crq() function.

Regards,

Ashley

Ashley I Naimi, PhD
Assistant Professor
Department Obstetrics and Gynecology
McGill University
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web: www.ashleyisaacnaimi.com<http://www.ashleyisaacnaimi.com>
email: ashley.naimi at mcgill.ca<mailto:ashley.naimi at mcgill.ca>
phone: 514.574.8946
fax: 514.834.1678
-----------------------

On Feb 6, 2015, at 2:51 PM, Allen Bingham <aebingham2 at gmail.com<mailto:aebingham2 at gmail.com>> wrote:

Ashley,

Looking at the code for the crq function it appears that with method="Portnoy" the tau value is not passed to the fitting function (crq.fit.por) and that function appears (I didn't delve into the code to make sure of this ...) to calculate the grid of tau values given the nature of the data, formula, etc. ---

--- more telling though is the following snippet I copied from the documentation of the crq function, specifically it states (in part) [I've split apart the pertinent section first]:

  "... Both the Portnoy and Peng-Huang estimators may be unable to compute estimates of
   the conditional quantile parameters in the upper tail of distribution.


  ... Like the Kaplan-Meier estimator, when censoring is heavy in the upper tail the
  estimated distribution is defective and quantiles are only estimable on a sub-interval
  of (0,1). The Peng and Huang estimator can be viewed as a generalization of the Nelson
  Aalen estimator of the cumulative hazard function, and can be formulated as a variant
  of the conventional quantile regression dual problem. See Koenker (2008) for further
  details. This paper is available from the package with vignette("crq"). ...  "

... so I'm guessing that using one of the other fitting methods may be get you what you need --- HOWEVER I'm only looking at the underlying code and documentation for same --- I'm completely ignorant of the statistical methods you are trying to implement --- and whether or not one of the other fitting methods is appropriate to your analyses.

Regardless it seems to me (IMHO) that the documentation for the crq function should indicate that the "tau" or alternatively the "taus" supplied to the crq function are only used with a subset of the method values.

Hope this helps-Allen
______________________________________
Allen Bingham
Bingham Statistical Consulting
aebingham2 at gmail.com<mailto:aebingham2 at gmail.com>

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-----Original Message-----
From: Ashley Isaac Naimi, Mr [mailto:ashley.naimi at mcgill.ca]
Sent: Tuesday, January 20, 2015 7:52 AM
To: r-help at r-project.org
Subject: [R] censored quantile regression

Hi there,

I've generated the following data:

library(quantreg)
library(survival)

set.seed(789)
N <- 2000
u <- runif(N)
x1 <- rbinom(N,1,.5)
x2 <- rbinom(N,1,.5)
x1x2<-x1*x2
lambda <- 1 + 1.5*x1 + 1.5*x2 + .5*x1x2
k <- 2
y <- lambda*((-log(1-u))^(1/k));max(y)
c <- runif(N,max=15)
event = as.numeric(y<=c)
mean(event);table(event)
cens <- 1-event
table(cens);mean(cens)
time <-as.matrix(ifelse(event==1,y,c))

St<-Surv(time,event,type="right")

To which I've fit the following censored quantile regression model:

q2 <- crq(St~x1 + x2 + x1x2,tau=.9,method="Portnoy")
summary(q2)

As one can see, I'm interested in the 0.9th quantile. But summary(q2) returns only the 20th to 80th percentiles (by 20). How can I get only the 0.9th quantile (aka the 90th percentile)?? All I actually need is the parameter estimate for the interaction (x1x2) for the 90th percentile. I know how to extract it if I were able to obtain estimates at tau=0.9, but no luck. Even though I request the 90th percentile in crq (i.e., "tau=0.9"), the summary function keeps returning the same set of (unwanted) percentiles (20th, 40th, 60th, 80th).

I’m using R version 3.1.2 (2014-10-31) -- "Pumpkin Helmet”, Platform: x86_64-apple-darwin13.4.0 (64-bit).

Cheers,

Ashley I Naimi

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