[R] Predictions from "coxph" or "cph" objects

[Göran Broström]

David and Axel,

I have two comments to your discussion:

(i) The area under the survival curve is equal to the mean of the 
distribution, so the estimate of the mean should be the sum of the areas 
of the rectangles defined by the estimated survival curve and the 
successive distances between observed event times.

Thus,

 > surv <- pred$surv
 > time <- pred$time
 > sum(surv * diff(time))

should give you the (estimated) mean). (Note that time[1] == 0, and 
length(time) == length(surv) + 1)

(I do not think that David's suggestion gives the same answer, but I may 
be wrong.)

(ii) With censored data, this may be a bad idea. For instance, when the 
largest observation is a censoring time, you may badly underestimate the 
mean. Your best hope is to be able to estimate a conditional mean of the 
type E(T | T < x).

This is essentially a non-parametric situation, and therefore it is 
better to stick to medians and quantiles.

Göran Broström

On 2014-07-06 06:17, David Winsemius wrote:
>
> On Jul 5, 2014, at 9:12 PM, David Winsemius wrote:
>
>>
>> On Jul 5, 2014, at 12:43 PM, Axel Urbiz wrote:
>>
>>> Thank you David. It is my understanding that using survfirsurvit
>>> below I get the median predicted survival. I actually was looking
>>> for the mean. I can't seem to find in the documentation how to get
>>> that.
>>>
>>> options(na.action=na.exclude) # retain NA in predictions
>>> fit <- coxph(Surv(time, status) ~ age + ph.ecog, lung)
>>> pred <- survfit(fit, newdata=lung)
>>> head(pred)
>>>
>> There might be a way. I don't know it if so, so I would probably
>> just use the definition of the mean:
>>
>> sum(summary(pred)$surv* summary(pred)$time)/sum(  summary(pred)$time)
>>
>
> Er, I think I meant to type:
>
> fit <- coxph(Surv(time, status) ~ age + ph.ecog, lung)
> pred <- survfit(fit)
>
>    sum(summary(pred)$surv* summary(pred)$time)/sum(  summary(pred)$surv)
> [1] 211.0943
>
>
>> (I continue to take effort to keep my postings in plain text despite
>> my mail-clients's efforts to match your formatted postings. It adds
>> to the work of responders when you post formatted questions and
>> responses.)
>>
>>
>>> Thanks again,
>>> Axel.
>>>
>>>
>>>
>>> On Sat, Jul 5, 2014 at 1:54 PM, David Winsemius <dwinsemius at comcast.net
>>>> wrote:
>>>
>>> On Jul 5, 2014, at 5:28 AM, Axel Urbiz wrote:
>>>
>>> Dear R users,
>>>
>>> My apologies for the simple question, as I'm starting to learn the
>>> concepts
>>> behind the Cox PH model. I was just experimenting with the survival
>>> and rms
>>> packages for this.
>>>
>>> I'm simply trying to obtain the expected survival time (as opposed
>>> to the
>>> probability of survival at a given time t).
>>>
>>> What does "expected survival time" actually mean? Do you want the
>>> median survival time?
>>>
>>>
>>> I can't seem to find an option
>>> from the "type" argument in the predict methods from
>>> coxph{survival} or
>>> cph{rms} that will give me expected survival times.
>>>
>>> library(rms)
>>> options(na.action=na.exclude) # retain NA in predictions
>>> fit <- coxph(Surv(time, status) ~ age + ph.ecog, lung)
>>> fit2 <-  cph(Surv(time, status) ~ age + ph.ecog, lung)
>>> head(predict(fit,type="lp"))
>>> head(predict(fit2,type="lp"))
>>>
>>> `predict` will return the results of the regression, i.e. the log-
>>> hazard ratios for each term in the RHS of the formula. What you
>>> want (as described in the Index for the survival package) is either
>>> `survfit` or `survexp`.
>>>
>>> require(survival)
>>> help(pack=survival)
>>> ?survfit
>>> ?survexp
>>> ?summary.survfit
>>> ?quantile.survfit   # to get the median
>>> ?print.summary.survfit
>>>
>>> require(rms)
>>> help(pack=rms)
>>>
>>> The rms-package also adds a `survfit.cph` function but I have found
>>> the `survest` function also provides useful added features, beyond
>>> those offered by survfit
>>>
>>>
>>>
>>> Thank you.
>>>
>>> Regards,
>>> Axel.
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> This is a plain text mailing list.
>>>
>>> --
>>>
>>> David Winsemius, MD
>>> Alameda, CA, USA
>>>
>>>
>>
>> David Winsemius, MD
>> Alameda, CA, USA
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> David Winsemius, MD
> Alameda, CA, USA
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>