Frank E Harrell Jr f.harrell at vanderbilt.edu
Sun Aug 2 04:00:24 CEST 2009

```zhu yao wrote:
> In this example, age was transformed with rcs. So the output was different
> between f and summary(f).
> If I need to publicate the results, how do I explation the hazard ratio of
> age?

David explained this.  Nonlinearity in age does not complicate the
explanation.  The estimate is the estimate of the ratio of hazard rate
at the upper quartile of age compared to the hazard ratio at the lower
quartile, with the ages corresponding to these 2 points shown in the output.

The output of f is not very useful for publication.  The output of
summary, Function, and latex are.

Frank

>
> 2009/8/1 David Winsemius <dwinsemius at comcast.net>
>
>> On Jul 31, 2009, at 11:24 PM, zhu yao wrote:
>>
>>  Could someone explain the summary(cph.object)?
>>> The example is in the help file of cph.
>>>
>>> n <- 1000
>>> set.seed(731)
>>> age <- 50 + 12*rnorm(n)
>>> label(age) <- "Age"
>>> sex <- factor(sample(c('Male','Female'), n,
>>>             rep=TRUE, prob=c(.6, .4)))
>>> cens <- 15*runif(n)
>>> h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
>>> dt <- -log(runif(n))/h
>>> label(dt) <- 'Follow-up Time'
>>> e <- ifelse(dt <= cens,1,0)
>>> dt <- pmin(dt, cens)
>>> units(dt) <- "Year"
>>>
>> This is process for  setting the range for the display of effects in Design
>> regression objects. See:
>>
>>
>> "q.effect
>> set of two quantiles for computing the range of continuous variables to use
>> in estimating regression effects. Defaults are c(.25,.75), which yields
>> inter-quartile-range odds ratios, etc."
>>
>> ?summary.Design
>> #---
>> " By default, inter-quartile range effects (odds ratios, hazards ratios,
>> etc.) are printed for continuous factors, ... "
>> #---
>> "Value
>> For summary.Design, a matrix of class summary.Design with rows
>> corresponding to factors in the model and columns containing the low and
>> high values for the effects, the range for the effects, the effect point
>> estimates (difference in predicted values for high and low factor values),
>> the standard error of this effect estimate, and the lower and upper
>> confidence limits."
>>
>> #---
>>
>>
>>  Srv <- Surv(dt,e)
>>> f <- cph(Srv ~ rcs(age,4) + sex, x=TRUE, y=TRUE)
>>> summary(f)
>>>
>>>                                        Effects              Response : Srv
>>>
>>> Factor            Low    High   Diff.  Effect S.E. Lower 0.95 Upper 0.95
>>> age               40.872 57.385 16.513 1.21   0.21 0.80       1.62
>>>  Hazard Ratio     40.872 57.385 16.513 3.35     NA 2.22       5.06
>>>
>> In this case with a 4 df regression spline, you need to look at  the
>> "effect" across the range of the variable. You ought to plot the age effect
>> and examine anova(f) ). In the untransformed situation the plot is on the
>> log hazards scale for cph. So the effect for age in this case should be the
>> difference in log hazard at ages 40.872 and 57.385. SE is the standard error
>> of that estimate and the Upper and Lower numbers are the confidence bounds
>> on the effect estimate. The Hazard Ratio row gives you exponentiated
>> results, so a difference in log hazards becomes a hazard ratio. {exp(1.21) =
>> 3.35}
>>
>>  sex - Female:Male  2.000  1.000     NA 0.64   0.15 0.35       0.94
>>>  Hazard Ratio      2.000  1.000     NA 1.91     NA 1.42       2.55
>>>
>>>
>>> Wat's the meaning of Effect, S.E. Lower, Upper?
>>>
>> You probably ought to read a bit more basic material. If you are asking
>> this question, Harrell's "Regression Modeling Strategies" might be over you
>> head, but it would probably be a good investment anyway. Venables and
>> Ripley's "Modern Applied Statistics" has a chapter on survival analysis.
>> Also consider Kalbfliesch and Prentice "Statistical Analysis of Failure Time
>> Data". I'm sure there are others;  those are the ones I have on my shelf.
>>
>> David Winsemius, MD
>> Heritage Laboratories
>> West Hartford, CT
>>
>>
>
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