Here's what I would do. Let's assume that you are presenting the
results of the example on the cph help page. I agree with you that
the results should be presented on the hazard ratio scale. The Design
package provides appropriate plotting tools for creation of
publication quality graphics. in your example I would issue the
following command:
plot(f, age=NA, sex= NA, #age will be on the x axis and separate
plots will be done for male and female
col= c("red", "blue"), # fortunately Frank constructed
plot.Design, so that both the main effects plots and the CI plots get
colored
fun = exp, # this results in the log
hazard effects on the y axis being transformed to the hazard ratio
scale
ylab = "Hazard Ratios") # and this adds a meaningful label
fo the y axis
An alternative plot would be to suppress the CI lines which might be
more effective in getting across the message:
plot(f, age=NA, sex= NA, col= c("red", "blue"), fun = exp, ylab =
"Hazard Ratios", conf.int=FALSE)
Given that the model forces the male-female curves to be equidistant
on the log hazards scale, I would also examine the possibility that
they were in "truth" different by creating an interaction model and
testing for difference between that model and the more simplistic
model. In this case it is no surprise that the statistical test fails
to support such a model:
f2 <- cph(Srv ~ rcs(age,4)* sex, x=TRUE, y=TRUE)
anova(f)
anova*f2)
Which mean I would not get the challenge of explaining to my audience
the notion of different forms of the age effect for men and women. You
would explain in your paper that the model shows that males are on
average exp(-0.6445) = 0.5249 times as likely to experience the event
of interest. Ths is not at all typical for ordinary humans and this
would require careful consideration and review of the experimental
situation. The hazard ratios at each age relative to a person of
average age are displayed on the graphic. They show a plateau in
mortality at young ages (which is typical of free-range humans) but
that risk then doubles each decade between ages 45 and 60 but the rise
tapers off somewhat at the extremes of age. Those features are typical
for human mortality and would not require as much commentary.
--
David
On Aug 1, 2009, at 8:53 PM, zhu yao wrote:
> Thx for your reply.
> 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?
>
> 2009/8/1 David Winsemius <dwinsem...@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"
> dd <- datadist(age, sex)
> options(datadist='dd')
>
> This is process for setting the range for the display of effects in
> Design regression objects. See:
>
> ?datadist
>
> "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
>
>
David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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