Hi Thierry,
I see what you want now---a significance test for the HR specifically.
See inline below
On Sat, Dec 10, 2011 at 6:40 PM, Thierry Julian Panje
tpa...@stanford.edu wrote:
Hi Josh,
Thank you for your quick response!
In several papers the results of a Cox Regression were presented in a table
showing the variable name, the hazard ratio for two values of this variable,
the 95% confidence interval of the hazard ratio and a p-value.
(e.g., Lett 2007. Social support and prognosis in patients at increased
psychosocial risk recovering from myocardial infarction. Health psychology
http://psycnet.apa.org/journals/hea/26/4/418.pdf; page 6 Table 2)
When I use summary() for a coxph() function, for example:
summary(mod.allison)
Call:
coxph(formula = Surv(week, arrest) ~ fin + age + race + wexp +
mar + paro + prio, data = Rossi)
n= 432, number of events= 114
coef exp(coef) se(coef) z Pr(|z|)
finyes -0.37942 0.68426 0.19138 -1.983 0.04742 *
age -0.05744 0.94418 0.02200 -2.611 0.00903 **
raceother -0.31390 0.73059 0.30799 -1.019 0.30812
wexpyes -0.14980 0.86088 0.21222 -0.706 0.48029
marnot married 0.43370 1.54296 0.38187 1.136 0.25606
paroyes -0.08487 0.91863 0.19576 -0.434 0.66461
prio 0.09150 1.09581 0.02865 3.194 0.00140 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
finyes 0.6843 1.4614 0.4702 0.9957
age 0.9442 1.0591 0.9043 0.9858
raceother 0.7306 1.3688 0.3995 1.3361
wexpyes 0.8609 1.1616 0.5679 1.3049
marnot married 1.5430 0.6481 0.7300 3.2614
paroyes 0.9186 1.0886 0.6259 1.3482
prio 1.0958 0.9126 1.0360 1.1591
Concordance= 0.64 (se = 0.027 )
Rsquare= 0.074 (max possible= 0.956 )
Likelihood ratio test= 33.27 on 7 df, p=2.362e-05
Wald test = 32.11 on 7 df, p=3.871e-05
Score (logrank) test = 33.53 on 7 df, p=2.11e-05
I thought, the value in the Pr(|z|) column indicated the significance of
the coefficient and not of a hazard ratio.
That is correct.
Is it possible to assess the statistical significance of a hazard ratio not
only with a confidence interval but also with a p-value and to compute that
in R?
I am hoping someone else will chime in here. I might naively try this
(but do validate before publishing). For the standard error of the
hazard ratio, I use exp(coef) * se, and then assume that (exp(coef) -
1)/(exp(coef) * se) is ~ x2(1). A quick look through Terry Therneau's
book, Modeling Survival Data did not turn up any particular ways to
get this automatically in R. Note that the confidence interval (and
this is consistent with summary()) is based on exponentiating the
linear predictor's lower and upper limits, not the SE of the
exponetiated predictor.
require(survival)
set.seed(1)
d - data.frame(
start = start - sample(1:10, 600, TRUE),
stop = start + sample(1:7, 600, TRUE),
event = event - rbinom(600, 1, .7),
x1 = event * rbinom(600, 1, .7),
x2 = rnorm(600, 0, 1))
m - coxph(Surv(start, stop, event) ~ x1 + x2, d)
beta - coef(m)
se - sqrt(diag(vcov(m)))
HR - exp(beta)
HRse - HR * se
summary(m)
round(cbind(coef = beta, se = se, z = beta/se, p = 1 - pchisq((beta/se)^2, 1),
HR = HR, HRse = HRse,
HRz = (HR - 1) / HRse, HRp = 1 - pchisq(((HR - 1)/HRse)^2, 1),
HRCILL = exp(beta - qnorm(.975, 0, 1) * se),
HRCIUL = exp(beta + qnorm(.975, 0, 1) * se)), 3)
Or is it usual to present a hazard ratio together with the p-value of the
coefficient?
usual probably depends on the area. I have seen the coefficients
presented with p-values, and the 95%CI of the hazard ratio. I do not
know that there is any one required set of statistics to be reported.
Or do the coefficient and any defined hazard ratio of a variable have in fact
the same p-value?
No, it is a nonlinear transformation and the p-values are not the same.
I would like to apologize if these were trivial questions and I fear they are
not totally R-specific. Thus I understand if you don't have the time to
answer them. However, I would greatly appreciate any help.
Aspects are not, but aspects are. Certainly, asking if there is a way
to get a test of the hazard ratio in R (without hacking something
together like I did) seems reasonable to me at least to ask.
Cheers,
Josh
Best,
Thierry
- Ursprüngliche Mail -
Von: Joshua Wiley jwiley.ps...@gmail.com
An: Thierry Julian Panje tpa...@stanford.edu
CC: r-help@r-project.org
Gesendet: Samstag, 10. Dezember 2011 13:53:00
Betreff: Re: [R] p-value for hazard ratio in Cox proportional hazards
regression?
Hi Thierry,
Could you give us an example of what exactly you are doing
(preferablly reproducible R code)? I may be misunderstanding you
