smoothHR: Smooth Hazard Ratio Curves Taking a Reference Value

Description Usage Arguments Value Author(s) References Examples

Description

Provides flexible hazard ratio curves allowing non-linear relationships between continuous predictors and survival. To better understand the effects that each continuous covariate has on the outcome, results are expressed in terms of hazard ratio curves, taking a specific covariate value as reference. Confidence bands for these curves are also derived.

Usage

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smoothHR(data, time=NULL, time2=NULL, status=NULL, formula=NULL, coxfit,
status.event=NULL)

Arguments

data

A data.frame in which to interpret the variables named in the formula or in the arguments time, time2, status and coxfit.

time

For right censored data, this is the follow up time. For interval data, the first argument is the starting time for the interval.

time2

Ending time of the interval for interval censored or counting process data only. Intervals are assumed to be open on the left and closed on the right, (start, end]. For counting process data, event indicates whether an event occurred at the end of the interval.

status

The status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE = death) or 1/2 (2=death). For interval censored data, the status indicator is 0=right censored, 1=event at time, 2=left censored, 3=interval censored. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have an event.

formula

A formula object, with the terms on the right after the ~ operator.

coxfit

An object of class coxph. This argument is optional, being an alternative to the arguments time, time2, status and formula.

status.event

The status indicator is a qualitative variable where usually the highest value is left for the event of interest (usually 0=alive, 1=dead). If that is not the case the status.event indicates which value denotes the event of interest.

Value

An object of class HR. There are methods for print, predict and plot. HR objects are implemented as a list with elements:

dataset

Dataset used.

coxfit

The object of class 'coxph' used.

phtest

Result from testing the proportional hazards assumption.

Author(s)

Artur Araújo and Luís Meira-Machado

References

Carmen Cadarso-Suarez, Luís Meira-Machado, Thomas Kneib and Francisco Gude. Flexible hazard ratio curves for continuous predictors in multi-state models: a P-spline approach. Statistical Modelling, 2010, 10:291-314.

Examples

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# Example 1
library(survival)
data(whas500)
fit <- coxph(Surv(lenfol, fstat)~age+hr+gender+diasbp+pspline(bmi)+pspline(los), data=whas500,
x=TRUE)
hr1 <- smoothHR(data=whas500, coxfit=fit)
print(hr1)

# Example 2
hr2 <- smoothHR( data=whas500, time="lenfol", status="fstat", formula=~age+hr+gender+diasbp+
pspline(bmi)+pspline(los) )
print(hr2)

Example output

Loading required package: survival
Loading required package: splines

Cox Proportional Hazards Model
Call:
coxph(formula = Surv(lenfol, fstat) ~ age + hr + gender + diasbp + 
    pspline(bmi) + pspline(los), data = whas500, x = TRUE)

                         coef se(coef)      se2    Chisq   DF       p
age                   0.05682  0.00668  0.00667 72.37950 1.00 < 2e-16
hr                    0.01391  0.00284  0.00283 23.94579 1.00 9.9e-07
gender               -0.25071  0.14393  0.14362  3.03404 1.00 0.08154
diasbp               -0.01188  0.00359  0.00357 10.96060 1.00 0.00093
pspline(bmi), linear -0.03725  0.01438  0.01435  6.70986 1.00 0.00959
pspline(bmi), nonlin                            10.48506 3.08 0.01598
pspline(los), linear  0.01310  0.01479  0.01465  0.78371 1.00 0.37601
pspline(los), nonlin                            10.70873 2.95 0.01280

Iterations: 4 outer, 15 Newton-Raphson
     Theta= 0.799 
     Theta= 0.366 
Degrees of freedom for terms= 1.0 1.0 1.0 1.0 4.1 3.9 
Likelihood ratio test=202  on 12 df, p=0  n= 500 

Proportional Hazards Assumption
             rho  chisq      p
age       0.0757  1.308 0.2528
hr        0.0570  0.693 0.4053
gender    0.0251  0.139 0.7091
diasbp    0.0788  1.547 0.2135
ps(bmi)3  0.1672  1.569 0.2103
ps(bmi)4  0.1695  2.502 0.1137
ps(bmi)5  0.1697  3.367 0.0665
ps(bmi)6  0.1626  3.252 0.0714
ps(bmi)7  0.1616  3.076 0.0795
ps(bmi)8  0.1825  3.866 0.0493
ps(bmi)9  0.1838  3.948 0.0469
ps(bmi)10 0.1664  3.279 0.0702
ps(bmi)11 0.1663  3.339 0.0677
ps(bmi)12 0.1581  3.499 0.0614
ps(bmi)13 0.1341  3.103 0.0782
ps(bmi)14 0.1116  2.164 0.1413
ps(los)3  0.2792  2.268 0.1320
ps(los)4  0.2541  5.105 0.0239
ps(los)5  0.2438  4.192 0.0406
ps(los)6  0.2577  4.186 0.0408
ps(los)7  0.2357  4.027 0.0448
ps(los)8  0.2496  4.721 0.0298
ps(los)9  0.2450  5.095 0.0240
ps(los)10 0.2060  2.845 0.0916
ps(los)11 0.1763  1.399 0.2369
ps(los)12 0.1558  0.767 0.3810
ps(los)13 0.1410  0.469 0.4936
ps(los)14 0.1300  0.311 0.5771
GLOBAL        NA 18.616 0.9096

Cox Proportional Hazards Model
Call:
coxph(formula = covar2, data = data, x = TRUE)

                         coef se(coef)      se2    Chisq   DF       p
age                   0.05682  0.00668  0.00667 72.37950 1.00 < 2e-16
hr                    0.01391  0.00284  0.00283 23.94579 1.00 9.9e-07
gender               -0.25071  0.14393  0.14362  3.03404 1.00 0.08154
diasbp               -0.01188  0.00359  0.00357 10.96060 1.00 0.00093
pspline(bmi), linear -0.03725  0.01438  0.01435  6.70986 1.00 0.00959
pspline(bmi), nonlin                            10.48506 3.08 0.01598
pspline(los), linear  0.01310  0.01479  0.01465  0.78371 1.00 0.37601
pspline(los), nonlin                            10.70873 2.95 0.01280

Iterations: 4 outer, 15 Newton-Raphson
     Theta= 0.799 
     Theta= 0.366 
Degrees of freedom for terms= 1.0 1.0 1.0 1.0 4.1 3.9 
Likelihood ratio test=202  on 12 df, p=0  n= 500 

Proportional Hazards Assumption
             rho  chisq      p
age       0.0757  1.308 0.2528
hr        0.0570  0.693 0.4053
gender    0.0251  0.139 0.7091
diasbp    0.0788  1.547 0.2135
ps(bmi)3  0.1672  1.569 0.2103
ps(bmi)4  0.1695  2.502 0.1137
ps(bmi)5  0.1697  3.367 0.0665
ps(bmi)6  0.1626  3.252 0.0714
ps(bmi)7  0.1616  3.076 0.0795
ps(bmi)8  0.1825  3.866 0.0493
ps(bmi)9  0.1838  3.948 0.0469
ps(bmi)10 0.1664  3.279 0.0702
ps(bmi)11 0.1663  3.339 0.0677
ps(bmi)12 0.1581  3.499 0.0614
ps(bmi)13 0.1341  3.103 0.0782
ps(bmi)14 0.1116  2.164 0.1413
ps(los)3  0.2792  2.268 0.1320
ps(los)4  0.2541  5.105 0.0239
ps(los)5  0.2438  4.192 0.0406
ps(los)6  0.2577  4.186 0.0408
ps(los)7  0.2357  4.027 0.0448
ps(los)8  0.2496  4.721 0.0298
ps(los)9  0.2450  5.095 0.0240
ps(los)10 0.2060  2.845 0.0916
ps(los)11 0.1763  1.399 0.2369
ps(los)12 0.1558  0.767 0.3810
ps(los)13 0.1410  0.469 0.4936
ps(los)14 0.1300  0.311 0.5771
GLOBAL        NA 18.616 0.9096

smoothHR documentation built on May 2, 2019, 8:20 a.m.