dfmacox: Degrees of freedom in multivariate additive Cox models

In smoothHR: Smooth Hazard Ratio Curves Taking a Reference Value

Description

Provides the degrees of freedom for flexible continuous covariates in multivariate additive Cox models.

Usage

dfmacox(time, time2=NULL, status, nl.predictors, other.predictors,
smoother, method, mindf=NULL, maxdf=NULL, ntimes=NULL, data)

Arguments

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.
nl.predictors	Vector with covariates to be introduced in the additive Cox model with a nonlinear effect.
other.predictors	Vector with remaining covariates to be introduced in the additive Cox model. This will include qualitative covariates or continuous covariates with a linear effect.
smoother	Smoothing method to be used in the additive Cox model. Possible options are ‘ns’ for natural spline smoothing or ‘pspline’ for penalized spline smoothing.
method	The desired method to obtain the optimal degrees of freedom. If method ="AIC", then the AIC = (loglik -df) is used to choose the "optimal" degrees of freedom. The corrected AIC of Hurvich et. al. (method="AICc") and the BIC criterion (method = "BIC") can also be used.
mindf	Vector with minimum degrees of freedom for each nonlinear predictor. By default this value is a vector of of the same length of nl.predictors all with value 1, if smoother is 'ns'; a vector with the same length of nl.predictors all with value 1.5, if smoother is 'pspline'.
maxdf	Vector with maximum degrees of freedom for each nonlinear predictor. By default, when penalized spline is used (smoother='pspline'), the corrected AIC from Hurvich obtained in the corresponding univariate additive Cox model is used. When penalized spline is used (smoother='ns') a vector with the same length of nl.predictors all with values 1.5.
ntimes	Internel procedure which involves repetion of some convergence steps to attain the optimal degrees of freedom. By deafault is 5.
data	A data.frame in which to interpret the variables named in the arguments time, time2, and status.

Value

An object of class list, basically a list including the elements:

df	Degrees of freedom of the 'nl.predictors'.
AIC	Akaike’s Information Criterion score of the fitted model.
AICc	Corrected Akaike’s Information Criterion score of the fitted model.
BIC	Bayesian Information Criterion score of the fitted model.
myfit	Fitted (additive Cox) model based on the chosen degrees of freedom.
method	The method used for obtaining the degrees of freedom.
nl.predictors	Vector with the nonlinear predictors.

Author(s)

Artur Araújo and Luís Meira-Machado

References

Eilers, Paul H. and Marx, Brian D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89-121. doi: 10.1214/ss/1038425655

Hurvich, C. M. and Simonoff, J. S. and Tsai, Chih-Ling (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion, JRSSB, 60(2), 271–293. doi: 10.1111/1467-9868.00125

Meira-Machado, L. and Cadarso-Suárez, C. and Gude, F. and Araújo, A. (2013). smoothHR: An R Package for Pointwise Nonparametric Estimation of Hazard Ratio Curves of Continuous Predictors, Computational and Mathematical Methods in Medicine, 2013, Article ID 745742, 11 pages. doi: 10.1155/2013/745742

Examples

# Example 1
library(survival)
data(whas500)
mydf_ns <- dfmacox(time="lenfol", status="fstat", nl.predictors=c("los", "bmi"),
other.predictors=c("age", "hr", "gender", "diasbp"), smoother="ns", data=whas500)
print(mydf_ns)

# Example 2
mydf_ps <- dfmacox(time="lenfol", status="fstat", nl.predictors=c("los", "bmi"),
other.predictors=c("age", "hr", "gender", "diasbp"), smoother="pspline", data=whas500)
print(mydf_ps)

Example output

Loading required package: survival
Loading required package: splines
Warning message:
In fitter(X, Y, strats, offset, init, control, weights = weights,  :
  Loglik converged before variable  1,2,3,4,5,6,7,8,9,10 ; beta may be infinite. 
$df
[1] 10  3

$AIC
[1] 2273.898

$AICc
[1] 2279.388

$BIC
[1] 2331.199

$myfit
Call:
coxph(formula = covar, data = data, x = TRUE)

                        coef exp(coef)  se(coef)     z       p
ns(los, df = 10)1  -1.14e+01  1.12e-05  8.17e+02 -0.01 0.98886
ns(los, df = 10)2   7.25e+01  3.08e+31  6.99e+03  0.01 0.99172
ns(los, df = 10)3  -4.27e+01  2.76e-19  3.72e+03 -0.01 0.99083
ns(los, df = 10)4   1.47e+01  2.45e+06  1.63e+03  0.01 0.99281
ns(los, df = 10)5   1.52e+01  3.99e+06  1.63e+03  0.01 0.99257
ns(los, df = 10)6   1.52e+01  3.96e+06  1.63e+03  0.01 0.99258
ns(los, df = 10)7   1.50e+01  3.34e+06  1.63e+03  0.01 0.99266
ns(los, df = 10)8   3.51e+00  3.35e+01  2.95e+02  0.01 0.99049
ns(los, df = 10)9   4.11e+01  7.38e+17  4.42e+03  0.01 0.99258
ns(los, df = 10)10 -6.08e+00  2.30e-03  1.80e+02 -0.03 0.97306
ns(bmi, df = 3)1   -1.35e+00  2.60e-01  3.68e-01 -3.67 0.00025
ns(bmi, df = 3)2   -1.64e+00  1.95e-01  9.86e-01 -1.66 0.09697
ns(bmi, df = 3)3    1.95e-01  1.21e+00  7.12e-01  0.27 0.78454
age                 5.80e-02  1.06e+00  6.70e-03  8.66 < 2e-16
hr                  1.51e-02  1.02e+00  2.94e-03  5.13 2.9e-07
gender             -1.68e-01  8.45e-01  1.51e-01 -1.11 0.26655
diasbp             -1.21e-02  9.88e-01  3.58e-03 -3.38 0.00071

Likelihood ratio test=215  on 17 df, p=0
n= 500, number of events= 215 

$method
[1] "AIC"

$nl.predictors
[1] "los" "bmi"

$df
[1] 5.706318 2.341832

$AIC
[1] 2277.054

$AICc
[1] 2280.871

$BIC
[1] 2317.581

$myfit
Call:
coxph(formula = covar, data = data, x = TRUE)

                              coef se(coef)      se2    Chisq   DF       p
pspline(los, df = 5.7), l  0.01216  0.01474  0.01461  0.68089 1.00 0.40928
pspline(los, df = 5.7), n                            14.12705 4.71 0.01201
pspline(bmi, df = 2.3), l -0.04164  0.01470  0.01466  8.02234 1.00 0.00462
pspline(bmi, df = 2.3), n                             6.58479 1.34 0.01725
age                        0.05686  0.00666  0.00665 72.84808 1.00 < 2e-16
hr                         0.01350  0.00284  0.00283 22.53556 1.00 2.1e-06
gender                    -0.24893  0.14445  0.14407  2.96997 1.00 0.08482
diasbp                    -0.01190  0.00356  0.00355 11.17489 1.00 0.00083

Iterations: 4 outer, 14 Newton-Raphson
     Theta= 0.263 
     Theta= 0.867 
Degrees of freedom for terms= 5.7 2.3 1.0 1.0 1.0 1.0 
Likelihood ratio test=202  on 12 df, p=0  n= 500 

$method
[1] "AIC"

$nl.predictors
[1] "los" "bmi"

smoothHR documentation built on Oct. 7, 2021, 9:21 a.m.