dfmacox: Degrees of freedom in multivariate additive Cox models
In smoothHR: Smooth Hazard Ratio Curves Taking a Reference Value

Description Usage Arguments Value Author(s) References Examples

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

1 2	dfmacox(time, time2=NULL, status, nl.predictors, other.predictors, smoother, method, mindf=NULL, maxdf=NULL, ntimes=NULL, data)

`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`.

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.

Artur Araújo and Luís Meira-Machado

Eilers, Paul H. and Marx, Brian D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89-121.

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, volume 60, 271–293.

# 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)

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"