dls {MapGAM} | R Documentation |
Calculating Derivatives of Partial Likelihood for Cox Proportional Hazard Additive Models
Description
Calculate the log partial likelihood and derivatives with respect to the subject log hazard ratio (compared to the baseline) for Cox proportional hazard additive model described in gamcox
. Results are used to update estimates in gamcox
function.
Usage
dls(Y,X,which,eta,span=0.5,adjust=TRUE)
Arguments
Y |
a list including two elements: |
X |
a data frame containing the variables in the model. The data must be structured so that the X and Y coordinates for two-dimensional predictor (e.g., geolocation) are in the 1st and 2nd columns, respectively. |
which |
matrix index for smooth term. |
eta |
current estimated subject log hazard ratio compared to the baseline. |
span |
smoothing parameter that been used to smoothing the second derivative of the log partial likelihood. |
adjust |
|
Details
For data that having tied failure times, Efron's approximation method is used to calculate the log partial likelihood and correspongding derivatives. Let \eta
denote the log hazard ratio, and l denote the partial likelihood. When fitting a Cox proportional hazard additive model, \eta
is updated by
\eta^{new} = \eta^{old} - \frac{dl/d{\eta}}{smooth(d^2l/d\eta^2)}
Value
deltaeta |
difference between the input |
w |
inverse of smoothed second derivatives. |
l |
partial likelihood baed on input |
Author(s)
Lu Bai and Scott Bartell
Send bug reports to sbartell@uci.edu.
References
Hastie TJ, Tibshirani RJ. Generalized Additive Models. (Chapman & Hall/CRC Monographs on Statistics & Applied Probability, Boca Raton, Florida, 1990).
Bristow RE, Chang J, Ziogas A, Gillen DL, Bai L, Vieira VM. Spatial Analysis of Advanced-stage Ovarian Cancer Mortality in California. American Journal of Obstetrics and Gynecology 2015, 213(1), e1-43).
See Also
Examples
data(CAdata)
Y = CAdata[,c("time","event")]
X = CAdata[,c(3:5)]
eta = coxph(Surv(time,event)~AGE,data=CAdata)$linear.predictors
result = dls(Y,X,1:2,eta,span=0.2)
plot(eta,result$deltaeta)