NPHazardRate (version 0.1)

SemiparamEst: Discrete hazard rate estimator

Description

Implements the semiparametric hazard rate estimator for discrete data developed in Patil and Bagkavos (2012). The estimate is obtained by semiparametric smoothing of the (nonsmooth) nonparametric maximum likelihood estimator, which is achieved by repeated multiplication of a Markov chain transition-type matrix. This matrix is constructed with basis a parametric discrete hazard rate model (vehicle model).

Usage

SemiparamEst(xin, cens, xout, Xdistr, Udistr, vehicledistr, Xpar1=1, Xpar2=0.5,
              Upar1=1, Upar2=0.5, vdparam1=1, vdparam2=0.5)

Arguments

xin

A vector of data points. Missing values not allowed.

cens

Censoring indicators as a vector of 1s and zeros, 1's indicate uncensored observations, 0's correspond to censored obs.

xout

Design points where the estimate will be calculated.

Xdistr

The distribution where the data are coming from, currently ignored

Udistr

Censoring distribution, currently ignored

vehicledistr

String specifying the vehicle hazard rate (the assumed parametric model)

Xpar1

Parameter 1 for the X distr, currently ignored

Xpar2

Parameter 2 for the X distr, currently ignored

Upar1

Parameter 1 for the Cens. distr., currently ignored

Upar2

Parameter 2 for the Cens. distr., currently ignored

vdparam1

Parameter 1 for the vehicle hazard rate.

vdparam2

Parameter 2 for the vehicle hazard rate.

Value

A vector with the values of the discrete hazard rate estimate, calculated at \(x=xout\).

Details

The semiparmaetric estimator implemented is defined in (1) in Patil and Bagkavos (2012) by $$\tilde \lambda = \hat \lambda \Gamma^S$$ where \(S\) determines the number of repetions and hence the amount of smoothing applied to the estimate. For \(S=0\) the semiparametric estimate equals the nonparmaetric estimate lambdahat. On the other hand, if the true unknown underlying probability model is known (up to an unknown constant or constants) then, the greater the \(S\), the closer the semiparmaetric estimate to the vehicle hazard rate model.

• TO DO: The extension to hazard rate estimation with covariates will be added in a future release.

• TO DO: Also, the data driven estimation of the parameter \(S\) will be also added in a future release; this will inlcude the \(SC\) product and \(C\) and \(\gamma\) parameter calculations.

References

Patil and Bagkavos (2012), Semiparametric smoothing of discrete failure time data, Biometrical Journal, 54, (2012), 5-19

See Also

lambdahat, TutzPritscher

Examples

# NOT RUN {
options(echo=FALSE)
xin<-c(7,34,42,63,64, 74, 83, 84, 91, 108, 112,129, 133,133,139,140,140,146,
      149,154,157,160,160,165,173,176,185, 218,225,241, 248,273,277,279,297,
      319,405,417,420,440, 523,523,583, 594, 1101, 1116, 1146, 1226, 1349,
      1412, 1417) #head and neck data set
cens<-c(1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
        1,0,1,1,1,1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,0,1) #censoring indicators
xin<-xin/30.438 #mean adjust the data
storage.mode(xin)<-"integer"  # turn the data to integers
xout<-seq(1,47, by=1) #design points where to calculate the estimate
arg<-TutzPritscher(xin,cens,xout) #Kernel smooth estimate
plot(xout, arg, type="l", ylim=c(0, .35), lty=2,  col=6)
argSM<-SemiparamEst(xin, cens, xout, "geometric", "uniform",
                    "geometric", 0.2, .6, 0, 90, .25, .9) #semipar. est.
lines(xout, argSM[,2], lty=3, col=5) #add tilde lambda to the plot
# }