# DiscreteHazRateEst: Discrete hazard rate estimator In NPHazardRate: Nonparametric Hazard Rate Estimation

## 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

 1 2 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.

## Details

The semiparmaetric estimator implemented is defined in (1) in Patil and Bagkavos (2012) by

\tilde λ = \hat λ Γ^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 γ parameter calculations.

## Value

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

## References

lambdahat, TutzPritscher
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 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