###PubH 7450: how to specify some parameters in muhaz(); 
###           this is related to Problem 6.2

library(muhaz)
data(ovarian)
attach(ovarian)
#default:
fit1 <- muhaz(futime, fustat)
plot(fit1)
summary(fit1)

Number of Observations .......... 26
Censored Observations ........... 14
Method used ..................... Local
Boundary Correction Type ........ Left and Right
Kernel type ..................... Epanechnikov
Minimum Time .................... 0
Maximum Time .................... 744
Number of minimization points ... 51
Number of estimation points ..... 101
Pilot Bandwidth ................. 56.58
Smoothing Bandwidth ............. 282.89
Minimum IMSE .................... 1e+30

#######to get estimated hazard rates at some given time point,
#######you have to specify 
min.time: Left bound of the time domain used in analysis. If missing,
          min.time is considered 0. 
max.time: Right bound of the time domain used in analysis. If missing,
          max.time is the time at which ten patients remain at risk. 
n.est.grid: Number of points in the estimation grid, where hazard
          estimates are computed. Default value is 101.

#######other parameters:
bw.grid: Bandwidth grid used in the MSE minimization. If
          bw.method="global" and bw.grid has one component only, no MSE
          minimization is performed.  The hazard estimates are computed
          for the value of bw.grid. If bw.grid is missing, then a
          bandwidth grid of 21 components is built, having as bounds:
                     [0.2*bw.pilot, 20*bw.pilot]

bw.pilot: Pilot bandwidth used in the MSE minimization. If missing, the
          default value is the one recommended by Mueller and Wang
          (1994):
             bw.pilot = (max.time-min.time) / (8*nz^0.2)
          where nz is the number of uncensored observations 

bw.method: Algorithm to be used.  Possible values are: "global" - same
          bandwidth for all grid points.  The optimal bandwidth is
          obtained by minimizing the IMSE. "local"  - different
          bandwidths at each grid point.  The optimal bandwidth at a
          grid point is obtained by minimizing the local MSE. "knn"   
          - k nearest neighbors distance bandwidth.  The optimal number
          of neighbors is obtained by minimizing the IMSE. Default
          value is "local". Only the first letter needs to be given
          (e.g. "g", instead of "global"). 

kern: Boundary kernel function to be used.  Possible values are:
          "rectangle", "epanechnikov", "biquadratic", "triquadratic".
          Default value is "epanechnikov". Only the first letter needs
          to be given (e.g. kern="b"). 

##for my above data: min.time=0, max.time=744, n.est.grid=101

fit2<-muhaz(futime, fustat, min.time=0, max.time=744, n.est.grid=745,
            bw.method="global", bw.grid=282.89, kern="rectangle")
#find hazard estimates:
fit2$est.grid[1:5]
#[1] 0 1 2 3 4
fit2$haz.est[1:5]
#[1] 0.0004373800 0.0004433674 0.0004491685 0.0004547879 0.0004602299
#in contrast,
fit1$est.grid[1:5]
#[1]  0.00  7.44 14.88 22.32 29.76
fit1$haz.est[1:5]
#[1] 0.0002554471 0.0002735475 0.0002927036 0.0003122007 0.0003319730

postscript("muhaz_example.ps")
plot(fit2, col="red")
lines(fit1)
dev.off()