R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("smoothSurv-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('smoothSurv')
Loading required package: survival
Loading required package: splines
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "a.to.c"
> 
> ### * a.to.c
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: a.to.c
> ### Title: Work Function for 'smoothSurvReg'
> ### Aliases: a.to.c
> ### Keywords: internal utilities
> 
> ### ** Examples
> 
> ccoef <- c(0.1, 0.2, 0.15, 0.3, 0.25)
> 
> ### Compute 'a' counterparts
> acoef <- c.to.a(ccoef, 1)
> print(acoef)
[1] 0.0000000 0.6931472 0.4054651 1.0986123 0.9162907
> 
> ### And back 'c', ccoef2 should be same as ccoef
> ccoef2 <- a.to.c(acoef)
> print(ccoef2)
[1] 0.10 0.20 0.15 0.30 0.25
> 
> 
> 
> cleanEx(); ..nameEx <- "c.to.a"
> 
> ### * c.to.a
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: c.to.a
> ### Title: Work Function for 'smoothSurvReg'
> ### Aliases: c.to.a
> ### Keywords: internal utilities
> 
> ### ** Examples
> 
> ccoef <- c(0.1, 0.2, 0.15, 0.3, 0.25)
> 
> ### Compute 'a' counterparts
> acoef <- c.to.a(ccoef, 1)
> print(acoef)
[1] 0.0000000 0.6931472 0.4054651 1.0986123 0.9162907
> 
> ### And back 'c', ccoef2 should be same as ccoef
> ccoef2 <- a.to.c(acoef)
> print(ccoef2)
[1] 0.10 0.20 0.15 0.30 0.25
> 
> 
> 
> cleanEx(); ..nameEx <- "dextreme"
> 
> ### * dextreme
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: extreme value
> ### Title: Density of the Extreme Value Distribution of a Minimum.
> ### Aliases: dextreme dstextreme
> ### Keywords: distribution
> 
> ### ** Examples
> 
> dextreme(1, (sqrt(6)/pi)*0.5772, sqrt(6)/pi)
[1] 0.3428868
> dstextreme(1)        ## approximately same result as on the previous row
[1] 0.3428868
> 
> 
> 
> cleanEx(); ..nameEx <- "dstlogis"
> 
> ### * dstlogis
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: standardized logistic
> ### Title: Density of Standardized Logistic Distribution.
> ### Aliases: dstlogis
> ### Keywords: distribution
> 
> ### ** Examples
> 
> dstlogis(0)
[1] 0.4534498
> dstlogis(seq(-3, 3, 0.2))
 [1] 0.007792275 0.011157620 0.015950279 0.022748323 0.032335707 0.045746471
 [7] 0.064286993 0.089495749 0.122969777 0.165956721 0.218615885 0.278965591
[13] 0.341842078 0.398647963 0.438853129 0.453449841 0.438853129 0.398647963
[19] 0.341842078 0.278965591 0.218615885 0.165956721 0.122969777 0.089495749
[25] 0.064286993 0.045746471 0.032335707 0.022748323 0.015950279 0.011157620
[31] 0.007792275
> 
> 
> 
> cleanEx(); ..nameEx <- "eval.Gspline"
> 
> ### * eval.Gspline
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: eval.Gspline
> ### Title: Evaluate a G-spline in a grid of values
> ### Aliases: eval.Gspline
> ### Keywords: dplot
> 
> ### ** Examples
> 
>   spline <- minPenalty(knots=seq(-4.2, 4.2, by=0.3), sdspline=0.2, difforder=3)$spline

Iter.: 0,  Penalty = -0.0259989,  Mean constr. = -2.63013e-17,  Var constr.= 8.88178e-16
Iter.: 1,  Penalty = -0.00650044,  Mean constr. = 1.68912e-16,  Var constr.= -5.51703e-06
Iter.: 2,  Penalty = -0.00162564,  Mean constr. = -2.53666e-17,  Var constr.= -1.54151e-06
Iter.: 3,  Penalty = -5.61756e-12,  Mean constr. = -4.52449e-15,  Var constr.= 2.59723e-06
Iter.: 4,  Penalty = 4.07663e-14,  Mean constr. = 1.96402e-17,  Var constr.= 1.0404e-10
Iter.: 5,  Penalty = 6.12424e-14,  Mean constr. = -2.08348e-17,  Var constr.= 1.03837e-10
Iter.: 6,  Penalty = -3.76587e-16,  Mean constr. = -4.40899e-17,  Var constr.= 1.03634e-10
Iter.: 7,  Penalty = 3.52339e-14,  Mean constr. = 2.34972e-17,  Var constr.= 9.07681e-11
     Convergence reached.
>   values <- eval.Gspline(spline, seq(-4.5, 4.5, by=0.05))
>   plot(values, type="l", bty="n", lwd=3)
> 
> 
> 
> cleanEx(); ..nameEx <- "find.c"
> 
> ### * find.c
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: find.c
> ### Title: Work Function for 'smoothSurvReg'
> ### Aliases: find.c
> ### Keywords: internal utilities
> 
> ### ** Examples
> 
> knots <- seq(-4, 4, 0.5)
> sd0 <- 0.3
> ccoef <- find.c(knots, sd0, dist = "dstlogis")
> 
> ### We plot the approximation together with the truth
> ###
> grid <- seq(-4, 4, 0.05)
> truth <- dstlogis(grid)
> 
> ### Following lines compute the values of the approximation
> grid.big <- matrix(grid, nrow = length(grid), ncol = length(knots))
> knots.big <- matrix(knots, nrow = length(grid), ncol = length(knots), byrow = TRUE)
> normals <- dnorm(grid.big, mean = knots.big, sd = sd0)
> approx <- normals %*% ccoef
> 
> ### Plot it
> plot(grid, approx, type = "l", xlab = "y", ylab = "f(y)", bty = "n")
> lines(grid, truth, lty = 2)
> legend(-4, 0.35, c("approx", "truth"), lty = 1:2, bty = "n")
> 
> 
> 
> cleanEx(); ..nameEx <- "give.c"
> 
> ### * give.c
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: give.c
> ### Title: Work Function for 'smoothSurvReg'
> ### Aliases: give.c
> ### Keywords: internal utilities
> 
> ### ** Examples
> 
> knots <- seq(-4, 4, 0.5)
> sd0 <- 0.3
> ccoef <- find.c(knots, sd0, dist = "dstlogis")
> 
> last.three <- c(3, 7, 10)
> c.rest <- ccoef[-last.three]
> ccoef2 <- give.c(knots, sd0, last.three, c.rest)
> 
> print(ccoef)
 [1] 0.0006121787 0.0013515103 0.0033765642 0.0082849182 0.0201061210
 [6] 0.0473784957 0.1037605134 0.1916892655 0.2445901615 0.1916892655
[11] 0.1037605134 0.0473784957 0.0201061210 0.0082849182 0.0033765642
[16] 0.0013515103 0.0006121787
> print(ccoef2)    ## Almost no change
 [1] 0.0006121787 0.0013515103 0.0054330551 0.0082849182 0.0201061210
 [6] 0.0473784957 0.0997256028 0.1916892655 0.2445901615 0.1959583899
[11] 0.1037605134 0.0473784957 0.0201061210 0.0082849182 0.0033765642
[16] 0.0013515103 0.0006121787
> 
> 
> 
> cleanEx(); ..nameEx <- "minPenalty"
> 
> ### * minPenalty
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: minPenalty
> ### Title: Minimize the penalty term under the two (mean and variance)
> ###   constraints
> ### Aliases: minPenalty
> ### Keywords: optimize
> 
> ### ** Examples
> 
> optimum <- minPenalty(knots=seq(-4.2, 4.2, by = 0.3), sdspline=0.2, difforder=3)

Iter.: 0,  Penalty = -0.0259989,  Mean constr. = -2.63013e-17,  Var constr.= 8.88178e-16
Iter.: 1,  Penalty = -0.00650044,  Mean constr. = 1.68912e-16,  Var constr.= -5.51703e-06
Iter.: 2,  Penalty = -0.00162564,  Mean constr. = -2.53666e-17,  Var constr.= -1.54151e-06
Iter.: 3,  Penalty = -5.61756e-12,  Mean constr. = -4.52449e-15,  Var constr.= 2.59723e-06
Iter.: 4,  Penalty = 4.07663e-14,  Mean constr. = 1.96402e-17,  Var constr.= 1.0404e-10
Iter.: 5,  Penalty = 6.12424e-14,  Mean constr. = -2.08348e-17,  Var constr.= 1.03837e-10
Iter.: 6,  Penalty = -3.76587e-16,  Mean constr. = -4.40899e-17,  Var constr.= 1.03634e-10
Iter.: 7,  Penalty = 3.52339e-14,  Mean constr. = 2.34972e-17,  Var constr.= 9.07681e-11
     Convergence reached.
> where <- optimum$spline
> print(where)
         Knot SD basis      c coef.     a coef.
knot[1]  -4.2      0.2 1.251632e-05 -9.18589776
knot[2]  -3.9      0.2 4.436442e-05 -7.92049348
knot[3]  -3.6      0.2 1.431808e-04 -6.74882285
knot[4]  -3.3      0.2 4.207528e-04 -5.67088586
knot[5]  -3.0      0.2 1.125800e-03 -4.68668253
knot[6]  -2.7      0.2 2.742756e-03 -3.79621285
knot[7]  -2.4      0.2 6.084224e-03 -2.99947682
knot[8]  -2.1      0.2 1.228896e-02 -2.29647444
knot[9]  -1.8      0.2 2.260046e-02 -1.68720571
knot[10] -1.5      0.2 3.784525e-02 -1.17167063
knot[11] -1.2      0.2 5.770287e-02 -0.74986921
knot[12] -0.9      0.2 8.010791e-02 -0.42180143
knot[13] -0.6      0.2 1.012618e-01 -0.18746730
knot[14] -0.3      0.2 1.165487e-01 -0.04686683
knot[15]  0.0      0.2 1.221410e-01  0.00000000
knot[16]  0.3      0.2 1.165487e-01 -0.04686683
knot[17]  0.6      0.2 1.012618e-01 -0.18746730
knot[18]  0.9      0.2 8.010791e-02 -0.42180143
knot[19]  1.2      0.2 5.770287e-02 -0.74986921
knot[20]  1.5      0.2 3.784525e-02 -1.17167063
knot[21]  1.8      0.2 2.260046e-02 -1.68720571
knot[22]  2.1      0.2 1.228896e-02 -2.29647444
knot[23]  2.4      0.2 6.084224e-03 -2.99947682
knot[24]  2.7      0.2 2.742756e-03 -3.79621285
knot[25]  3.0      0.2 1.125800e-03 -4.68668253
knot[26]  3.3      0.2 4.207528e-04 -5.67088586
knot[27]  3.6      0.2 1.431808e-04 -6.74882285
knot[28]  3.9      0.2 4.436442e-05 -7.92049348
knot[29]  4.2      0.2 1.251632e-05 -9.18589776
> show <- eval.Gspline(where, seq(-4.2, 4.2, by=0.05))
> plot(show, type="l", bty="n", lwd=2)
> 
> 
> 
> cleanEx(); ..nameEx <- "piece"
> 
> ### * piece
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: piece
> ### Title: Left Continuous Piecewise Constant Function with a Finite
> ###   Support.
> ### Aliases: piece
> ### Keywords: utilities
> 
> ### ** Examples
> 
> my.breaks <- c(-2, 1.5, 4, 7)
> my.values <- c(0.5, 0.9, -2)
> grid <- seq(-3, 8, by = 0.25)
> piece(grid, my.breaks, my.values)
 [1]  0.0  0.0  0.0  0.0  0.0  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5
[16]  0.5  0.5  0.5  0.5  0.9  0.9  0.9  0.9  0.9  0.9  0.9  0.9  0.9  0.9 -2.0
[31] -2.0 -2.0 -2.0 -2.0 -2.0 -2.0 -2.0 -2.0 -2.0 -2.0 -2.0  0.0  0.0  0.0  0.0
> 
> 
> 
> cleanEx(); ..nameEx <- "smoothSurvReg"
> 
> ### * smoothSurvReg
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: smoothSurvReg
> ### Title: Regression for a Survival Model with Smoothed Error Distribution
> ### Aliases: smoothSurvReg
> ### Keywords: survival smooth
> 
> ### ** Examples
> 
> ### We generate interval censored data and fit a model with few artificial covariates
> x1 <- rbinom(50, 1, 0.4)                                         ## binary covariate
> x2 <- rnorm(50, 180, 10)                                         ## continuous covariate
> y1 <- 0.5*x1 - 0.01*x2 + 0.005 *x1*x2 + 1.5*rnorm(50, 0, 1)      ## generate log(T), left limit
> t1 <- exp(y1)                                                    ## left limit of the survival time
> t2 <- t1 + rgamma(50, 1, 1)                                      ## right limit of the survival time
> surv <- Surv(t1, t2, type = "interval2")                         ## survival object
> 
> ## Fit the model with an interaction
> fit1 <- smoothSurvReg(surv ~ x1 * x2, logscale = ~1, info = FALSE, lambda = exp(2:(-1)))

Fit with Log(Lambda) = 2,  AIC(7.389056) = -88.61158,  df(7.389056) = 5.946675,  5 iterations,  fail = 0
Fit with Log(Lambda) = 1,  AIC(2.718282) = NA,  df(2.718282) = NA,  NA iterations,  fail = 103
Fit with Log(Lambda) = 0,  AIC(1) = -87.31,  df(1) = 6.65778,  14 iterations,  fail = 0
Fit with Log(Lambda) = -1,  AIC(0.3678794) = -86.80626,  df(0.3678794) = 6.991268,  16 iterations,  fail = 0
> 
> ## Print the summary information
> summary(fit1, spline = TRUE)
Call:
smoothSurvReg(formula = surv ~ x1 * x2, logscale = ~1, lambda = exp(2:(-1)), 
    info = FALSE)

Estimated Regression Coefficients:
               Value Std.Error Std.Error2       Z      Z2      p      p2
(Intercept)  1.24499   4.19250    3.25489  0.2970  0.3825 0.7665 0.70209
x1           5.23252   5.05405    4.10865  1.0353  1.2735 0.3005 0.20283
x2          -0.01060   0.02276    0.01758 -0.4656 -0.6026 0.6415 0.54677
x1:x2       -0.02557   0.02722    0.02257 -0.9391 -1.1328 0.3477 0.25729
Log(scale)  -0.14146   0.10245    0.08511 -1.3809 -1.6622 0.1673 0.09647

Scale = 0.8681 

Details on (Fitted) Error Distribution:
         Knot SD basis   c coef. Std.Error.c Std.Error2.c       Z       Z2
knot[1]  -6.0      0.2 1.160e-30   7.296e-29    3.170e-29 0.01590  0.03660
knot[2]  -5.7      0.2 1.674e-27   9.059e-26    4.059e-26 0.01848  0.04124
knot[3]  -5.4      0.2 1.591e-24   7.335e-23    3.397e-23 0.02169  0.04683
knot[4]  -5.1      0.2 9.952e-22   3.868e-20    1.856e-20 0.02573  0.05363
knot[5]  -4.8      0.2 4.099e-19   1.327e-17    6.610e-18 0.03090  0.06202
knot[6]  -4.5      0.2 1.112e-16   2.953e-15    1.533e-15 0.03765  0.07254
knot[7]  -4.2      0.2 1.985e-14   4.256e-13    2.309e-13 0.04665  0.08599
knot[8]  -3.9      0.2 2.334e-12   3.959e-11    2.254e-11 0.05896  0.10354
knot[9]  -3.6      0.2 1.807e-10   2.368e-09    1.422e-09 0.07631  0.12707
knot[10] -3.3      0.2 9.210e-09   9.057e-08    5.770e-08 0.10169  0.15963
knot[11] -3.0      0.2 3.091e-07   2.200e-06    1.497e-06 0.14051  0.20650
knot[12] -2.7      0.2 6.830e-06   3.359e-05    2.461e-05 0.20336  0.27756
knot[13] -2.4      0.2 9.936e-05   3.177e-04    2.528e-04 0.31276  0.39303
knot[14] -2.1      0.2 9.518e-04   1.823e-03    1.585e-03 0.52208  0.60041
knot[15] -1.8      0.2 6.003e-03   6.166e-03    5.778e-03 0.97357  1.03896
knot[16] -1.5      0.2 2.494e-02   1.214e-02    1.061e-02 2.05409  2.35137
knot[17] -1.2      0.2 6.846e-02   1.669e-02          NaN 4.10171      NaN
knot[18] -0.9      0.2 1.262e-01   2.278e-02    9.521e-03 5.54110 13.25504
knot[19] -0.6      0.2 1.611e-01   3.020e-02    2.497e-02 5.33412  6.45070
knot[20] -0.3      0.2 1.510e-01   3.458e-02          NaN 4.36627      NaN
knot[21]  0.0      0.2 1.147e-01   2.779e-02          NaN 4.12634      NaN
knot[22]  0.3      0.2 7.966e-02   1.817e-02    5.694e-03 4.38334 13.98965
knot[23]  0.6      0.2 5.669e-02   1.495e-02    1.109e-02 3.79252  5.11156
knot[24]  0.9      0.2 4.464e-02   1.692e-02    5.439e-03 2.63771  8.20758
knot[25]  1.2      0.2 3.971e-02   1.941e-02          NaN 2.04611      NaN
knot[26]  1.5      0.2 3.802e-02   1.895e-02          NaN 2.00660      NaN
knot[27]  1.8      0.2 3.511e-02   1.280e-02          NaN 2.74386      NaN
knot[28]  2.1      0.2 2.726e-02   6.962e-03    3.959e-03 3.91611  6.88741
knot[29]  2.4      0.2 1.607e-02   9.250e-03          NaN 1.73682      NaN
knot[30]  2.7      0.2 6.833e-03   7.627e-03          NaN 0.89590      NaN
knot[31]  3.0      0.2 2.066e-03   3.799e-03    1.341e-03 0.54380  1.54098
knot[32]  3.3      0.2 4.429e-04   1.249e-03    6.639e-04 0.35471  0.66702
knot[33]  3.6      0.2 6.727e-05   2.785e-04    1.678e-04 0.24155  0.40083
knot[34]  3.9      0.2 7.239e-06   4.250e-05    2.649e-05 0.17034  0.27332
knot[35]  4.2      0.2 5.521e-07   4.453e-06    2.757e-06 0.12397  0.20026
knot[36]  4.5      0.2 2.983e-08   3.214e-07    1.939e-07 0.09282  0.15386
knot[37]  4.8      0.2 1.142e-09   1.603e-08    9.339e-09 0.07127  0.12231
knot[38]  5.1      0.2 3.099e-11   5.539e-10    3.106e-10 0.05595  0.09977
knot[39]  5.4      0.2 5.957e-13   1.330e-11    7.172e-12 0.04477  0.08306
knot[40]  5.7      0.2 8.114e-15   2.227e-13    1.154e-13 0.03644  0.07029
knot[41]  6.0      0.2 7.831e-17   2.603e-15    1.298e-15 0.03009  0.06031
                 p        p2
knot[1]  9.873e-01 9.708e-01
knot[2]  9.853e-01 9.671e-01
knot[3]  9.827e-01 9.627e-01
knot[4]  9.795e-01 9.572e-01
knot[5]  9.753e-01 9.505e-01
knot[6]  9.700e-01 9.422e-01
knot[7]  9.628e-01 9.315e-01
knot[8]  9.530e-01 9.175e-01
knot[9]  9.392e-01 8.989e-01
knot[10] 9.190e-01 8.732e-01
knot[11] 8.883e-01 8.364e-01
knot[12] 8.389e-01 7.813e-01
knot[13] 7.545e-01 6.943e-01
knot[14] 6.016e-01 5.482e-01
knot[15] 3.303e-01 2.988e-01
knot[16] 3.997e-02 1.870e-02
knot[17] 4.101e-05       NaN
knot[18] 3.006e-08 4.219e-40
knot[19] 9.601e-08 1.113e-10
knot[20] 1.264e-05       NaN
knot[21] 3.686e-05       NaN
knot[22] 1.169e-05 1.803e-44
knot[23] 1.491e-04 3.195e-07
knot[24] 8.347e-03 2.257e-16
knot[25] 4.075e-02       NaN
knot[26] 4.479e-02       NaN
knot[27] 6.072e-03       NaN
knot[28] 8.999e-05 5.682e-12
knot[29] 8.242e-02       NaN
knot[30] 3.703e-01       NaN
knot[31] 5.866e-01 1.233e-01
knot[32] 7.228e-01 5.048e-01
knot[33] 8.091e-01 6.885e-01
knot[34] 8.647e-01 7.846e-01
knot[35] 9.013e-01 8.413e-01
knot[36] 9.260e-01 8.777e-01
knot[37] 9.432e-01 9.027e-01
knot[38] 9.554e-01 9.205e-01
knot[39] 9.643e-01 9.338e-01
knot[40] 9.709e-01 9.440e-01
knot[41] 9.760e-01 9.519e-01

Penalized Loglikelihood and Its Components:
     Log-likelihood: -79.81499 
            Penalty: -0.8711076 
   Penalized Log-likelihood: -80.6861 

Degree of smoothing:
   Number of parameters: 43 
                   Mean parameters: 4 
                  Scale parameters: 1 
                 Spline parameters: 38 

                   Lambda: 0.3678794 
              Log(Lambda): -1 
                       df: 6.991268 

AIC (higher is better):  -86.80626 

Number of Newton-Raphson Iterations:  16 
n = 50 
> 
> ## Plot the fitted error distribution
> plot(fit1)
> 
> ## Plot the fitted error distribution with its components
> plot(fit1, components = TRUE)
> 
> ## Plot the cumulative distribution function corresponding to the error density
> survfit(fit1, cdf = TRUE)
> 
> ## Plot survivor curves for persons with (x1, x2) = (0, 180) and (1, 180)
> cov <- matrix(c(0, 180, 0,   1, 180, 180), ncol = 3, byrow = TRUE)
> survfit(fit1, cov = cov)
> 
> ## Plot hazard curves for persons with (x1, x2) = (0, 180) and (1, 180)
> cov <- matrix(c(0, 180, 0,   1, 180, 180), ncol = 3, byrow = TRUE)
> hazard(fit1, cov = cov)
> 
> ## Plot densities for persons with (x1, x2) = (0, 180) and (1, 180)
> cov <- matrix(c(0, 180, 0,   1, 180, 180), ncol = 3, byrow = TRUE)
> fdensity(fit1, cov = cov)
> 
> ## Compute estimates expectations of survival times for persons with
> ## (x1, x2) = (0, 180), (1, 180), (0, 190), (1, 190), (0, 200), (1, 200)
> ## and estimates of a difference of these expectations:
> ## T(0, 180) - T(1, 180), T(0, 190) - T(1, 190), T(0, 200) - T(1, 200),
> cov1 <- matrix(c(0, 180, 0,   0, 190, 0,   0, 200, 0), ncol = 3, byrow = TRUE)
> cov2 <- matrix(c(1, 180, 180,   1, 190, 190,   1, 200, 200), ncol = 3, byrow = TRUE)
> print(estimTdiff(fit1, cov1 = cov1, cov2 = cov2))

Covariate Values Compared:
   Covariate values for T1:
        x1  x2 x1:x2
Value 1  0 180     0
Value 2  0 190     0
Value 3  0 200     0

   Covariate values for T2:
        x1  x2 x1:x2
Value 1  1 180   180
Value 2  1 190   190
Value 3  1 200   200


Estimates of Expectations:
            T1 Std.Error      Z      p
Value 1 0.8059     1.320 0.6107 0.5414
Value 2 0.7248     1.184 0.6123 0.5403
Value 3 0.6520     1.082 0.6023 0.5470

            T2 Std.Error      Z      p
Value 1 1.5138     2.499 0.6058 0.5446
Value 2 1.0545     1.751 0.6021 0.5471
Value 3 0.7345     1.236 0.5944 0.5522

         T1 - T2 Std.Error       Z      p
Value 1 -0.70800    1.2249 -0.5780 0.5633
Value 2 -0.32962    0.6211 -0.5307 0.5956
Value 3 -0.08251    0.3629 -0.2274 0.8201

> 
> ## More involved examples can be found in script files
> ## used to perform analyses  and draw pictures 
> ## presented in /doc/paper1.pdf and /doc/paper2.pdf of this library.
> ## These scripts can be found as *.tar.gz files in the same directory.
> ##
> ## I am not sure whether Windows precombiled binary distributions
> ## of contributed packages contain this directory.
> ## If not, download source version of the library from CRAN
> ## (tar.gz file), unpack it and you find it.
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "std.data"
> 
> ### * std.data
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: std.data
> ### Title: Standardization of the Data
> ### Aliases: std.data
> ### Keywords: manip
> 
> ### ** Examples
> 
> variable1 <- rnorm(30)
> variable2 <- rbinom(30, 1, 0.4)
> variable3 <- runif(30)
> data.example <- data.frame(variable1, variable2, variable3)
> ## We standardize only the first and the third column.
> data.std <- std.data(data.example, c("variable1", "variable3"))

Number of standardized columns:  2 

Used means and sd's: 
      variable1 variable3
mean 0.08245817 0.5161663
sd   0.92412083 0.2853755
> print(data.std)
      variable1 variable2  variable3
1  -0.767120446         1 -0.9690280
2   0.109493425         0 -1.6022114
3  -0.993470503         0  0.4419510
4   1.637039863         0  1.2618565
5   0.267334741         1  0.9207111
6  -0.977065475         0  0.9851671
7   0.438222871         0 -0.2133744
8   0.709719461         1 -0.3717284
9   0.533829741         0  1.0326884
10 -0.419692475         1  0.3110534
11  1.546684110         0  0.4855275
12  0.332624325         1 -0.5710686
13 -0.761479160         0 -0.8616931
14 -2.485776741         0  1.6697921
15  1.128069748         0  0.4111320
16 -0.137851865         1 -1.0616122
17 -0.106748415         1 -1.3553858
18  0.932105430         0 -0.1333269
19  0.799422547         1  1.4293735
20  0.553437533         1  0.2894246
21  0.905205442         0  1.6119267
22  0.757128408         1  0.7555877
23 -0.008541293         0 -0.5587002
24 -2.241925304         0 -0.2967759
25  0.581490604         1 -1.2893703
26 -0.149966223         0 -1.7629007
27 -0.257816586         1  0.6987278
28 -1.680744021         0 -1.4471530
29 -0.606639531         0 -0.2448771
30  0.363029790         0  0.4342866
> print(c(mean(data.std$variable1), sd(data.std$variable1)))
[1] -9.251859e-18  1.000000e+00
> print(c(mean(data.std$variable3), sd(data.std$variable3)))
[1] -9.621933e-17  1.000000e+00
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  7.19 9.75 17.1 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')