smoothSurvReg: Regression for a Survival Model with Smoothed Error...

Description Usage Arguments Details Value Author(s) References Examples

View source: R/smoothSurvReg.R

Description

Regression for a survival model. These are all time-transformed location models, with the most useful case being the accelerated failure models that use a log transformation. Error distribution is assumed to be a mixture of G-splines. Parameters are estimated by the penalized maximum likelihood method.

Usage

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smoothSurvReg(formula = formula(data), logscale = ~1, 
   data = parent.frame(), subset, na.action = na.fail,
   init.beta, init.logscale, init.c, init.dist = "best",
   update.init = TRUE, aic = TRUE, lambda = exp(2:(-9)),
   model = FALSE, control = smoothSurvReg.control(), ...)

Arguments

formula

A formula expression as for other regression models. See the documentation for lm and formula for details. Use Surv on the left hand side of the formula.

logscale

A formula expression to determine a possible dependence of the log-scale on covariates.

data

Optional data frame in which to interpret the variables occurring in the formula.

subset

Subset of the observations to be used in the fit.

na.action

Function to be used to handle any NAs in the data. It's default value is na.fail. It is not recommended to change it in the case when logscale depends on covariates.

init.beta

Optional vector of the initial values of the regression parameter beta (intercept and regression itself).

init.logscale

Optional value of the initial value of the parameters that determines the log-scale parameter log(sigma).

init.c

Optional vector of the initial values for the G-spline coefficients c, all values must lie between 0 and 1 and must sum up to 1.

init.dist

A character string specifying the distribution used by survreg to find the initial values for parameters (if not given by the user). It is assumed to name "best" or an element from survreg.distributions. These include "weibull", "exponential", "gaussian", "logistic", "lognormal" and "loglogistic". If "best" is specified one of "lognormal", "weibull" and "loglogistic" giving the highest likelihood is used.

update.init

If TRUE, the initial values are updated during the grid search for the lambda parameter giving the optimal AIC. Otherwise, fits with all lambdas during the grid search start with same initials determine at the beginning either from the values of init.beta, init.scale, init.c or from the initial survreg fit as determined by the parameter init.dist.

aic

If TRUE the optimal value of the tuning parameter lambda is determined via a grid search through the values specified by the parameter lambda. If FALSE, only the model with lambda = lambda[1] is fitted.

lambda

A grid of values of the tuning parameter lambda searched for the optimal value if aic = TRUE.

model

If TRUE, the model frame is returned.

control

A list of control values, in the format producted by smoothSurvReg.control.

...

Other arguments which will be passed to smoothSurvReg.control. See its help page for more options to control the fit and for the possibility to fix some values and not to estimate them.

Details

Read the papers referred below.

There is a slight difference in the definition of the penalty used by the R function compared to what is written in the paper. The penalized log-likelihood given in the paper has a form

l_P(theta) = l(theta) - (lambda/2) * sum[j in (m+1):g] (Delta^m a[j])^2,

while the penalized log-likelihood used in the R function multiplies the tuning parameter lambda given by lambda by a sample size n to keep default values more or less useful for samples of different sizes. So that the penalized log-likelihood which is maximized by the R function has the form

l_P(theta) = l(theta) - ((lambda*n)/2) * sum[j in (m+1):g] (Delta^m a[j])^2.

Value

An object of class smoothSurvReg is returned. See smoothSurvReg.object for details.

Author(s)

Arnošt Komárek arnost.komarek[AT]mff.cuni.cz

References

Komárek, A., Lesaffre, E., and Hilton, J. F. (2005). Accelerated failure time model for arbitrarily censored data with smoothed error distribution. Journal of Computational and Graphical Statistics, 14, 726–745.

Lesaffre, E., Komárek, A., and Declerck, D. (2005). An overview of methods for interval-censored data with an emphasis on applications in dentistry. Statistical Methods in Medical Research, 14, 539–552.

Examples

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##### EXAMPLE 1:  Common scale
##### ========================
### We generate interval censored data and fit a model with few artificial covariates
set.seed(221913282)
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)))

## Print the summary information
summary(fit1, spline = TRUE)

## 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))


##### EXAMPLE 2:  Scale depends on covariates
##### =======================================
### We generate interval censored data and fit a model with few artificial covariates
set.seed(221913282)
x1 <- rbinom(50, 1, 0.4)                                        ## binary covariate
x2 <- rnorm(50, 180, 10)                                        ## continuous covariate
x3 <- runif(50, 0, 1)                                           ## covariate for the scale parameter
logscale <- 1 + x3
scale <- exp(logscale)
y1 <- 0.5*x1 - 0.01*x2 + 0.005 *x1*x2 + scale*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
fit2 <- smoothSurvReg(surv ~ x1 * x2, logscale = ~x3, info = FALSE, lambda = exp(2:(-1)))

## Print the summary information
summary(fit2, spline = TRUE)

## Plot the fitted error distribution
plot(fit2)

## Plot the fitted error distribution with its components
plot(fit2, components = TRUE)

## Plot survivor curves for persons with (x1, x2) = (0, 180) and (1, 180)
## x3 = 0.8 and 0.9
cov <- matrix(c(0, 180, 0,   1, 180, 180), ncol = 3, byrow = TRUE)
logscale.cov <- c(0.8, 0.9)
survfit(fit2, cov = cov, logscale.cov = logscale.cov)

## Plot hazard curves for persons with (x1, x2) = (0, 180) and (1, 180)
## x3 = 0.8 and 0.9
cov <- matrix(c(0, 180, 0,   1, 180, 180), ncol = 3, byrow = TRUE)
logscale.cov <- c(0.8, 0.9)
hazard(fit2, cov = cov, logscale.cov=c(0.8, 0.9))

## Plot densities for persons with (x1, x2) = (0, 180) and (1, 180)
## x3 = 0.8 and 0.9
cov <- matrix(c(0, 180, 0,   1, 180, 180), ncol = 3, byrow = TRUE)
logscale.cov <- c(0.8, 0.9)
fdensity(fit2, cov = cov, logscale.cov = logscale.cov)


## More involved examples can be found in script files
## used to perform analyses  and draw pictures 
## presented in above mentioned references.
## These scripts and some additional files can be found as *.tar.gz files
## in the /inst/doc directory of this package.
##

Example output

Loading required package: survival

### Survival Regression with Smoothed Error Distribution 
### Arnost Komarek

### See citation("smoothSurv") or toBibtex(citation("smoothSurv")) for the best way to cite
### the package if you find it useful.



Fit with Log(Lambda) = 2,  AIC(7.389056) = -74.87861,  df(7.389056) = 5.778042,  5 iterations,  fail = 0
Fit with Log(Lambda) = 1,  AIC(2.718282) = -74.72757,  df(2.718282) = 5.998688,  5 iterations,  fail = 0
Fit with Log(Lambda) = 0,  AIC(1) = -75.57301,  df(1) = 7.650132,  11 iterations,  fail = 0
Fit with Log(Lambda) = -1,  AIC(0.3678794) = -75.26248,  df(0.3678794) = 8.1979,  24 iterations,  fail = 10
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) -1.798245   3.28004    3.08262 -0.5482 -0.5833 0.58353 0.55966
x1          -3.776777   4.40587    4.31387 -0.8572 -0.8755 0.39133 0.38130
x2           0.006289   0.01805    0.01700  0.3484  0.3700 0.72750 0.71137
x1:x2        0.025351   0.02442    0.02387  1.0381  1.0620 0.29924 0.28823
Log(scale)  -0.251601   0.13887    0.12862 -1.8118 -1.9561 0.07002 0.05045

Scale = 0.7776 

Details on (Fitted) Error Distribution:
         Knot SD basis   c coef. Std.Error.c Std.Error2.c       Z       Z2
knot[1]  -6.0      0.2 3.739e-07   1.088e-05    1.076e-05 0.03435  0.03474
knot[2]  -5.7      0.2 9.482e-07   2.357e-05    2.360e-05 0.04023  0.04017
knot[3]  -5.4      0.2 2.348e-06   4.923e-05    4.999e-05 0.04770  0.04698
knot[4]  -5.1      0.2 5.680e-06   9.901e-05    1.020e-04 0.05736  0.05567
knot[5]  -4.8      0.2 1.341e-05   1.912e-04    2.001e-04 0.07016  0.06701
knot[6]  -4.5      0.2 3.093e-05   3.532e-04    3.762e-04 0.08758  0.08221
knot[7]  -4.2      0.2 6.965e-05   6.215e-04    6.747e-04 0.11207  0.10323
knot[8]  -3.9      0.2 1.531e-04   1.035e-03    1.148e-03 0.14797  0.13345
knot[9]  -3.6      0.2 3.288e-04   1.617e-03    1.835e-03 0.20337  0.17920
knot[10] -3.3      0.2 6.893e-04   2.337e-03    2.721e-03 0.29491  0.25331
knot[11] -3.0      0.2 1.411e-03   3.061e-03    3.656e-03 0.46079  0.38581
knot[12] -2.7      0.2 2.817e-03   3.510e-03    4.247e-03 0.80266  0.66331
knot[13] -2.4      0.2 5.484e-03   3.388e-03    3.750e-03 1.61902  1.46245
knot[14] -2.1      0.2 1.038e-02   3.430e-03    6.893e-04 3.02711 15.06442
knot[15] -1.8      0.2 1.902e-02   6.483e-03    3.908e-03 2.93345  4.86679
knot[16] -1.5      0.2 3.330e-02   1.220e-02    1.232e-02 2.72943  2.70295
knot[17] -1.2      0.2 5.470e-02   1.771e-02    2.056e-02 3.08817  2.66120
knot[18] -0.9      0.2 8.214e-02   1.946e-02    2.286e-02 4.22049  3.59363
knot[19] -0.6      0.2 1.098e-01   1.672e-02    1.392e-02 6.56935  7.89018
knot[20] -0.3      0.2 1.284e-01   1.649e-02          NaN 7.78790      NaN
knot[21]  0.0      0.2 1.308e-01   2.054e-02    1.682e-02 6.36685  7.77455
knot[22]  0.3      0.2 1.174e-01   2.109e-02    2.312e-02 5.56659  5.07795
knot[23]  0.6      0.2 9.511e-02   1.763e-02    1.895e-02 5.39448  5.01909
knot[24]  0.9      0.2 7.131e-02   1.354e-02    9.280e-03 5.26455  7.68362
knot[25]  1.2      0.2 5.056e-02   1.045e-02          NaN 4.84034      NaN
knot[26]  1.5      0.2 3.430e-02   7.953e-03          NaN 4.31219      NaN
knot[27]  1.8      0.2 2.224e-02   5.918e-03    3.833e-03 3.75691  5.80084
knot[28]  2.1      0.2 1.366e-02   4.590e-03    4.756e-03 2.97635  2.87256
knot[29]  2.4      0.2 7.876e-03   3.800e-03    3.787e-03 2.07276  2.07988
knot[30]  2.7      0.2 4.227e-03   3.099e-03    2.315e-03 1.36411  1.82558
knot[31]  3.0      0.2 2.102e-03   2.315e-03    1.039e-03 0.90802  2.02380
knot[32]  3.3      0.2 9.673e-04   1.548e-03          NaN 0.62504      NaN
knot[33]  3.6      0.2 4.113e-04   9.231e-04          NaN 0.44561      NaN
knot[34]  3.9      0.2 1.616e-04   4.930e-04          NaN 0.32787      NaN
knot[35]  4.2      0.2 5.868e-05   2.367e-04          NaN 0.24795      NaN
knot[36]  4.5      0.2 1.968e-05   1.025e-04          NaN 0.19200      NaN
knot[37]  4.8      0.2 6.101e-06   4.020e-05          NaN 0.15176      NaN
knot[38]  5.1      0.2 1.747e-06   1.431e-05          NaN 0.12212      NaN
knot[39]  5.4      0.2 4.622e-07   4.631e-06          NaN 0.09981      NaN
knot[40]  5.7      0.2 1.130e-07   1.366e-06          NaN 0.08271      NaN
knot[41]  6.0      0.2 2.552e-08   3.679e-07          NaN 0.06937      NaN
                 p        p2
knot[1]  9.726e-01 9.723e-01
knot[2]  9.679e-01 9.680e-01
knot[3]  9.620e-01 9.625e-01
knot[4]  9.543e-01 9.556e-01
knot[5]  9.441e-01 9.466e-01
knot[6]  9.302e-01 9.345e-01
knot[7]  9.108e-01 9.178e-01
knot[8]  8.824e-01 8.938e-01
knot[9]  8.388e-01 8.578e-01
knot[10] 7.681e-01 8.000e-01
knot[11] 6.449e-01 6.996e-01
knot[12] 4.222e-01 5.071e-01
knot[13] 1.054e-01 1.436e-01
knot[14] 2.469e-03 2.776e-51
knot[15] 3.352e-03 1.134e-06
knot[16] 6.344e-03 6.873e-03
knot[17] 2.014e-03 7.786e-03
knot[18] 2.438e-05 3.261e-04
knot[19] 5.053e-11 3.017e-15
knot[20] 6.813e-15       NaN
knot[21] 1.929e-10 7.572e-15
knot[22] 2.598e-08 3.815e-07
knot[23] 6.872e-08 5.192e-07
knot[24] 1.405e-07 1.547e-14
knot[25] 1.296e-06       NaN
knot[26] 1.616e-05       NaN
knot[27] 1.720e-04 6.598e-09
knot[28] 2.917e-03 4.072e-03
knot[29] 3.819e-02 3.754e-02
knot[30] 1.725e-01 6.791e-02
knot[31] 3.639e-01 4.299e-02
knot[32] 5.319e-01       NaN
knot[33] 6.559e-01       NaN
knot[34] 7.430e-01       NaN
knot[35] 8.042e-01       NaN
knot[36] 8.477e-01       NaN
knot[37] 8.794e-01       NaN
knot[38] 9.028e-01       NaN
knot[39] 9.205e-01       NaN
knot[40] 9.341e-01       NaN
knot[41] 9.447e-01       NaN

Penalized Loglikelihood and Its Components:
     Log-likelihood: -68.72888 
            Penalty: -0.3006102 
   Penalized Log-likelihood: -69.02949 

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

                   Lambda: 2.718282 
              Log(Lambda): 1 
                       df: 5.998688 

AIC (higher is better):  -74.72757 

Number of Newton-Raphson Iterations:  5 
n = 50 

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
and Their 95% Confidence Intervals
           ET1 Std.Error Lower Upper      Z      p
Value 1 0.7054    0.8824     0 2.435 0.7994 0.4241
Value 2 0.7512    0.9612     0 2.635 0.7815 0.4345
Value 3 0.7999    1.0658     0 2.889 0.7505 0.4529

          ET2 Std.Error Lower  Upper      Z      p
Value 1 1.549     1.963     0  5.397 0.7888 0.4302
Value 2 2.125     2.731     0  7.477 0.7782 0.4364
Value 3 2.916     3.866     0 10.492 0.7543 0.4506

                  E(T1 - T2) Std.Error  Lower Upper       Z      p
Value 1 - Value 1    -0.8433     1.121 -3.040 1.353 -0.7525 0.4518
Value 2 - Value 2    -1.3739     1.831 -4.963 2.215 -0.7502 0.4531
Value 3 - Value 3    -2.1161     2.929 -7.858 3.625 -0.7224 0.4701


Fit with Log(Lambda) = 2,  AIC(7.389056) = -200.8978,  df(7.389056) = 6.948282,  10 iterations,  fail = 0
Fit with Log(Lambda) = 1,  AIC(2.718282) = -201.2179,  df(2.718282) = 7.434986,  4 iterations,  fail = 0
Fit with Log(Lambda) = 0,  AIC(1) = -201.5309,  df(1) = 7.939519,  4 iterations,  fail = 0
Fit with Log(Lambda) = -1,  AIC(0.3678794) = -201.7619,  df(0.3678794) = 8.483009,  4 iterations,  fail = 0
Call:
smoothSurvReg(formula = surv ~ x1 * x2, logscale = ~x3, lambda = exp(2:(-1)), 
    info = FALSE)

Estimated Regression Coefficients:
                        Value Std.Error Std.Error2        Z       Z2         p
(Intercept)         23.132322  10.06787   10.26891  2.29764  2.25266 2.158e-02
x1                 -29.360492  12.08206   12.05034 -2.43009 -2.43649 1.510e-02
x2                  -0.130182   0.05607    0.05722 -2.32159 -2.27494 2.025e-02
x1:x2                0.170231   0.06693    0.06676  2.54357  2.54978 1.097e-02
LScale.(Intercept)   0.007919   0.25811    0.25668  0.03068  0.03085 9.755e-01
LScale.x3            2.053904   0.46946    0.47152  4.37503  4.35593 1.214e-05
                          p2
(Intercept)        2.428e-02
x1                 1.483e-02
x2                 2.291e-02
x1:x2              1.078e-02
LScale.(Intercept) 9.754e-01
LScale.x3          1.325e-05

Details on (Fitted) Error Distribution:
         Knot SD basis   c coef. Std.Error.c Std.Error2.c        Z       Z2
knot[1]  -6.0      0.2 5.582e-13   8.208e-12    6.655e-12  0.06801  0.08389
knot[2]  -5.7      0.2 8.220e-12   1.042e-10    8.649e-11  0.07886  0.09504
knot[3]  -5.4      0.2 1.045e-10   1.132e-09    9.627e-10  0.09230  0.10857
knot[4]  -5.1      0.2 1.148e-09   1.051e-08    9.168e-09  0.10919  0.12522
knot[5]  -4.8      0.2 1.089e-08   8.327e-08    7.457e-08  0.13075  0.14600
knot[6]  -4.5      0.2 8.918e-08   5.616e-07    5.172e-07  0.15879  0.17244
knot[7]  -4.2      0.2 6.309e-07   3.218e-06    3.051e-06  0.19608  0.20676
knot[8]  -3.9      0.2 3.854e-06   1.561e-05    1.527e-05  0.24694  0.25246
knot[9]  -3.6      0.2 2.034e-05   6.385e-05    6.452e-05  0.31854  0.31520
knot[10] -3.3      0.2 9.267e-05   2.189e-04    2.290e-04  0.42328  0.40468
knot[11] -3.0      0.2 3.647e-04   6.242e-04    6.770e-04  0.58423  0.53869
knot[12] -2.7      0.2 1.240e-03   1.462e-03    1.646e-03  0.84811  0.75291
knot[13] -2.4      0.2 3.638e-03   2.753e-03    3.224e-03  1.32148  1.12863
knot[14] -2.1      0.2 9.224e-03   4.027e-03    4.880e-03  2.29041  1.89003
knot[15] -1.8      0.2 2.020e-02   4.310e-03    5.178e-03  4.68753  3.90119
knot[16] -1.5      0.2 3.825e-02   3.802e-03    2.833e-03 10.06011 13.49941
knot[17] -1.2      0.2 6.269e-02   6.650e-03    5.294e-03  9.42765 11.84106
knot[18] -0.9      0.2 8.932e-02   1.132e-02    1.223e-02  7.88978  7.30470
knot[19] -0.6      0.2 1.115e-01   1.355e-02    1.587e-02  8.22597  7.02281
knot[20] -0.3      0.2 1.233e-01   1.199e-02    1.359e-02 10.28690  9.07296
knot[21]  0.0      0.2 1.228e-01   8.869e-03    7.187e-03 13.84087 17.07876
knot[22]  0.3      0.2 1.113e-01   8.488e-03    5.770e-03 13.11203 19.28735
knot[23]  0.6      0.2 9.280e-02   1.015e-02    1.048e-02  9.14767  8.85348
knot[24]  0.9      0.2 7.180e-02   1.042e-02    1.221e-02  6.88817  5.87926
knot[25]  1.2      0.2 5.198e-02   8.709e-03    1.047e-02  5.96848  4.96609
knot[26]  1.5      0.2 3.547e-02   5.966e-03    6.822e-03  5.94580  5.19981
knot[27]  1.8      0.2 2.293e-02   3.466e-03    3.114e-03  6.61613  7.36579
knot[28]  2.1      0.2 1.407e-02   2.252e-03    1.444e-03  6.24772  9.74550
knot[29]  2.4      0.2 8.182e-03   2.194e-03    2.314e-03  3.72900  3.53535
knot[30]  2.7      0.2 4.502e-03   2.155e-03    2.657e-03  2.08934  1.69440
knot[31]  3.0      0.2 2.339e-03   1.824e-03    2.340e-03  1.28210  0.99941
knot[32]  3.3      0.2 1.146e-03   1.346e-03    1.736e-03  0.85178  0.66020
knot[33]  3.6      0.2 5.297e-04   8.833e-04    1.131e-03  0.59969  0.46848
knot[34]  3.9      0.2 2.308e-04   5.235e-04    6.604e-04  0.44079  0.34943
knot[35]  4.2      0.2 9.477e-05   2.830e-04    3.504e-04  0.33494  0.27045
knot[36]  4.5      0.2 3.669e-05   1.404e-04    1.703e-04  0.26134  0.21540
knot[37]  4.8      0.2 1.339e-05   6.426e-05    7.629e-05  0.20839  0.17552
knot[38]  5.1      0.2 4.607e-06   2.723e-05    3.161e-05  0.16921  0.14573
knot[39]  5.4      0.2 1.494e-06   1.071e-05    1.216e-05  0.13953  0.12290
knot[40]  5.7      0.2 4.567e-07   3.917e-06    4.349e-06  0.11661  0.10502
knot[41]  6.0      0.2 1.316e-07   1.335e-06    1.450e-06  0.09858  0.09076
                 p        p2
knot[1]  9.458e-01 9.331e-01
knot[2]  9.371e-01 9.243e-01
knot[3]  9.265e-01 9.135e-01
knot[4]  9.131e-01 9.004e-01
knot[5]  8.960e-01 8.839e-01
knot[6]  8.738e-01 8.631e-01
knot[7]  8.445e-01 8.362e-01
knot[8]  8.050e-01 8.007e-01
knot[9]  7.501e-01 7.526e-01
knot[10] 6.721e-01 6.857e-01
knot[11] 5.591e-01 5.901e-01
knot[12] 3.964e-01 4.515e-01
knot[13] 1.863e-01 2.591e-01
knot[14] 2.200e-02 5.875e-02
knot[15] 2.765e-06 9.572e-05
knot[16] 8.291e-24 1.576e-41
knot[17] 4.194e-21 2.394e-32
knot[18] 3.027e-15 2.779e-13
knot[19] 1.936e-16 2.175e-12
knot[20] 8.073e-25 1.158e-19
knot[21] 1.444e-43 2.136e-65
knot[22] 2.810e-39 6.860e-83
knot[23] 5.818e-20 8.483e-19
knot[24] 5.651e-12 4.121e-09
knot[25] 2.395e-09 6.832e-07
knot[26] 2.751e-09 1.995e-07
knot[27] 3.687e-11 1.761e-13
knot[28] 4.165e-10 1.928e-22
knot[29] 1.922e-04 4.072e-04
knot[30] 3.668e-02 9.019e-02
knot[31] 1.998e-01 3.176e-01
knot[32] 3.943e-01 5.091e-01
knot[33] 5.487e-01 6.394e-01
knot[34] 6.594e-01 7.268e-01
knot[35] 7.377e-01 7.868e-01
knot[36] 7.938e-01 8.295e-01
knot[37] 8.349e-01 8.607e-01
knot[38] 8.656e-01 8.841e-01
knot[39] 8.890e-01 9.022e-01
knot[40] 9.072e-01 9.164e-01
knot[41] 9.215e-01 9.277e-01

Penalized Loglikelihood and Its Components:
     Log-likelihood: -193.9495 
            Penalty: -0.1709077 
   Penalized Log-likelihood: -194.1204 

Degree of smoothing:
   Number of parameters: 44 
                   Mean parameters: 4 
                  Scale parameters: 2 
                 Spline parameters: 38 

                   Lambda: 7.389056 
              Log(Lambda): 2 
                       df: 6.948282 

AIC (higher is better):  -200.8978 

Number of Newton-Raphson Iterations:  10 
n = 50 

smoothSurv documentation built on July 8, 2020, 5:46 p.m.