Description Usage Arguments Value References See Also Examples

Specifies a penalised spline basis for the predictor. This is done by fitting a comparatively small set of splines and penalising the integrated second derivative. Traditional smoothing splines use one basis per observation, but several authors have pointed out that the final results of the fit are indistinguishable for any number of basis functions greater than about 2-3 times the degrees of freedom. Eilers and Marx point out that if the basis functions are evenly spaced, this leads to significant computational simplification, they refer to the result as a p-spline.

1 2 3 4 |

`x` |
for psline: a covariate vector. The function does not apply to factor variables. For psplineinverse x will be the result of a pspline call. |

`df` |
the desired degrees of freedom.
One of the arguments |

`theta` |
roughness penalty for the fit. It is a monotone function of the degrees of freedom, with theta=1 corresponding to a linear fit and theta=0 to an unconstrained fit of nterm degrees of freedom. |

`nterm` |
number of splines in the basis |

`degree` |
degree of splines |

`eps` |
accuracy for |

`method` |
the method for choosing the tuning parameter |

`...` |
optional arguments to the control function |

`Boundary.knots` |
the spline is linear beyond the boundary knots. These default to the range of the data. |

`intercept` |
if TRUE, the basis functions include the intercept. |

`penalty` |
if FALSE a large number of attributes having to do with penalized fits are excluded. This is useful to create a pspline basis matrix for other uses. |

`combine` |
an optional vector of increasing integers. If two
adjacent values of |

Object of class `pspline, coxph.penalty`

containing the spline basis,
with the appropriate attributes to be
recognized as a penalized term by the coxph or survreg functions.

For psplineinverse the original x vector is reconstructed.

Eilers, Paul H. and Marx, Brian D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89-121.

Hurvich, C.M. and Simonoff, J.S. and Tsai, Chih-Ling (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion, JRSSB, volume 60, 271–293.

1 2 3 4 5 6 7 8 9 | ```
lfit6 <- survreg(Surv(time, status)~pspline(age, df=2), lung)
plot(lung$age, predict(lfit6), xlab='Age', ylab="Spline prediction")
title("Cancer Data")
fit0 <- coxph(Surv(time, status) ~ ph.ecog + age, lung)
fit1 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,3), lung)
fit3 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,8), lung)
fit0
fit1
fit3
``` |

```
Call:
coxph(formula = Surv(time, status) ~ ph.ecog + age, data = lung)
coef exp(coef) se(coef) z p
ph.ecog 0.443485 1.558128 0.115831 3.829 0.000129
age 0.011281 1.011345 0.009319 1.211 0.226082
Likelihood ratio test=19.06 on 2 df, p=7.279e-05
n= 227, number of events= 164
(1 observation deleted due to missingness)
Call:
coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 3),
data = lung)
coef se(coef) se2 Chisq DF p
ph.ecog 0.44802 0.11707 0.11678 14.64453 1.00 0.00013
pspline(age, 3), linear 0.01126 0.00928 0.00928 1.47231 1.00 0.22498
pspline(age, 3), nonlin 2.07924 2.08 0.37143
Iterations: 4 outer, 12 Newton-Raphson
Theta= 0.861
Degrees of freedom for terms= 1.0 3.1
Likelihood ratio test=21.9 on 4.08 df, p=2e-04
n= 227, number of events= 164
(1 observation deleted due to missingness)
Call:
coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 8),
data = lung)
coef se(coef) se2 Chisq DF p
ph.ecog 0.47640 0.12024 0.11925 15.69732 1.00 7.4e-05
pspline(age, 8), linear 0.01172 0.00923 0.00923 1.61161 1.00 0.20
pspline(age, 8), nonlin 6.93188 6.99 0.43
Iterations: 5 outer, 15 Newton-Raphson
Theta= 0.691
Degrees of freedom for terms= 1 8
Likelihood ratio test=27.6 on 8.97 df, p=0.001
n= 227, number of events= 164
(1 observation deleted due to missingness)
```

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