# Non Proportional Hazard and Non Log-Linear effect

### Description

Generate the design matrix of spline basis for both non log-linear and non proportional effect.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
NPHNLL(x,
timevar,
model = c("additive", "multiplicative"),
Spline = c("b-spline", "tp-spline", "tpi-spline"),
Knots = NULL,
Degree = 3,
Intercept = FALSE,
Boundary.knots = range(x),
Knots.t = NULL,
Degree.t = 3,
Intercept.t = (model == "multiplicative"),
Boundary.knots.t = range(timevar),
outer.ok = TRUE,
Keep.duplicates = TRUE,
xdimnames = ":XxXxXXxXxX ",
tdimnames = ":TtTtTTtTtT ")
``` |

### Arguments

`x` |
the predictor variable. |

`timevar` |
the time variable. |

`model` |
character string specifying the type of model for both non-proportionnal and non linear effects.
The model |

`Spline` |
a character string specifying the type of spline basis. "b-spline" for B-spline basis, "tp-spline" for truncated power basis and "tpi-spline" for monotone (increasing) truncated power basis. |

`Knots` |
the internal breakpoints that define the spline used to estimate the NLL part of effect. By default there are none. |

`Degree` |
degree of splines of variable which are considered. |

`Intercept` |
a logical value indicating whether intercept/first basis of spline should be considered. |

`Boundary.knots` |
range of variable which is analysed. |

`Knots.t` |
the internal breakpoints that define the spline used to estimate the NPH part of effect. By default there are none. |

`Degree.t` |
degree of splines of time variable which are considered. |

`Intercept.t` |
a logical value indicating whether intercept/first basis of spline should be considered. |

`Boundary.knots.t` |
range of time period which is analysed. |

`Keep.duplicates` |
Should duplicate interior knots be kept or removed. Defaults is |

`outer.ok` |
logical indicating how are managed |

`xdimnames` |
string to build dimnames of |

`tdimnames` |
string to build dimnames of |

### Details

`NPHNLL`

is based on package `orthogonalsplinebasis`

### References

Mahboubi, A., M. Abrahamowicz, et al. (2011). "Flexible modeling of the effects of continuous prognostic factors in relative survival." Stat Med 30(12): 1351-1365. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("DOI:10.1002/sim.4208")}

Remontet, L., N. Bossard, et al. (2007). "An overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies." Stat Med 26(10): 2214-2228. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("10.1002/sim.2656")}

### See Also

`NPH`

and
`NLL`

.