aisoph {aisoph} | R Documentation |

## Fit Additive Isotonic Proportional Hazards Model

### Description

Nonparametric estimation of additive isotonic covariate effects for proportional hazards model.

### Usage

```
aisoph(time, status, z1, z2, x, shape1, shape2, K1, K2, maxiter, eps)
```

### Arguments

`time` |
survival time. It must be greater than 0. |

`status` |
censoring indication. It must be 0 or 1. |

`z1` |
First covariate under order-restriction. |

`z2` |
Second covariate under-order restriction. |

`x` |
Additional covariates (vector or data.frame). This argument is optional |

`shape1` |
Shape-restriction for |

`shape2` |
Shape-restriction for |

`K1` |
anchor constraint for |

`K2` |
anchor constraint for |

`maxiter` |
maximum number of iteration (default is 10^5). |

`eps` |
stopping convergence criteria (default is 10^-3). |

### Details

The aisoph function allows to analyze additive isotonic proportional hazards model, which is defined as

` \lambda(t|z1, z2, x)=\lambda0(t)exp(\psi1(z1)+\psi2(z2)+\beta x), `

where ` \lambda0 `

is an unspecified baseline hazard function, ` \psi1 `

and ` \psi2 `

are monotone increasing (or decreasing) functions in `z1`

and `z2`

, respectively, `x`

is a covariate, and ` \beta `

is a regression paramter. If ` x `

is omitted in the formulation above, ` \psi1 `

and ` \psi2 `

are only estimated.

The model is not identifiable without the anchor constraint, `\psi1(K1)=0`

and `\psi2(K2)=0`

. By default, `K1`

and `K2`

are set to medians of `z1`

and `z2`

values, respectively. The choice of the anchor points is less important in the sense that hazard ratios do not depend on the anchors.

### Value

A list of class isoph:

`iso1` |
data.frame estimated |

`iso2` |
data.frame estimated |

`est` |
data.frame with estimated |

`conv` |
status of algorithm convergence. |

`shape1` |
shape-constrain for |

`shape2` |
shape-constrain for |

`K1` |
anchor point for K1. |

`K2` |
anchor point for K2. |

### Author(s)

Yunro Chung [aut, cre]

### References

Yunro Chung, Anastasia Ivanova, Jason P. Fine, Additive isotonic proportional hazards models (working in progress).

### Examples

```
#require(survival)
#require(Iso)
###
# 1. time-independent covariate with monotone increasing effect
###
# 1.1. create a test data set 1
time= c(1, 6, 3, 6, 7, 8, 1, 4, 0, 2, 1, 5, 8, 7, 4)
status=c(1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
z1= c(3, 1, 2, 4, 8, 3, 3, 4, 1, 9, 4, 2, 2, 8, 5)
z2= c(1, 3, 5, 6, 1, 7, 6, 8, 3, 4, 8, 8, 5, 2, 3)
# 1.2. Fit isotonic proportional hazards model
res1 = aisoph(time=time, status=status, z1=z1, z2=z2,
shape1="increasing", shape2="increasing")
# 1.3. print result
res1
#1.4. plot
plot(res1)
###
# 2. time-independent covariate with monotone increasing effect
###
# 2.1. create a test data set 1
time= c(0,4,8,9,5,6,9,8,2,7,4,2,6,2,5,9,4,3,8,2)
status=c(0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1)
z1= c(3,2,1,1,3,1,8,4,3,6,2,9,9,0,7,7,2,3,4,6)
z2= c(3,6,9,9,4,3,9,8,4,7,2,3,1,3,7,0,1,6,4,1)
trt= c(0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1)
# 2.2. Fit isotonic proportional hazards model
res2 = aisoph(time=time, status=status, z1=z1, z2=z2, x=trt,
shape1="increasing", shape2="increasing")
# 2.3. print result
res2
#2.4. plot
plot(res2)
```

*aisoph*version 0.4 Index]