# Incident/Dynamic (I/D) ROC curve, AUC and integrated AUC (iAUC) estimation of censored survival data

### Description

This function estimates the time-varying parameter estimate
*β(t)* of non-proportional
hazard model using local-linear Cox regression as discussed in
Heagerty and Zheng, 2005.

### Usage

1 |

### Arguments

`Stime` |
For right censored data, this is the follow up time. For left truncated data, this is the ending time for the interval. |

`entry` |
For left truncated data, this is the entry time of the interval. The default is set to NULL for right censored data. |

`status` |
Survival status. |

`marker` |
Marker value. |

`span` |
bandwidth parameter that controls the size of a local neighborhood. |

`p` |
1 if only the time-varying coefficient is of interest and 2 if the derivative of time-varying coefficient is also of interest, default is 1 |

`window` |
Either of "asymmetric" or "symmetric", default is asymmetric. |

### Details

This function calculates the parameter estimate *β(t)*
of non-proportional hazard model using local-linear Cox regression as
discussed in Heagerty and Zheng, 2005. This estimation is based on a
time-dependent Cox model (Cai and Sun, 2003). For *p=1*, the
return item *beta* has two columns, the first column is the
time-varying parameter estimate, while the second column is the
derivative. However, if the derivative of the time-varying parameter
is of interest, then we suggest to use *p=2*. In this case,
*beta* has four columns, the first two columns are the same when
*p=1*, while the last two columns estimates the coefficients of
squared marker value and its derivative.

### Value

Returns a list of following items:

`time` |
unique failure times |

`beta` |
estimate of time-varying parameter |

### Author(s)

Patrick J. Heagerty

### References

Heagerty, P.J., Zheng Y. (2005)
Survival Model Predictive Accuracy and ROC curves
*Biometrics*, **61**, 92 – 105

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
data(pbc)
## considering only randomized patients
pbc1 <- pbc[1:312,]
## create new censoring variable combine 0,1 as 0, 2 as 1
survival.status <- ifelse( pbc1$status==2, 1, 0)
survival.time <- pbc1$fudays
pbc1$status1 <- survival.status
fit <- coxph( Surv(fudays,status1) ~ log(bili) +
log(protime) +
edema +
albumin +
age,
data=pbc1 )
eta5 <- fit$linear.predictors
x <- eta5
nobs <- length(survival.time[survival.status==1])
span <- 1.0*(nobs^(-0.2))
## Not run:
bfnx1 <- llCoxReg(Stime=survival.time, status=survival.status, marker=x,
span=span, p=1)
plot(bfnx1$time, bfnx1$beta[,1], type="l", xlab="Time", ylab="beta(t)")
## End(Not run)
``` |