# Comparison of two risk scores based on the differences and ratio of their APs.

### Description

This function estimates the difference between and the ratio of two APs in order to compare two markers for censored time to event data or binary data. The corresponding confidence intervals are provided.

### Usage

1 2 3 |

### Arguments

`status` |
Binary indicator. For binary data, 1 indicates case and 0 otherwise. For survival data, 1 indicates event and 0 otherwise. |

`marker1` |
Risk score 1 (to be compared to risk score 2). Its length is required to be the same as the length of status. |

`marker2` |
Risk score 2 (to be compared to risk score 1). Its length is required to be the same as the length of status. |

`stime` |
Censored event time. If dealing with binary outcome, skip this argument which is set to be NULL. |

`t0.list` |
Prediction time intervals of interest for event time outcome. It could be one numerical value or a vector of numerical values, which must be in the range of stime. It is set to be NULL if stime is NULL. |

`method` |
Method to obtain confidence intervals. The default is method = "none", in which case only point estimates will be given without confidence intervals. If method= "perturbation", then perturbation based CI will be calculated. If method = "bootstrap", then nonparametric bootstrap based CI will be calculated. |

`alpha` |
Confidence level. The default level is 0.95. |

`B` |
Number of resampling for obtaining a confidence interval. The default value is 1000. |

`weight` |
Optional argument for event time data, i.e. stime is not NULL. Its default value is NULL, in which the observations are weighted by the inverse of the probability that their respective time-dependent event status (whether the event occurs within a specified time period) is observed. In estimating the probability, the survival function of the censoring time is estimated by a Kaplan-Meier estimator under the assumption that the censoring time is independent of both the event time and risks score. Users can use their own weights, in which case the t0.list should be a scalar and the length of weight is required to be the same as the length of status. |

`Plot` |
Optional argument for event time data, i.e. stime is not NULL. For binary data, it is set to FALSE. For event time data, its default value is TRUE and three plots are generated: 1) the time-dependent AUC of two markers; 2) the time-dependent AP of two markers; and 3) the time-dependent ratio of APs, all versus the prediction time intervals. The quantities in 1)-3) are evaluated at the time points which partition the range of the event times of the data to 100 intervals. |

### Value

`dap_summary` |
Summary of the APs of two markers and the differences (AP1-AP2) and their ratio (AP1/AP2). For event time data, these quantities are estimated at the specified prediction time intervals. The output includes the estimated event rate/proportion of cases, point estimates of the APs of the two markers, point estimates of the difference between and ratio of the two APs as well as their respective confidence intervals. |

### References

Yuan Y*, Zhou Q*, Li B, Chow E, Armstrong G. (2016) A threshold-free prospective prediction accuracy measure for censored time to event data. http://arxiv.org/abs/1606.04172. arXiv:1606.04172v1 [stat.ME] (*:Co-first authors)

Yuan, Y., Su, W., and Zhu, M. (2015). Threshold-free measures for assessing the performance of medical screening tests. Frontiers in Public Health, 3.57.

Bingying Li (2015) Threshold-free Measure for Assessing the Performance of Risk Prediction with Censored Data, MSc. thesis, Simon Fraser University, Canada

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
library(APtools)
status=c(rep(1,10),rep(0,1),rep(1,18),rep(0,11),rep(1,25),
rep(0,44),rep(1,85),rep(0,176))
marker1=c(rep(7,11),rep(6,29),rep(5,69),rep(4,261))
marker2=c(rep(7,17),rep(6,29),rep(5,70),rep(4,254))
out_binary <- CompareAP(status,marker1,marker2)
out_binary
data(mayo)
t0.list=seq(from=min(mayo[,1]),to=max(mayo[,1]),length.out=5)[-c(1,5)]
out_survival <- CompareAP(status=mayo[,2],marker1=mayo[,3],
marker2=mayo[,4],stime=mayo[,1],t0.list=t0.list,
method='bootstrap',alpha=0.90,B=1000,
weight=rep(1,nrow(mayo)),Plot=FALSE)
out_survival
``` |