APSurv {APtools}

Estimating the Time-dependent AP and AUC for Censored Time to Event Outcome Data.

Description

This function calculates the estimates of the AP and AUC for censored time to event data as well as their confidence intervals using the perturbation or the nonparametric bootstrap resampling method. The estimation method is based on Yuan, Y., Zhou, Q. M., Li, B., Cai, H., Chow, E. J., Armstrong, G. T. (2018). A threshold-free summary index of prediction accuracy for censored time to event data. Statistics in medicine, 37(10), 1671-1681.

Usage

  APSurv(stime, status, marker, t0.list, cut.values = NULL,
    method = "none", alpha = 0.95, B = 1000,
    weight = NULL, Plot = TRUE)

Arguments

stime

Censored event time.

status

Binary indicator of censoring. 1 indicates observing event of interest, 0 otherwise. Other values will be treated as competing risk event.

marker

Numeric risk score. Data can be continuous or ordinal.

t0.list

Prediction time intervals of interest. It could be one numerical value or a vector of numerical values, which must be in the range of stime.

cut.values

Risk score values to use as a cut-off for calculation of time-dependent positive predictive values (PPV) and true positive fractions (TPF). The default value 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 to obtain a confidence interval. The default value is 1000.

weight

Optional. The default value is NULL, in which case 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

Whether to plot the time-dependent AP versus the prediction time intervals. The default value is TRUE, in which case the AP is evaluated at the time points which partition the range of the event times of the data into 100 intervals.

Value

An object of class "APsurv" which is a list with components:

ap_summary

Summary of estimated AP(s) at the specified prediction time intervals of interest. For each prediction time interval, the output includes the estimated event rate, a point estimate of the AP, the estimated scaled AP (ratio of the AP versus event rate), and their corresponding confidence intervals.

auc_summary

Summary of AUC at the specified prediction time intervals of interest. For each prediction time intervals, the output includes the estimated event rate and a point estimate of AUC with a confidence interval.

PPV

Available object, time-dependent positive predictive values at the unique risk score in the data.

TPF

Available object, time-dependent true positive fractions at the unique risk score in the data.

References

Yuan, Y., Zhou, Q. M., Li, B., Cai, H., Chow, E. J., Armstrong, G. T. (2018). A threshold-free summary index of prediction accuracy for censored time to event data. Statistics in medicine, 37(10), 1671-1681.

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

Examples

library(APtools)
data(mayo)
t0.list=seq(from=min(mayo[,1]),to=max(mayo[,1]),length.out=5)[-c(1,5)]
cut.values=seq(min(mayo[,3]),max(mayo[,3]),length.out=10)[-10]
out <- APSurv(stime=mayo[,1],status=mayo[,2],marker=mayo[,3],
	t0.list=t0.list,cut.values=cut.values,method='bootstrap',
	alpha=0.90,B=500,weight=rep(1,nrow(mayo)),Plot=FALSE)
out