ABSTRACT
University of Rochester, School of Nursing & Department of Biostatistics and
Computational Biology, School of Medicine, Rochester, New York, USA
Lili Yu, Karl E. Peace
Jiang-Ping Hsu College of Public Health, Georgia Southern University, States-
boro, Georgia, USA
Jianguo Sun
Department of Statistics, University of Missouri, Columbia, Missouri, USA
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
11.2 Data and Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
11.2.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
11.2.2 Statistical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
11.3 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
11.3.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
11.3.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
11.3.3 Coverage Probability on “IntCox” . . . . . . . . . . . . . . . . . . . . . . . 323
11.4 HIV Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
11.5 Discussions and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
312 Interval-Censored Time-to-Event Data: Methods and Applications
Bias and Its Remedy in Interval-Censored Time-to-Event Applications 313
314 Interval-Censored Time-to-Event Data: Methods and Applications
Bias and Its Remedy in Interval-Censored Time-to-Event Applications 315
316 Interval-Censored Time-to-Event Data: Methods and Applications
Bias and Its Remedy in Interval-Censored Time-to-Event Applications 317
318 Interval-Censored Time-to-Event Data: Methods and Applications
TABLE 11.1: Bias (%) for Treatment Comparison
p Month IntCox Cox.Right Cox.Mid
0.1 1 2.17 −2.93 0.02 0.2 1 −0.21 −8.73 −3.09 0.3 1 -0.86 −13.14 −5.78 0.4 1 2.14 −13.18 −3.98 0.5 1 2.00 −14.72 −3.89 0.6 1 0.52 −21.67 −9.39 0.7 1 0.16 −15.82 −2.55 0.8 1 0.40 −19.68 −3.90 0.1 3 6.42 −18.48 −12.21 0.2 3 0.65 −26.65 −16.81 0.3 3 −6.58 −30.51 −17.91 0.4 3 −8.41 −37.36 −21.33 0.5 3 −11.67 −39.37 −23.02 0.6 3 −11.81 −44.75 −27.21 0.7 3 −12.96 −51.84 −32.73 0.8 3 −10.71 −39.13 −18.39
Bias and Its Remedy in Interval-Censored Time-to-Event Applications 319
FIGURE 11.1: Biases for all parameter estimates
320 Interval-Censored Time-to-Event Data: Methods and Applications
FIGURE 11.2: MSE for Month=1
Bias and Its Remedy in Interval-Censored Time-to-Event Applications 321
FIGURE 11.3: Histograms for the estimated treatment parameter β1
322 Interval-Censored Time-to-Event Data: Methods and Applications
TABLE 11.2: Significance for Treatment Effect
p Month IntCox Cox.Right Cox.Mid
0.1 1 1 1 1
0.2 1 1 1 1
0.3 1 0 1 1
0.4 1 0 1 1
0.5 1 1 1 1
0.6 1 0 1 1
0.7 1 1 1 1
0.8 1 0 1 1
0.9 1 1 1 1
0.1 3 0 1 1
0.2 3 0 1 1
0.3 3 1 1 1
0.4 3 1 1 1
0.5 3 1 1 1
0.6 3 1 1 1
0.7 3 1 1 1
0.8 3 1 1 1
Bias and Its Remedy in Interval-Censored Time-to-Event Applications 323
324 Interval-Censored Time-to-Event Data: Methods and Applications
Bias and Its Remedy in Interval-Censored Time-to-Event Applications 325
FIGURE 11.4: Turnbull’s nonparametric estimator overlaid with IntCox
estimator for both treatments.
