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Table 1 The results of parametric and non-parametric estimates of CIF based on a four-parameter log-logistic and Sparling simulation for different times.

From: A parametric method for cumulative incidence modeling with a new four-parameter log-logistic distribution

 

Time

 

0.75

1.00

1.25

1.50

2.00

3.00

5.00

True value of CIF for event 1

0.11

0.23

0.36

0.49

0.68

0.85

0.92

Distribution

       

   Four-parameter log-logistic

       

CIF

0.06

0.18

0.32

0.45

0.64

0.82

0.91

Bias

-0.05

-0.05

-0.04

-0.04

-0.04

-0.03

-0.01

MSE × 102

0.30

0.30

0.20

0.20

0.20

0.10

0.01

   Sparling

       

CIF

0.07

0.17

0.30

0.44

0.65

0.83

0.91

Bias

-0.04

-0.06

-0.06

-0.05

-0.03

-0.02

-0.01

MSE × 102

0.17

0.40

0.39

0.32

0.12

0.05

0.02

Nonparametric

       

CIF

0.07

0.18

0.31

0.44

0.64

0.82

0.91

Bias

-0.04

-0.05

-0.05

-0.05

-0.04

-0.03

-0.01

MSE x102

0.20

0.27

0.26

0.29

0.22

0.10

0.02

True value of CIF for event 2

0.020

0.030

0.033

0.037

0.043

0.050

0.052

Distribution

       

   Four-parameter log-logistic

       

CIF

0.052

0.054

0.055

0.055

0.056

0.057

0.057

Bias

0.032

0.024

0.022

0.018

0.013

0.007

0.005

MSE × 102

0.100

0.100

0.010

0.040

0.020

0.010

0.010

   Sparling

       

CIF

0.048

0.053

0.056

0.058

0.060

0.061

0.062

Bias

0.028

0.023

0.023

0.021

0.017

0.011

0.010

MSE × 102

0.100

0.100

0.100

0.100

0.040

0.020

0.020

Nonparametric

       

CIF

0.059

0.059

0.059

0.059

0.059

0.059

0.059

Bias

0.039

0.029

0.026

0.023

0.016

0.009

0.007

MSE × 102

0.150

0.100

0.070

0.050

0.030

0.010

0.010

  1. The true model is a two-parameter log-logistic distribution.