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On bias reduction in parametric estimation in stage structured development models

  • Hoa Pham EMAIL logo , Huong T. T. Pham and Kai Siong Yow
Published/Copyright: January 31, 2024
Monte Carlo Methods and Applications
From the journal Monte Carlo Methods and Applications Volume 30 Issue 2

Abstract

Multi-stage models for cohort data are popular statistical models in several fields such as disease progressions, biological development of plants and animals, and laboratory studies of life cycle development. A Bayesian approach on adopting deterministic transformations in the Metropolis–Hastings (MH) algorithm was used to estimate parameters for these stage structured models. However, the biases in later stages are limitations of this methodology, especially the accuracy of estimates for the models having more than three stages. The main aim of this paper is to reduce these biases in parameter estimation. In particular, we conjoin insignificant previous stages or negligible later stages to estimate parameters of a desired stage, while an adjusted MH algorithm based on deterministic transformations is applied for the non-hazard rate models. This means that current stage parameters are estimated separately from the information of its later stages. This proposed method is validated in simulation studies and applied for a case study of the incubation period of COVID-19. The results show that the proposed methods could reduce the biases in later stages for estimates in stage structured models, and the results of the case study can be regarded as a valuable continuation of pandemic prevention.

Keywords: Multi-stage models; stage structured models; stage duration data; stage frequency data; Bayesian analysis; incubation period of COVID-19
MSC 2020: 62N02; 62F15; 62P10; 62P12

A Appendix

Table 5

Summary of MCMC convergence diagnostic tests of shape a j , j = 1 , 2 , 3 , and rate λ j , j = 1 , 2 , 3 , estimates for the three-stage non-hazard rate model.

Gelman and Rubin diagnostic Geweke diagnostic
Potential scale reduction factors Fraction in 1st window 0.1
Point est. Upper CI Fraction in 2nd window 0.5
a 1 1.00 1.00 a 1 0.638
λ 1 1.00 1.00 λ 1 0.532
Multivariable psrf 1.00
a 2 1.00 1.01 a 2 1.105
λ 2 1.00 1.00 λ 2 0.865
Multivariable psrf 1.00
a 3 1.01 1.00 a 3 −1.136
λ 3 1.01 1.01 λ 3 −1.235
Multivariable psrf 1.01
Table 6

Summary of MCMC convergence diagnostic tests of shape a j , j = 1 , 2 , 3 , 4 , 5 , and rate λ j , j = 1 , 2 , 3 , 4 , 5 , estimates for the five-stage non-hazard rate model.

Gelman and Rubin diagnostic Geweke diagnostic
Potential scale reduction factors Fraction in 1st window 0.1
Point est. Upper CI Fraction in 2nd window 0.5
a 1 1.00 1.00 a 1 0.571
λ 1 1.00 1.00 λ 1 0.688
Multivariable psrf 1.00
a 2 1.00 1.01 a 2 1.783
λ 2 1.00 1.00 λ 2 1.568
Multivariable psrf 1.00
a 3 1.00 1.00 a 3 −0.436
λ 3 1.00 1.00 λ 3 −0.735
Multivariable psrf 1.01
a 4 1.01 1.03 a 4 1.368
λ 4 1.02 1.01 λ 4 1.529
Multivariable psrf 1.00
a 5 1.01 1.01 a 5 −1.231
λ 5 1.02 1.01 λ 5 −1.412
Multivariable psrf 1.02
Table 7

Summary of MCMC convergence diagnostic tests of shape a j , j = 1 , 2 , 3 , 4 , 5 , 6 , 7 , and rate λ j , j = 1 , 2 , 3 , 4 , 5 , 6 , 7 , estimates for the seven-stage non-hazard rate model.

Gelman and Rubin diagnostic Geweke diagnostic
Potential scale reduction factors Fraction in 1st window 0.1
Point est. Upper CI Fraction in 2nd window 0.5
a 1 1.01 1.00 a 1 −1.138
λ 1 1.00 1.00 λ 1 −1.331
Multivariable psrf 1.00
a 2 1.01 1.01 a 2 0.705
λ 2 1.00 1.00 λ 2 0.865
Multivariable psrf 1.00
a 3 1.01 1.00 a 3 −0.536
λ 3 1.01 1.01 λ 3 −0.675
Multivariable psrf 1.01
a 4 1.00 1.03 a 4 0.798
λ 4 1.01 1.01 λ 4 0.980
Multivariable psrf 1.01
a 5 1.02 1.03 a 5 1.302
λ 5 1.01 1.04 λ 5 1.033
Multivariable psrf 1.01
a 6 1.01 1.02 a 6 −1.359
λ 6 1.02 1.01 λ 6 −1.560
Multivariable psrf 1.02
a 7 1.02 1.03 a 7 1.736
λ 7 1.01 1.05 λ 7 1.975
Multivariable psrf 1.03
Table 8

The incubation period of COVID-19 data.

𝑡 Expose stage The incubation stage Final stage
0 98 0 0
1 89 9 0
2 78 11 9
3 66 12 20
4 56 10 32
5 47 9 42
6 40 7 51
7 33 7 58
8 28 5 65
9 23 5 70
10 18 5 75
11 15 3 80
12 12 3 83
13 10 2 86
14 8 2 88
15 6 2 90
16 5 1 92
17 4 1 93
18 3 1 94
19 2 1 95
20 1 1 96
21 0 1 97
22 0 0 98

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Received: 2023-07-15
Revised: 2023-12-22
Accepted: 2024-01-10
Published Online: 2024-01-31
Published in Print: 2024-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Likelihood and decoding problems for mixed space hidden Markov model
  3. A weight Monte Carlo estimation of fluctuations in branching processes
  4. Choice of a constant in the expression for the error of the Monte Carlo method
  5. Estimation in shape mixtures of skew-normal linear regression models via ECM coupled with Gibbs sampling
  6. An improved unbiased particle filter
  7. Partitions for stratified sampling
  8. A gradient method for high-dimensional BSDEs
  9. On bias reduction in parametric estimation in stage structured development models
https://doi.org/10.1515/mcma-2024-2001
Keywords for this article
Multi-stage models; stage structured models; stage duration data; stage frequency data; Bayesian analysis; incubation period of COVID-19

Articles in the same Issue

  1. Frontmatter
  2. Likelihood and decoding problems for mixed space hidden Markov model
  3. A weight Monte Carlo estimation of fluctuations in branching processes
  4. Choice of a constant in the expression for the error of the Monte Carlo method
  5. Estimation in shape mixtures of skew-normal linear regression models via ECM coupled with Gibbs sampling
  6. An improved unbiased particle filter
  7. Partitions for stratified sampling
  8. A gradient method for high-dimensional BSDEs
  9. On bias reduction in parametric estimation in stage structured development models
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