Illness-death model: statistical perspective and differential equations

被引：8

作者：

Brinks, Ralph ^{[1
]}

Hoyer, Annika ^{[2
]}

机构：

[1] Univ Hosp Duesseldorf, Hiller Res Unit Rheumatol, Dusseldorf, Germany

[2] German Diabet Ctr, Inst Epidemiol & Biometry, Dusseldorf, Germany

来源：

LIFETIME DATA ANALYSIS | 2018年 / 24卷 / 04期

关键词：

Fix-Neyman competing risks model; Illness-death model; Multistate models; Non-parametric estimation of transition rates; Incidence; Prevalence; Markov processes; Kolmogorov Differential Equations; AGE-SPECIFIC INCIDENCE; PREVALENCE; DISEASES;

D O I：

10.1007/s10985-018-9419-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

引用

下载

页码：743 / 754

页数：12

共 50 条

[31] Nonparametric estimation of the probability of illness in the illness-death model under cross-sectional sampling
Mandel, M.
Fluss, R.
BIOMETRIKA, 2009, 96 (04) : 861 - 872
[32] Methods for testing the Markov condition in the illness-death model: a comparative study
Rodriguez-Girondo, Mar
de Una-Alvarez, Jacobo
STATISTICS IN MEDICINE, 2016, 35 (20) : 3549 - 3562
[33] Nonparametric estimation of transition probabilities in a non-Markov illness-death model
Meira-Machado, Luis
de Una-Alvarez, Jacobo
Cadarso-Suarez, Carmen
LIFETIME DATA ANALYSIS, 2006, 12 (03) : 325 - 344
[34] THE ILLNESS-DEATH MODEL FOR ESTIMATING THE IMPACT OF RISK FACTORS ON THE RISKS OF DEMENTIA AND DEATH IN ELDERLY COHORTS
Leffondre, K.
Joly, P.
Helmer, C.
AMERICAN JOURNAL OF EPIDEMIOLOGY, 2010, 171 : S143 - S143
[35] Nonparametric estimation of quality adjusted lifetime distribution in a simple illness-death model
Pradhan, Biswabrata
Dewanji, Anup
Goswami, Alok
STATISTICS, 2013, 47 (05) : 1030 - 1046
[36] Comparison of joint modeling and landmarking for dynamic prediction under an illness-death model
Suresh, Krithika
Taylor, Jeremy M. G.
Spratt, Daniel E.
Daignault, Stephanie
Tsodikov, Alexander
BIOMETRICAL JOURNAL, 2017, 59 (06) : 1277 - 1300
[37] An accelerated failure time regression model for illness-death data: A frailty approach
Kats, Lea
Gorfine, Malka
BIOMETRICS, 2023, 79 (04) : 3066 - 3081
[38] Lexis Diagram and Illness-Death Model: Simulating Populations in Chronic Disease Epidemiology
Brinks, Ralph
Landwehr, Sandra
Fischer-Betz, Rebecca
Schneider, Matthias
Giani, Guido
PLOS ONE, 2014, 9 (09):
[39] Estimation of Transition Probabilities for the Illness-Death Model: Package TP.idm
Balboa, Vanesa
de Una-Alvarez, Jacobo
JOURNAL OF STATISTICAL SOFTWARE, 2018, 83 (10): : 1 - 19
[40] Direct modeling of regression effects for transition probabilities in the progressive illness-death model
Azarang, Leyla
Scheike, Thomas
de Una-Alvarez, Jacobo
STATISTICS IN MEDICINE, 2017, 36 (12) : 1964 - 1976

← 1 2 3 4 5 →