Literature DB >> 29374340

Illness-death model: statistical perspective and differential equations.

Ralph Brinks1, Annika Hoyer2.   

Abstract

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.

Entities:  

Keywords:  Fix-Neyman competing risks model; Illness-death model; Incidence; Kolmogorov Differential Equations; Markov processes; Multistate models; Non-parametric estimation of transition rates; Prevalence

Mesh：

Year:  2018        PMID： 29374340     DOI： 10.1007/s10985-018-9419-6

Source DB:  PubMed          Journal:  Lifetime Data Anal        ISSN： 1380-7870            Impact factor:   1.588


  23 in total

1.  Event history analysis and the cross-section.

Authors:  Niels Keiding
Journal:  Stat Med       Date:  2006-07-30       Impact factor: 2.373

2.  A simple stochastic model of recovery, relapse, death and loss of patients.

Authors:  E FIX; J NEYMAN
Journal:  Hum Biol       Date:  1951-09       Impact factor: 0.553

3.  Deriving age-specific incidence from prevalence with an ordinary differential equation.

Authors:  Ralph Brinks; Sandra Landwehr; Andrea Icks; Michael Koch; Guido Giani
Journal:  Stat Med       Date:  2012-10-04       Impact factor: 2.373

4.  The Prevalence and Incidence of Diabetes in Germany.

Authors:  Teresa Tamayo; Ralph Brinks; Annika Hoyer; Oliver S Kuß; Wolfgang Rathmann
Journal:  Dtsch Arztebl Int       Date:  2016-03-18       Impact factor: 5.594

5.  Mathematical modeling and the epidemiological research process.

Authors:  Mikayla C Chubb; Kathryn H Jacobsen
Journal:  Eur J Epidemiol       Date:  2009-10-27       Impact factor: 12.434

6.  Change rates and prevalence of a dichotomous variable: simulations and applications.

Authors:  Ralph Brinks; Sandra Landwehr
Journal:  PLoS One       Date:  2015-03-06       Impact factor: 3.240

7.  Projected effect of increased active travel in German urban regions on the risk of type 2 diabetes.

Authors:  Ralph Brinks; Annika Hoyer; Oliver Kuss; Wolfgang Rathmann
Journal:  PLoS One       Date:  2015-04-07       Impact factor: 3.240

8.  Global and regional mortality from 235 causes of death for 20 age groups in 1990 and 2010: a systematic analysis for the Global Burden of Disease Study 2010.

Authors:  Rafael Lozano; Mohsen Naghavi; Kyle Foreman; Stephen Lim; Kenji Shibuya; Victor Aboyans; Jerry Abraham; Timothy Adair; Rakesh Aggarwal; Stephanie Y Ahn; Miriam Alvarado; H Ross Anderson; Laurie M Anderson; Kathryn G Andrews; Charles Atkinson; Larry M Baddour; Suzanne Barker-Collo; David H Bartels; Michelle L Bell; Emelia J Benjamin; Derrick Bennett; Kavi Bhalla; Boris Bikbov; Aref Bin Abdulhak; Gretchen Birbeck; Fiona Blyth; Ian Bolliger; Soufiane Boufous; Chiara Bucello; Michael Burch; Peter Burney; Jonathan Carapetis; Honglei Chen; David Chou; Sumeet S Chugh; Luc E Coffeng; Steven D Colan; Samantha Colquhoun; K Ellicott Colson; John Condon; Myles D Connor; Leslie T Cooper; Matthew Corriere; Monica Cortinovis; Karen Courville de Vaccaro; William Couser; Benjamin C Cowie; Michael H Criqui; Marita Cross; Kaustubh C Dabhadkar; Nabila Dahodwala; Diego De Leo; Louisa Degenhardt; Allyne Delossantos; Julie Denenberg; Don C Des Jarlais; Samath D Dharmaratne; E Ray Dorsey; Tim Driscoll; Herbert Duber; Beth Ebel; Patricia J Erwin; Patricia Espindola; Majid Ezzati; Valery Feigin; Abraham D Flaxman; Mohammad H Forouzanfar; Francis Gerry R Fowkes; Richard Franklin; Marlene Fransen; Michael K Freeman; Sherine E Gabriel; Emmanuela Gakidou; Flavio Gaspari; Richard F Gillum; Diego Gonzalez-Medina; Yara A Halasa; Diana Haring; James E Harrison; Rasmus Havmoeller; Roderick J Hay; Bruno Hoen; Peter J Hotez; Damian Hoy; Kathryn H Jacobsen; Spencer L James; Rashmi Jasrasaria; Sudha Jayaraman; Nicole Johns; Ganesan Karthikeyan; Nicholas Kassebaum; Andre Keren; Jon-Paul Khoo; Lisa Marie Knowlton; Olive Kobusingye; Adofo Koranteng; Rita Krishnamurthi; Michael Lipnick; Steven E Lipshultz; Summer Lockett Ohno; Jacqueline Mabweijano; Michael F MacIntyre; Leslie Mallinger; Lyn March; Guy B Marks; Robin Marks; Akira Matsumori; Richard Matzopoulos; Bongani M Mayosi; John H McAnulty; Mary M McDermott; John McGrath; George A Mensah; Tony R Merriman; Catherine Michaud; Matthew Miller; Ted R Miller; Charles Mock; Ana Olga Mocumbi; Ali A Mokdad; Andrew Moran; Kim Mulholland; M Nathan Nair; Luigi Naldi; K M Venkat Narayan; Kiumarss Nasseri; Paul Norman; Martin O'Donnell; Saad B Omer; Katrina Ortblad; Richard Osborne; Doruk Ozgediz; Bishnu Pahari; Jeyaraj Durai Pandian; Andrea Panozo Rivero; Rogelio Perez Padilla; Fernando Perez-Ruiz; Norberto Perico; David Phillips; Kelsey Pierce; C Arden Pope; Esteban Porrini; Farshad Pourmalek; Murugesan Raju; Dharani Ranganathan; Jürgen T Rehm; David B Rein; Guiseppe Remuzzi; Frederick P Rivara; Thomas Roberts; Felipe Rodriguez De León; Lisa C Rosenfeld; Lesley Rushton; Ralph L Sacco; Joshua A Salomon; Uchechukwu Sampson; Ella Sanman; David C Schwebel; Maria Segui-Gomez; Donald S Shepard; David Singh; Jessica Singleton; Karen Sliwa; Emma Smith; Andrew Steer; Jennifer A Taylor; Bernadette Thomas; Imad M Tleyjeh; Jeffrey A Towbin; Thomas Truelsen; Eduardo A Undurraga; N Venketasubramanian; Lakshmi Vijayakumar; Theo Vos; Gregory R Wagner; Mengru Wang; Wenzhi Wang; Kerrianne Watt; Martin A Weinstock; Robert Weintraub; James D Wilkinson; Anthony D Woolf; Sarah Wulf; Pon-Hsiu Yeh; Paul Yip; Azadeh Zabetian; Zhi-Jie Zheng; Alan D Lopez; Christopher J L Murray; Mohammad A AlMazroa; Ziad A Memish
Journal:  Lancet       Date:  2012-12-15       Impact factor: 79.321

9.  A general HIV incidence inference scheme based on likelihood of individual level data and a population renewal equation.

Authors:  Guy Severin Mahiane; Rachid Ouifki; Hilmarie Brand; Wim Delva; Alex Welte
Journal:  PLoS One       Date:  2012-09-12       Impact factor: 3.240

10.  Development and demonstration of a state model for the estimation of incidence of partly undetected chronic diseases.

Authors:  Ralph Brinks; Barbara H Bardenheier; Annika Hoyer; Ji Lin; Sandra Landwehr; Edward W Gregg
Journal:  BMC Med Res Methodol       Date:  2015-11-11       Impact factor: 4.615
View more

北京卡尤迪生物科技股份有限公司 © 2022-2023.