Implementation of the simplified stochastic model of ageing for longitudinal osteoarthritis data assessment

Abstract

Background: Occurrence and progression of age-related irreversible degradations of skeletal joints, osteoarthritis (OA), has a stochastic nature. However, it is commonly described using polynomial models, which may not necessarily be optimal.

Aim: To implement a stochastic model of gradual accumulation of the distinct changes for estimating individuals' putative age at onset and risk of the process advancing in the OA longitudinal data.

Subjects and methods: The model was formulated as a discrete Markov process. It was applied to radiographic knee osteoarthritis (RKOA) data: 243 Kellgren-Lawrence (K/L) and 207 osteophytes (OP) score histories from the 15-year follow-up Chingford study.

Results: The model performance was examined in Monte-Carlo simulations. The mean age at onset of knee osteoarthritis was: 53.04 and 53.23 years and the average annual risk of one K/L and one OP grade appearance was: 0.066 and 0.025, respectively. The analysis also suggested that there is 3–4 years difference between the inferred age at onset and the age when knee osteoarthritis becomes detectable on radiograph.

Conclusion: The stochastic model provides more accurate description of the empiric data compared with the corresponding polynomial model. The model-based individual's estimates could be used as an important tool to fit age-related patterns of the corresponding diseases and conditions.

Keywords::

• Knee osteoarthritis
• Kellgren/Lawrence
• age-dependent degeneration
• maximum likelihood
• Monte-Carlo simulation

Acknowledgements

The study was supported by Israel Ministry of Health, Chief Scientist Grant #3-4101.We would like to thank all the participants of the Chingford Women Study and Maxine Daniels and Dr Alan Hakim for their time and dedication and Arthritis Research UK for their funding support to the study.

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.