Abstract: Stochastic Processes in the Causation of Rheumatic Disease

Stochastic Processes in the Causation of Rheumatic Disease

PETER J. ROBERTS-THOMSON, MICHAEL E. JONES, JENNIFER G. WALKER, JAMES G. MACFARLANE, MALCOLM D. SMITH, and MICHAEL J. AHERN

ABSTRACT.

Objective. Rheumatic disorders arise in certain individuals depending on the interaction of genetic and environmental factors, the contribution for each varying with the specific rheumatic disorder. However, a third variable, i.e., random or stochastic processes, may be important, but this has been poorly studied. We examined 3 rheumatic disorders to determine whether a simple stochastic process might be consistent with the incidence data.

Methods. A questionnaire and clinical survey of patients with ankylosing spondylitis, rheumatoid arthritis, and systemic sclerosis was performed to determine age at onset of first symptom. Population data were obtained from the Australian Bureau of Statistics. Computer modeling of the equation

dN
^___
dt

= kP₀t^r^-1exp(-kt^r/r)

was performed, where dN/dt is the age-specific incidence rate, P₀is the proportion of population at risk, t is the age at onset, k is a constant, and r is the number of random events that must occur before the disease manifests.

Results. Analysis of the age-specific incidence for each of these 3 rheumatic disorders was consistent with the stochastic model, where r varied from 4 to 9.

Conclusion. An examination of the age-specific incidence suggests that only a small number of random events need to occur in a predisposed population to allow the emergence of the rheumatic disorder. These random events might be environmental (e.g., infections or exposure to toxins) or due to acquired genetic changes (e.g., somatic mutations involving pivotal immune or growth/repair genes). (J Rheumatol 2002;29:2628-34)

Key Indexing Terms:

AGE-SPECIFIC INCIDENCE
SYSTEMIC SCLEROSIS
RHEUMATOID ARTHRITIS
ANKYLOSING SPONDYLITIS
STOCHASTIC PROCESS

From the Departments of Immunology, Allergy and Arthritis and Anatomy and Histology, Flinders Medical School, Bedford Park, Adelaide, Australia.

P.J. Roberts-Thomson, MD, DPhil (Oxon), Professor and Chairman, Department of Immunology, Allergy and Arthritis; M.J. Jones, MBBS, PhD, Associate Professor, Department of Anatomy and Histology; J.G. Walker, MBBS, Department of Immunology, Allergy and Arthritis; J.G. Macfarlane, Medical Student, Oxford University, Oxford, UK; M.D. Smith, MBBS, PhD, Professor; M.J. Ahern, MD, Associate Professor, Department of Immunology, Allergy and Arthritis.

Address reprint requests to Prof. P.J. Roberts-Thomson, Department of Immunology, Allergy and Arthritis, Flinders Medical Centre, Bedford Park SA 5042, Australia.

Submitted November 20, 2001; revision accepted June 13, 2002.