TY - JOUR
T1 - A mathematical model for assessing the temporal association between health disorders and medical treatments
AU - Jacobson, Sheldon H.
AU - Morrice, Douglas J.
N1 - Funding Information:
The authors would like to thank Dr. Edward Wegman, and the two anonymous referees and Dr. Edward Sewell for their comments and suggestions that resulted in significant improvements in the manuscript. The authors would also like to thank Dr. Richard A. Beauchamp from the Texas Department of Health, Austin, Texas and Dr. Merwin W. Hemphill from the Texas Air Control Board, Austin, Texas for their help and advice on this research. The first author acknowledges support from the National Science Foundation (DMI-9409266, DMI-9423929) and the Air Force Office of Scientific Research (F49620-95-1-0124). The second author acknowledges the financial support of the CBA/GSB Faculty Research Committee of the College of Business.
PY - 1998/8/1
Y1 - 1998/8/1
N2 - Statistical analysis is often used in medical studies to provide evidence for an association between a treatment and a patient condition. The work in this paper is motivated by a recent medical study which analyzes the temporal association between a treatment (i.e., an implant procedure) and the rare autoimmune disorders, polymyositis and dermatomyositis (PM/DM). To address this association mathematically, this paper develops a probability model based on the multinomial distribution that can be used to make statistical inferences about the timing of incidences of a treatment/condition pair. The model is empirically studied using Monte Carlo simulation. It is also analytically solved using the two ball and urn model formulations and a convolution formulation. Solution algorithms are given that can be executed in polynomial time and thus have the potential to be used as real-time decision support tools. Data from the medical study illustrate the application of this model and its results.
AB - Statistical analysis is often used in medical studies to provide evidence for an association between a treatment and a patient condition. The work in this paper is motivated by a recent medical study which analyzes the temporal association between a treatment (i.e., an implant procedure) and the rare autoimmune disorders, polymyositis and dermatomyositis (PM/DM). To address this association mathematically, this paper develops a probability model based on the multinomial distribution that can be used to make statistical inferences about the timing of incidences of a treatment/condition pair. The model is empirically studied using Monte Carlo simulation. It is also analytically solved using the two ball and urn model formulations and a convolution formulation. Solution algorithms are given that can be executed in polynomial time and thus have the potential to be used as real-time decision support tools. Data from the medical study illustrate the application of this model and its results.
KW - Combinatorial analysis
KW - Medicine
KW - Monte Carlo simulation
KW - Probability
UR - http://www.scopus.com/inward/record.url?scp=0040685891&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0040685891&partnerID=8YFLogxK
U2 - 10.1016/s0378-3758(98)00083-4
DO - 10.1016/s0378-3758(98)00083-4
M3 - Article
AN - SCOPUS:0040685891
SN - 0378-3758
VL - 71
SP - 209
EP - 228
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 1-2
ER -