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Effect of model fitting artifacts on the stepwise approach to identifying patterns of attachment loss
Author(s) -
Cohen M. E.
Publication year - 1996
Publication title -
journal of periodontal research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.31
H-Index - 83
eISSN - 1600-0765
pISSN - 0022-3484
DOI - 10.1111/j.1600-0765.1996.tb00458.x
Subject(s) - logarithm , exponential function , mathematics , logarithmic scale , curvature , linear model , nonlinear system , statistics , clinical attachment loss , stepwise regression , curvilinear coordinates , exponential growth , linear regression , periodontitis , statistical physics , econometrics , mathematical analysis , geometry , dentistry , physics , medicine , quantum mechanics , acoustics
The stepwise approach to the determination of periodontal attachment loss involves fitting linear, logarithmic, and exponential models to individual site data and concluding that the form of loss is consistent with the model that has the greatest r‐value, provided that the model predicts loss in excess of a site‐specific threshold. Logarithmic and exponential fits are considered to define early and late bursts, respectively, while linear fit describes loss at a constant rate. In a recently published study, the stepwise approach was applied to 6,935 sites in patients with established periodontitis and, of 581 loss detections, 195 (33.6%) were linear, 224 (38.6%) logarithmic, and 162 (27.9%) exponential. However, curvilinear patterns may occur by chance and regression algorithms that can fit such curvature may have an advantage unrelated to the true mchanism(s) of periodontal destruction. To investigate the implications of this possibility, proportions of linear, logarithmic, and exponential fit were estimated by simulation under four different conditions. These conditions incorporated random or random plus tineas change, but no nonlinear effects. The relative proportions of model fits described in the published study were approximated in all of these conditions. It would appear that the observed proportions are ubiquitous to the modelling approach itself, and do not constitute evidence of a causal nonlinear biological mechanism. The stepwise approach may be useful for detecting change but relevance to causal processes seems problematic.