Evaluating the burst hypothesis at a site-specific level using the lack-of-fit test

It has been hypothesized that periodontal disease progresses by means of sudden losses of periodontal attachment surface area. Obtaining reliable tests of this burst hypothesis has proven to be difficult; the signal (true model of disease progression) often gets lost in the noise. The purpose of this study was to determine how reliably we could distinguish sudden changes from linear disease progression at a site using a time series of clinical attachment levels. Specifically, the following question was investigated: If, in reality, disease progresses by means of sudden changes in clinical attachment level (bursts), and a linear model is fitted to these data, what is the likelihood of rejecting the linear model using the lack-of-fit test? This likelihood was determined as a function of the probing measurement error (range: 0.2 to 1.0 mm) and the number of clinical examinations over time. The results suggested that bursts of 2 mm or smaller cannot be reliably distinguished from linear disease progression using the lack-of-fit test, except under unusual clinical circumstances. Under typical clinical circumstances, burst sizes needed to be 3 to 5 mm in order to be reliably distinguished from linear disease progression. These results are probably overly optimistic. The ability to verify the burst hypothesis at the site level is likely to be even less than our results indicate because of various assumptions that were required. We conclude that the lack-of-fit test will reliably reject the linear model at a site-specific level only if true disease progresses in such a fashion that a handful of sudden changes leads to a tooth mortality event.