Discussion: Clinical measurements of periodontitis

and the assumptions are that the e, are independently normally distribtited with mean zero and (common) variance a^, e,~NID (0,(7̂ ). Focusing first on the structure of the model itself (Fig. 1), to test H:)8=0, is to test no change versus linear change and thus, according to the model, to reject H is to conclude that linear change has occurred, i.e., progressive change at a constant rate. To the extent that the data fit a line, the data are giving testimony favoring the slow, continuous disease hypothesis. To test the "random burst" hypothesis, we would like a procedure that would test no change versus change in the level of a stationary time series (Fig. 2), but this is not consistent with the choice of the SLR model. If one believes in the random burst hypothesis, choosing the SLR model is choosing a model believed to be inappropriate. Indeed, the SLR model would be the model of choice only if one believed that periodontal disease was a continuous, progressive process. Thus without questioning any of the assumptions of SLR, without considering the sequential application of SLR, without considering the choice of sites as experimental units, there is a problem: the SLR model is logically inconsistent with the random burst hypothesis.