Prospective Longitudinal Changes in the Periodontal Inflamed Surface Area Following Active Periodontal Treatment for Chronic Periodontitis

. 2021 Mar 10;10(6):1165. doi: 10.3390/jcm10061165

\begin{array}{l} - L 1 : P I S A {(T o o t h l e v e l)}_{i j} & = π_{0 j} + π_{1 i j} {(A g e)}_{i j} + π_{2 j} {(S e x)}_{i j} + π_{3 j} {(S a l i v a r y l e v e l s o f A . a)}_{i j} + π_{4 j} {(S a l i v a r y l e v e l s o f P . g)}_{i j} \\ + π_{5 j} {(S a l i v a r y l e v e l s o f P . i)}_{i j} + ε_{i j} \end{array}

(1)

- L 2 : π_{0 j} = β_{0 j} + β_{1 j} (M e a n C A L) + β_{2 j} (P l i) + \sum_{m = 1}^{3} β_{3 j}^{(m)} {(t o o t h m o b i l i t y)}_{j} + \sum_{m = 1}^{6} β_{4 j}^{(m)} {(T o o t h t y p e)}_{j} + \sum_{m = 1}^{5} β_{05}^{(m)} {(t i m e)}_{j} + r_{j}

(2)

e_{i j} ~ N (0, δ_{e}^{2}), r_{o j} ~ N (0, δ_{r}^{2})

Fixed effect;
Patient-level: Age, sex, days, salivary levels of A. actinomycetemcomitans, P. gingivalis, and P. intermedia
Tooth-level: Mean CAL, PlI, tooth mobility, tooth type, time
Random effect: Patients, random intercept
Covariance Type: AR1
Link functions: Gamma