The (published) picture above had been created based on fixed estimates of a multivariate multilevel time series model of gingival dimensions after the implantation of a bioresorbable membrane for surgical root coverage. One may intuitively compare the multilevel model with a microscope here since raw data or presentation of means and standard deviations would hardly give a similarly elegant impression of what is actually going on after implantation of a membrane for guided tissue regeneration.
The fourth chapter of my new MLwiN manual using own data has been proofread and those who are still interested in “happy multilevel modeling” are encouraged to click here.
4 Multivariate Response Models
In the previous chapter, increasingly complex time series models have been set up in order to model gingival thickness, its width, the position of the mucogingival border relative to the cemento-enamel junction, and gingival recession after surgical implantation of a bio-resorbable membrane for guided tissue regeneration for the treatment of gingival recession. While some of these variables, such as thickness and width of gingiva might be positively related, others are not, for example gingival thickness and recession. Mucosal thickness had been measured at three locations: at the gingival margin, as well as at and below the mucogingival border (Müller et al. 2000d). In order to create general predictions of alterations of gingival dimensions after surgery, one single model would be preferred which might include mucosal thickness as measured at different locations as three different responses.
Multivariate response data are most conveniently incorporated into a multilevel model by creating a lower level below the original level 1 units. This will define the multivariate structure. Here we want to set up a 4-level model with multivariate responses (level 1) measured at different occasions (level 2) nested in higher-level units, i.e. teeth (level 3) and patients (level 4).
3 October 2014 @ 8:47 am.
Last modified October 3, 2014.
After a long hiatus due to other projects, final exams and, well, some vacation, the next chapter of my multilevel modeling manual was overdue, but here it comes.
MULTILEVEL MODELING OF PERIODONTAL DATA
Manual version 2014.1
3 Time Series Models
In the two previous chapters, observations have been modeled which had been made at teeth which were nested in subjects. Now, consider that observations had been repeated in a longitudinal way, for example after therapy. For that purpose, we want to define a lower level (one) as repeated measures, or occasion, while teeth and subjects would define levels two and three, respectively.
Consider, for instance changes of the entire gingival unit after the implantation of a bio-resorbable membrane for surgical root coverage employing the principle of guided tissue regeneration. Apart from achievable root coverage, the implantation of the membrane and concomitant coronal advancement of the mucoperiosteal flap leads to an immediate increase in thickness of gingiva and later in width of keratinized tissue. Of course, the mucogingival border is displaced but may re-establish itself later in its original position. Note that these alterations at teeth are non-linear and, since wound healing proceeds and regenerated tissue matures over time, non-monotonic (see example (C) in Fig. 13.1 in Rasbash et al. 2012). And they certainly depend on the subject. So, we have a three-level structure with a sample of subjects in which we study gingival dimensions at teeth, which have been surgically treated, over time. The data had been analyzed by multilevel modeling in some detail by Müller (2008).
In this chapter we want to introduce the data set which had been created in a longitudinal study (Müller et al. 2000d) and set up several multilevel models further elaborating the basic time series model.
3.1 Repeated Measures Data on Gingival Dimensions after Surgical Root Coverage
The data set consists of observations which have been made in 14 patients who had presented with a large variety of recession types at altogether 31 teeth. They had been treated according to the principles of guided tissue regeneration employing a bio-resorbable membrane. Surgical root coverage consisted, after periosteal dissection, of a coronally advanced flap which was secured with sling sutures. Several preoperative clinical parameters and intrasurgical observations were assessed. Patients were followed up for 1 year, and re-examinations of the clinical situation were carried out after 3, 6, 9 and 12 months.
14 August 2014 @ 8:01 am.
Last modified August 14, 2014.