Tooth decay is ubiquitous among humans and is one of the most prevalent oral diseases. Although this condition is largely preventable, more than half of all adults over the age of eighteen present early signs of the disease, and at some point in life about three out of four adults will develop the disease. Tooth decay is also common among children as young as five and remains the most common chronic disease of children aged five to seventeen years. It is estimated that tooth decay is four times more prevalent than asthma in childhood (Todem, 2008). Tooth decay and its correlates such as poor oral health place an enormous burden on the society. Poor oral health and a propensity to dental caries have been related to decreased school performance, poor social relationships and less success later in life. It is estimated that about 51 million school hours per year are lost in the U.S. alone because of dental-related illness. In older adults, tooth decay is one of the leading causes of tooth loss which has a dramatic impact on chewing ability leading to detrimental changes in food selection. This, in turn, may increase the risk of systemic diseases such as cardiovascular diseases and cancer.
The etiology of dental caries is well established. It is a localized, progressive demineraliza-tion of the hard tissues of the crown and root surfaces of teeth. The demineralization is caused by acids produced by bacteria, particularly mutans Streptococci and possibly Lactobacilli, that ferment dietary carbohydrates. This occurs within a bacteria-laden gelatinous material called dental plaque that adheres to tooth surfaces and becomes colonized by bacteria. Thus, dental caries results from the interplay of three main factors over time: dietary carbohydrates, cariogenic bacteria within dental plaque, and susceptible hard tooth surfaces. Dental caries is also a dynamic process since periods of demineralization alternate with periods of remineralization through the action of fluoride, calcium and phosphorous contained in oral fluids.
The evaluation of the severity of tooth decay is often performed at the tooth surface level. According to the World Health Organization, both the shape and the depth of a carious lesion at the tooth surface level can be scored on a four-point scale, D1 to D4. Level D1 refers to clinically detectable enamel lesions with non-cavitated surfaces; D2 for clinically detectable cavities limited to the enamel; D3 for clinically detectable lesions in dentin; and finally D4 for lesions into the pulp. Despite these detailed tooth-level data, most epidemiological studies often rely on the decayed, missing and filled (DMF) index, developed in the 1930s by Klein et al. (see for example Klein and Palmer, 1938). This index is applied to all the teeth (DMFT) or to all surfaces (DMFS), and represents the cumulative severity of dental caries experience for each individual. These scores have well documented shortcomings regarding their ability to describe the intra-oral distribution of dental caries (Lewsey and Thomson, 2004). But they continue to be instrumental in evaluating and comparing the risks of dental caries across population groups. Most importantly, they remain popular in dental caries research for their ability to conduct historical comparisons in population-based studies.
Statistical analysis of dental caries data relies heavily on the research question under study. These questions can be classified into two groups. The first group represents questions that can be answered using mouth-level outcomes generated using aggregated scores such as the DMF index. The second group refers to questions that necessitate the use of tooth or tooth-surface level outcomes. A very important issue to address for the data analyst is the modeling strategy to adopt for the response variable under investigation. Broadly, two fairly different views are advocated. The first view, supported by large-sample properties, states that normal theory should be applied as much as possible, even to non-normal data such as counts (Verbeke and Molenberghs, 2000). This view is strengthened by the notion that, normal models, despite being a member of the generalized linear models (GLIM), are much further developed than any other GLIM (e.g. model checks and diagnostic tools), and that they enjoy unique properties (e.g., the existence of closed form solutions, exact distributions for test statistics, unbiased estimators, etc...). Although this is correct in principle, it fails to acknowledge that normal models may not be adequate for some types of data. As an example, the abundance of zeros in DMF scores rules out any attempt to use normal models, such as linear models, even after a suitable transformation. While a transformation may normalize the distribution of nonzero response values, no transformation could spread the zeros (Hall, 2000). A different modeling view is that each type of outcome should be analyzed using tools that exploit the nature of the data. For dental data, features to be accommodated include the discrete nature of the data (count responses for mouth-level data and binary response for intra-oral data), the abundance of zeros for example in the DMF/S scoring, and the clustering in intra-oral responses. The clustering of participants as a result of the study design is another important feature.
This chapter reviews common statistical parametric models to answer questions that arise in dental caries research, with an eye to discerning their relative strengths and limitations. Missing data problems arising in caries dental reasrch will also be discussed but touched on briefly.
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