Statistical methods
To test the hypothesis probit analysis was used. Probit analysis is a method for examining any dose-response relationship where the dependent variable, i.e. caries, is dichotomous (caries/no caries). Since all tooth surfaces may not 'respond' in a similar manner, the problem must be formulated in terms of the proportion responding (diagnosed as caries) at each level of challenge. With probit analysis, any changes are constant in proportion so that changes on a log scale will also be constant. In a probit transformation each of the observed proportions were translated into the value of the standard normal curve below which the observed proportion of the area was found. For example, if half the subjects in a caries trial had one particular site carious, the probit value would be 0, since half the area in a standard normal distribution falls below a z score of 0.
When using standard normal values, negative scores can occur. To overcome this, the constant 5 was added. For example, if a particular surface scored 1 and half the subjects studied had caries, the probit value would be 0, since half of the area in a standard normal curve falls below a z score of 0. When the constant is added, the transformed value for the proportion becomes 5. If the observed proportion of individuals in whom the site was carious was 0.84, the probit value would be 0.34, i.e. a z score of 1, which would give a transformed value of 6. The actual proportion of each of the tooth sites recorded carious at each DMF-S level was calculated and replaced with the value of the standard normal curve below which the observed proportion of the area below the curve was found.
The logarithmic transformation of the data provides a linear relationship between the probability of an event occurring for any given value. The proportion of each surface within a population diagnosed as carious at a particular DMF-S score can be calculated. For example, take the occlusal surface of the first right lower molar. At a DMF of 1, a certain proportion of this site within a population would be carious. This proportion would increase for a DMF of 2, and so on.
For each DMF-S score, the percentage of tooth surfaces exhibiting caries was calculated to give a probability score of between 0 and 1. Subsequently, the log transformation of the probabilities for each DMF-S against the actual DMF-S score was plotted for every surface. The common reference value, of 0.5 outlined above was used to establish the susceptibility of each surface to a given caries challenge. As some random variation can be expected, the susceptibilities are grouped within bands rather than as individual sites.
To establish whether a hierarchy for caries susceptibility exists, the probability of finding each site carious for a given DMF-S score was calculated. The probability was calculated by adopting a common reference value for the proportion of the tooth sites that become carious. In the present study 0.5 was used to provide the most accurate value, although any value of proportion can be used. The question can then be phrased in terms of the value of the DMF-S at which 50% of the sites or teeth would be expected to have become carious. The probability scores derived are then aggregated to produce an overall picture of tooth and site susceptibilities.
The probability of an event occurring ranges from zero to 1. As the overall DMF score rises, the probabilities of any site being carious will change. For example, if a group of 128 individuals, each having a DMF-S score of 1 with all sites exhibiting the same propensity for caries. The distribution of sites affected within the mouth should be random, the probability for a particular site being carious would then be 1/128. If, however, the group all had a DMF-S of 128, the relative probability of finding a particular site carious remains the same, but this time the absolute probability changes from 1/128 to 1.
As the DMF score increases the probabilities alter. However, once a probability of 1 has been reached no further increase is possible. Thus, when examining changes in the distribution of caries at different DMF-S scores, the ratio between individual probability scores is unimportant. The crucial factor is the overall ranking exhibited by the probabilities for each site. The order of susceptibly will be determined by the relative values of the probabilities. Whether an individual site is twice as likely to become carious as another cannot be determined using this approach. However, certain sites may exhibit similar probabilities. For example, a particular site on the left hand side of the mouth may have a similar mean probability as the corresponding site on the right hand side. Other factors may influence the distribution of probabilities. For example, it has been suggested that fluoride has a more beneficial effect on approximal sites when compared to occlusal.
The probabilities derived are for each site for each individual and are then aggregated for the sample population. The aggregation of probabilities gives rise to a distribution, approximately normal in character, and the mean of this distribution is subsequently reported and used in the analyses.
Data analyses were performed using SPSS. The data files of the NPDDP were supplied by the Rand Corporation in ASCII format and subsequently read onto the mainframe system. Two of the five data files were utilised in this project: the master file containing the demographic information of each individual and the clinical file containing the status of each tooth site.