Variables aleatorias discretas
Ejemplo 4.3.1. Sea la variable aleatoria X, número de mimetismos que escapan a la detec ción del Ejemplo 4.2.1 La densidad f para X viene dada por
4.4. LA DISTRIBUCIÓN BINOMIAL
This section will summarise the frequencies of dental caries across the Library site sample (Phases A, B and C), and within the individual phases (B and C), and compare frequencies of caries between phases and to other European samples.
6.3.1 All phases (A, B, C)
A summary of the frequencies of dental caries by sex and age for all phases of the sample is presented in Table 6.7, which displays these by tooth and individual counts. The difference between the number of teeth with carious lesions and the total number of carious lesions appeared to be important and this difference is reflected in the Total Caries and Total Carious Teeth columns. The overall percentage of caries in the adult sample was 4.5% by tooth count and 30.7% of carious teeth had two or more lesions. Of individuals with
127
assessable dentition, 45 presented with carious lesions (26.2%). Of these, 19.8% of female individuals exhibited at least one carious lesion, as did 31.8% of males.
Male dentition had a higher frequency of teeth with two or more caries (40%), than female dentition (31.0%). This was even more marked when comparing the frequency in young males (46.2%) to young females (33.3%). Caries on the occlusal surface were the
predominant location in females (56.1% of carious lesions), followed by pit caries (19.5%). This was reversed in the male dentition with 47.8% of lesions located in pits and 40.6% on the occlusal surface. Examinations of the location of dental caries confirmed their presence in both the maxilla and mandible. All of the carious lesions occurred in the posterior dentition, representing caries on 5.2% of assessable posterior teeth.
Table 6.8 presents the results of pair-wise comparisons of sex and age interactions for dental caries by tooth, caries count and by individual across all phases of the Library site sample, derived from GLM analysis. A statistically significant higher frequency of caries occurred in male teeth (5.2%, P = 0.019) when compared to female teeth (2.6%). By individual, 32.3% of males had carious lesions as opposed to 17.9% of females, although this difference was not statistically significant (P = 0.055). Across the age groups there was a statistically significant difference between the frequencies of caries by tooth in old male (4.7%, P = 0.019) and old females (1.8%). However, this was not the case when young females (3.0%) and young males (5.6%, P =0.115) were compared. Comparisons of the frequencies of adult individuals with caries also reflected these relationships, although none of these differences were statistically significant.
Investigations into the frequencies of carious teeth with two or more lesions revealed no statistically significant differences between any of the groups. Breakdowns of carious lesions by individual and multiple lesions were not further modelled by phase as the outcomes of GLM modelling were not robust. This was likely due to the limited data available for these particular aspects of the pathology.
128
Table 6.7: Summary table of sex and age frequency of dental caries in all phases of the Library site sample
N1 N2 N3 ant/post Obs. caries ant/post4 Proportion of caries ant/post N5 max/man Obs. caries max/man Proportion of caries max/man Total carious teeth % caries6 Total teeth 2+ caries % caries7 TP OS P MC MR DC DR BS BR LS LR Total caries Caries individual8 (%) Female YA 48 603 80/523 0/18 0.0/3.4 328/275 10/8 3.0/2.9 18 3.0 6 33.3 4 16 5 0 0 0 0 0 0 0 0 25 10/48 (20.8) OA 36 330 31/299 0/6 0.0/2.0 164/166 4/2 2.4/1.2 6 1.8 2 33.3 0 5 2 1 0 0 0 0 0 0 0 8 5/36 (13.9) ?Adult 2 25 4/21 0/5 0.0/23.8 8/17 2/3 25.0/17.6 5 16.0 1 20.0 0 2 1 2 0 1 0 2 0 0 0 8 2/2 (100.0) Subtotal 86 958 115/843 0/29 0.0/3.4 500/458 16/10 3.2/2.2 29 4.4 9 31.0 4 23 8 3 0 1 0 2 0 0 0 41 17/86 (19.8) % 9.8 56.1 19.5 7.32 0.0 2.44 0 4.88 0.0 0.0 0.0 100.0 Male YA 37 468 72/396 0/26 0.0/6.5 253/215 12/14 4.7/6.5 26 5.6 12 46.2 0 21 24 0 0 0 0 5 0 1 0 51 12/37 (32.4) OA 28 299 37/262 0/14 0.0/5.3 145/154 6/8 4.1/5.2 14 4.7 4 28.6 1 7 9 0 1 0 0 0 0 0 0 18 9/28 (32.1) ?Adult 1 3 1/2 0/0 0.0/0.0 3/0 0/0 0.0/0.0 0 0.0 0 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0/1 (0.0) Subtotal 66 770 110/660 0/40 0.0/6.1 401/369 18/22 4.5/6.0 40 5.2 16 40.0 1 28 33 0 1 0 0 5 0 1 0 69 21/66 (31.8) % 1.4 40.6 47.8 0.0 1.4 0.0 0.0 7.2 0.0 1.4 0.0 100.0 ?Sex YA 13 147 20/127 0/12 0.0/10.2 62/85 3/9 4.8/11.8 12 8.2 1 8.3 0 4 3 1 0 0 0 5 0 0 0 13 5/13 (38.5) OA 6 72 12/60 0/7 0.0/13.3 36/36 4/3 13.9/8.3 7 9.7 1 14.3 0 2 6 0 0 0 0 0 0 0 0 8 2/6 (33.3) ?Adult 1 5 1/4 0/0 0.0/0.0 0/5 0/0 0.0/0.0 0 0.0 0 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0/1 (0.0) Subtotal 20 224 33/191 0/19 0.0/11.0 98/126 7/12 8.2/10.3 19 9.4 2 10.5 0 6 9 1 0 0 0 5 0 0 0 21 7/20 (35.0) % 0.0 28.6 42.9 4.8 0.0 0.0 0.0 23.8 0.0 0.0 0.0 100.0 Total 172 1952 258/1694 0/88 0.0/5.2 999/953 39/45 3.9/4.7 88 4.5 27 30.7 5 57 50 4 1 1 0 12 0 1 0 131 45/172 (26.2) % 3.8 43.5 38.2 3.1 0.8 0.8 0.0 9.2 0.0 0.8 0.0 100.0
YA: young adult; OA: old adult; ?Adult: adult of undetermined age; ?Sex: adult of undetermined sex; ant: anterior; post: posterior; max: maxilla; man: mandible
TP: tooth presence, absence, carious; OS: occlusal surface; P: pit; MC: mesial contact; MR: mesial root; DC: distal contact; DR: distal root; BS: buccal smooth; BR: buccal root; LS: lingual smooth; LR: lingual root
1
number of individuals with 1+ assessable teeth
2
number of preserved teeth
3
number of preserved anterior/posterior teeth
4
number of teeth with observable caries
5
number of preserved maxillary/preserved mandibular teeth
6
teeth with 1+ caries/total assessable teeth for category x 100
7
teeth with 2+ caries/total carious teeth x 100
8
129
Table 6.8: Summary table of dental caries by tooth, caries count and individual associated with the pair-wise comparisons (p-values) of sex, age and interactions of sex and age in all phases
derived from generalised linear modelling
Variable % Dental Caries1 P2 % 2+ Caries3 P2 % Caries Individual4 P2 Sex F 2.6 33.3 17.9 M 5.2 40.0 32.3 Age YA 4.1 40.9 25.9 OA 3.2 30.0 21.9 Sex*Age F YA 3.0 33.3 20.8 OA 1.8 33.3 13.9 M YA 5.6 46.2 32.4 OA 4.7 28.6 32.1 Age*Sex YA F 3.0 33.3 20.8 M 5.6 46.2 32.4 OA F 1.8 33.3 13.9 M 4.7 28.6 32.1
F: female; M: male; YA: young adult; OA: old adult
1
percentage of dental caries by tooth count
2p‐value; bold numbers indicate significance; significance is considered as values ≤0.05 3percentage ofcarious teeth with 2 or more lesions
4percentage of caries by individual count
Category 0.019 0.707 0.055 0.420 0.556 0.593 0.320 1.000 0.404 0.688 0.464 0.983 0.115 0.564 0.265 0.019 0.884 0.097
130
6.3.2 Phase B
A summary of the frequencies of dental caries by sex and age for Phase B of the sample is presented in Table 6.9, which displays these by tooth count and individual count. Overall, the frequency of carious teeth in Phase B of the sample was 2.1%, with 2.7% of male dentition affected, and 2.0% of female dentition. Higher frequencies were evident in the older adult groups. Of these carious teeth, a total of 30.0% had more than one lesion, the majority of these being male dentition. All of the young male carious teeth presented with at least two carious lesions, compared to no young females presenting with more than one lesion. Around 40.0% of old female carious teeth had more than one lesion, but the number of carious teeth overall was small.
Of the 83 adult individuals with assessable teeth, 11 of these had at least one carious lesion (20.3%). Of these, 17.0% of females and 10.0% of males had caries. Old females were the group with the highest frequency of carious lesions by individual (21.1%), but this was not replicated when considering the frequency of carious lesions by tooth, where old males had the highest percentage of teeth affected (3.3%). There were no anterior caries, with all lesions limited to the posterior teeth (2.4%). Frequencies of dental caries in the maxillary dentition (2.2%) and mandibular dentition (2.0%) were approximately equal. The occlusal surface and pits of the dentition were the most prominent locations for carious lesions. Table 6.10 presents the results of pair-wise comparisons of sex and age interactions for dental caries by tooth count in Phase B of the Library site sample, derived from GLM analysis. Unlike examinations of the Library site sample across the three phases, modelling of the frequencies of dental caries in Phase B did not reveal any significant relationships.
131
Table 6.9: Summary table of sex and age frequency of dental caries in Phase B of the Library site sample
n1 N2 N3 ant/post