201
Statistical Properties of Some Clinical Measures of Gingivitis and Periodontitis Joseph L. Fleiss, * Livia Turgeon, * Neal W. Chilton,
*
and Max A.
Listgarten f
Various statistical properties of the plaque index, the gingival index, and the wholemouth averages of pocket depth and attachment level measurements were examined using data from a 4-year randomized trial of 80 patients with a history of treated periodontal disease. Departures from normality were assessed by the median of the standardized distribution, by the coefficients of skewness and kurtosis, and by the Kolmogorov goodness-of-fit test. The relative precisions of probing pocket depth and of attachment level were measured, as were correlations between repeated measurements over time for the four clinical measures. The distribution of the plaque index was far from normal, but the distribution of its logarithm was more nearly normal. The distributions of the other clinical measures were effectively normal to varying degrees of approximation. With only rare exceptions, correlations between repeated measurements on the same clinical variable remained relatively constant no matter how far apart in time the measurements were made, at least up to 4 years. The whole-mouth mean of the attachment level measurements seemed to be relatively more precise than the whole-mouth mean of the pocket depth measurements. J Periodontol 1990;61:201-205.
Key Words: Gingival index; plaque index; periodontal index; periodontal attachment
Repeated measurements studies, in which patients are randomly assigned to different treatment groups and are measured at prescribed times during the course of their treatment, are popular in clinical trials of treatments for gingivitis and Periodontitis. The application of the classical repeated measurements analysis of variance to the resulting data,1 especially with regard to testing hypotheses concerning changes in responses over time, is valid only when the data are approximately normally distributed and when the standard deviations and the correlations satisfy certain conditions.2 In this paper we report on analyses of data from a large repeated measurements study3,4 to determine whether some important clinical measures of gingivitis and Periodontitis, or transformations of them, were approximately normally
were of variation over time of the standard deviations and correlations. Four clinical variables were examined: the Silness and Löe plaque index,5 the Löe and Silness gingival index,6 probing pocket depth, and periodontal attachment level (the latter two variables were measured to the nearest millimeter). In addition, the relative precisions of attachment level and probing pocket depth were calculated and compared.
distributed, and what the patterns
'Division of Biostatistics, Columbia University School of Public Health, New York, NY. Department of Periodontics, University of Pennsylvania School of Dental Medicine, Philadelphia, PA.
MATERIALS AND METHODS A sample of 116 adult patients with a history of treated Periodontitis were enrolled in a randomized trial that compared the effects of maintenance by means of regular quar-
terly visits for a periodontal prophylaxis (control treatment) against the effects of maintenance at intervals determined by the results of microscopic analyses of subgingival plaque samples (test treatment).7 All patients in both treatment groups were scheduled to receive a periodontal examination every 6 months for 4 years. Eighty patients, 33 in the test group
and 47 in the control group, were seen at each scheduled visit. The examination consisted of full-mouth recordings of the plaque index, the gingival index, probing pocket depth, and attachment level. Four sites were measured on each tooth: the mesial, midtooth, and distal sites on the buccal surface and the midtooth site alone on the lingual surface. Whole-mouth averages for these four measures were obtained and analyzed. Clinical results have been reported for the effects of 2 years of treatment3 and of 4 years of treatment.4 In neither case were there statistically significant differences between the treatment and control groups. The distributions of whole-mouth averages, of the natural logarithms of the averages, and of the square roots of the averages were obtained nine times for each of the four clinical variables, once at each of the nine examinations (at
J Periodontol April 1990
FLEISS, TURGEON, CHILTON, LISTGARTEN
202
are typical of the results for the other seven examinations, the values are tabulated for the distributions at baseline and at the final (4-year) examination only. For the measurement of plaque at baseline, none of the distributions was quite normal, although both the logarithmic and the square root transformations of the plaque index were successful in producing more nearly normal distributions than that of the index itself. For the plaque index at the 4-year examination, the distribution of the logarithms was the most nearly normal and the distribution of the untransformed index was the least normal. The baseline and 4-year distributions of the gingival index itself were both well-approximated by a normal distribution. The effects of transformation were trivial and perhaps even slightly deleterious. The patterns of results seem to be different for the baseline versus the 4-year distributions of the whole-mouth average pocket depth and its transformations. Except for the uniformly non-significant P-values for the Kolmogorov test, there does not seem to be much consistency across the statistical measures. Overall, the square root transformation appeared to produce more nearly normal distributions than its two competitors, but the baseline and 4-year distributions of the untransformed whole-mouth means themselves were not far from normal. By all four statistical criteria, the distribution of the logarithm of the whole-mouth average attachment level was the least normal at baseline, but was the most normal at 4 years. Consistently, however, the distribution of square roots was more nearly normal than the distribution of wholemouth means (the measure of kurtosis at the fourth year was the only exception). The distributions of the whole-
baseline plus eight semiannual examinations afterwards). The constant 1/2 was added to each whole-mouth average before its logarithm was calculated. The distributions were standardized by subtracting the mean and dividing by the standard deviation, and were then assessed for departures from normality. Four criteria for normality were examined: the median, the coefficient of skewness, the coefficient of kurtosis minus 3 (each of which should be close to 0 if the measurements are approximately normally distributed), and the P-value for the Kolmogorov goodness-of-fit test for normality. The significance of the Kolmogorov statistic was assessed by the method of Stephens.8 The variances for all nine time points, and the covariances for all pairs of time points, were calculated separately for each of the clinical variables as measured as well as for their logarithms and square roots. The relative precisions of probing pocket depth and attachment level were measured from a random effects repeated-measurements analysis of variance (80 patients each measured nine times) for each variable. Intraclass correlation coefficients were calculated from the between-patient mean square and the withinpatient mean square.9 Because there were no differences between the two treatment groups that even approached statistical significance, all of the analyses were performed on the sample of 80 patients as a whole. RESULTS Distributions Table 1 presents the values of the four statistics pertinent to the issue of approximate normality for the measures themselves as well as after transformation. Because they
Table 1: Values of Statistics Informative About the Approximate and Their Logarithmic and Square Root Transformations
Normality of the Distributions
at Baseline and 4 Years of 4 Clinical Variables
P-Value for Skewness
Median Transformation
BL*
4-year
BL
Kurtosis
4-year
BL
4-year
Kolmogorov Test BL 4-year
Plaque Index Untransformed index
Logarithm Square root
1.715 -0.089 0.327
3.436 0.053 0.693
0.15
0.10
Statistical Properties of Some Clinical Measures of Gingivitis and Periodontitis Joseph L. Fleiss, * Livia Turgeon, * Neal W. Chilton,
*
and Max A.
Listgarten f
Various statistical properties of the plaque index, the gingival index, and the wholemouth averages of pocket depth and attachment level measurements were examined using data from a 4-year randomized trial of 80 patients with a history of treated periodontal disease. Departures from normality were assessed by the median of the standardized distribution, by the coefficients of skewness and kurtosis, and by the Kolmogorov goodness-of-fit test. The relative precisions of probing pocket depth and of attachment level were measured, as were correlations between repeated measurements over time for the four clinical measures. The distribution of the plaque index was far from normal, but the distribution of its logarithm was more nearly normal. The distributions of the other clinical measures were effectively normal to varying degrees of approximation. With only rare exceptions, correlations between repeated measurements on the same clinical variable remained relatively constant no matter how far apart in time the measurements were made, at least up to 4 years. The whole-mouth mean of the attachment level measurements seemed to be relatively more precise than the whole-mouth mean of the pocket depth measurements. J Periodontol 1990;61:201-205.
Key Words: Gingival index; plaque index; periodontal index; periodontal attachment
Repeated measurements studies, in which patients are randomly assigned to different treatment groups and are measured at prescribed times during the course of their treatment, are popular in clinical trials of treatments for gingivitis and Periodontitis. The application of the classical repeated measurements analysis of variance to the resulting data,1 especially with regard to testing hypotheses concerning changes in responses over time, is valid only when the data are approximately normally distributed and when the standard deviations and the correlations satisfy certain conditions.2 In this paper we report on analyses of data from a large repeated measurements study3,4 to determine whether some important clinical measures of gingivitis and Periodontitis, or transformations of them, were approximately normally
were of variation over time of the standard deviations and correlations. Four clinical variables were examined: the Silness and Löe plaque index,5 the Löe and Silness gingival index,6 probing pocket depth, and periodontal attachment level (the latter two variables were measured to the nearest millimeter). In addition, the relative precisions of attachment level and probing pocket depth were calculated and compared.
distributed, and what the patterns
'Division of Biostatistics, Columbia University School of Public Health, New York, NY. Department of Periodontics, University of Pennsylvania School of Dental Medicine, Philadelphia, PA.
MATERIALS AND METHODS A sample of 116 adult patients with a history of treated Periodontitis were enrolled in a randomized trial that compared the effects of maintenance by means of regular quar-
terly visits for a periodontal prophylaxis (control treatment) against the effects of maintenance at intervals determined by the results of microscopic analyses of subgingival plaque samples (test treatment).7 All patients in both treatment groups were scheduled to receive a periodontal examination every 6 months for 4 years. Eighty patients, 33 in the test group
and 47 in the control group, were seen at each scheduled visit. The examination consisted of full-mouth recordings of the plaque index, the gingival index, probing pocket depth, and attachment level. Four sites were measured on each tooth: the mesial, midtooth, and distal sites on the buccal surface and the midtooth site alone on the lingual surface. Whole-mouth averages for these four measures were obtained and analyzed. Clinical results have been reported for the effects of 2 years of treatment3 and of 4 years of treatment.4 In neither case were there statistically significant differences between the treatment and control groups. The distributions of whole-mouth averages, of the natural logarithms of the averages, and of the square roots of the averages were obtained nine times for each of the four clinical variables, once at each of the nine examinations (at
J Periodontol April 1990
FLEISS, TURGEON, CHILTON, LISTGARTEN
202
are typical of the results for the other seven examinations, the values are tabulated for the distributions at baseline and at the final (4-year) examination only. For the measurement of plaque at baseline, none of the distributions was quite normal, although both the logarithmic and the square root transformations of the plaque index were successful in producing more nearly normal distributions than that of the index itself. For the plaque index at the 4-year examination, the distribution of the logarithms was the most nearly normal and the distribution of the untransformed index was the least normal. The baseline and 4-year distributions of the gingival index itself were both well-approximated by a normal distribution. The effects of transformation were trivial and perhaps even slightly deleterious. The patterns of results seem to be different for the baseline versus the 4-year distributions of the whole-mouth average pocket depth and its transformations. Except for the uniformly non-significant P-values for the Kolmogorov test, there does not seem to be much consistency across the statistical measures. Overall, the square root transformation appeared to produce more nearly normal distributions than its two competitors, but the baseline and 4-year distributions of the untransformed whole-mouth means themselves were not far from normal. By all four statistical criteria, the distribution of the logarithm of the whole-mouth average attachment level was the least normal at baseline, but was the most normal at 4 years. Consistently, however, the distribution of square roots was more nearly normal than the distribution of wholemouth means (the measure of kurtosis at the fourth year was the only exception). The distributions of the whole-
baseline plus eight semiannual examinations afterwards). The constant 1/2 was added to each whole-mouth average before its logarithm was calculated. The distributions were standardized by subtracting the mean and dividing by the standard deviation, and were then assessed for departures from normality. Four criteria for normality were examined: the median, the coefficient of skewness, the coefficient of kurtosis minus 3 (each of which should be close to 0 if the measurements are approximately normally distributed), and the P-value for the Kolmogorov goodness-of-fit test for normality. The significance of the Kolmogorov statistic was assessed by the method of Stephens.8 The variances for all nine time points, and the covariances for all pairs of time points, were calculated separately for each of the clinical variables as measured as well as for their logarithms and square roots. The relative precisions of probing pocket depth and attachment level were measured from a random effects repeated-measurements analysis of variance (80 patients each measured nine times) for each variable. Intraclass correlation coefficients were calculated from the between-patient mean square and the withinpatient mean square.9 Because there were no differences between the two treatment groups that even approached statistical significance, all of the analyses were performed on the sample of 80 patients as a whole. RESULTS Distributions Table 1 presents the values of the four statistics pertinent to the issue of approximate normality for the measures themselves as well as after transformation. Because they
Table 1: Values of Statistics Informative About the Approximate and Their Logarithmic and Square Root Transformations
Normality of the Distributions
at Baseline and 4 Years of 4 Clinical Variables
P-Value for Skewness
Median Transformation
BL*
4-year
BL
Kurtosis
4-year
BL
4-year
Kolmogorov Test BL 4-year
Plaque Index Untransformed index
Logarithm Square root
1.715 -0.089 0.327
3.436 0.053 0.693
0.15
0.10
