Correspondence ASSESSING PRECISION AND ACCURACY IN BWOD GAS PROFICIENCY TESTING
To the Editor: The purpose of this letter is to bring to the attention 0 f the authors, Hansen and colleagues (Assessing precision and accuracy in blood gas proficiency testing. Am Rev Respir Dis 1990; 11:1190-1193), an error that appears in the parenthetical remark on page 1190,column 8, sentence 1 under the paragraph Precision Assessment: "the customary standard deviation of three measures by each instrument multipled by 1.128 to give an unbiased estimate of the SD." The number 1.128 is the approximation for
Regardless of the term or abbreviation used, there should be no disagreement regarding the validity of the correlation coefficients, the statistical significance levels derived from the data, the finding that precision of analyte measurement in proficiencytesting materials correlates positively with other measures of analyte precision and accuracy, and the suggested conclusion that features unique to each model significantly affect precision. JAMES E. HANSEN, M.D. RICHARD CASABURI, PH.D., M.D. UCLA School of Medicine Torrance, CA ROBERT O. CRAPO, M.D. ROBERT L. JENSEN, PH.D. University of Utah College of Medicine Salt Lake City, UT
2
V'fC Therefore, the authors are actually estimating 2
-.[1t 0 which is the mean difference and not the SD, as the authors state. Hence, "SD" in the statement should replace with "MD (mean difference.)" There are several erroneous references to SD in the article. If the true intention of the authors is, as stated in the paragraph referenced above, to use the MD as the measure of precision, then these references ought to be the MD (mean difference). This parameter is known in the statistical literature as Gini's mean difference (Kendall MG and Stuart A, The advanced theory of statistics. Vol. 1, 1963, London: Charles Griffin and Company Limited, 42, 43, 47, and 241). It is the average (mean) absolute difference between pairs of measurements generated under identical conditions. When the measurements have a normal distribution with standard deviation 0, the parameter has the value 2
-.[1t
0
This parameter is also the "mean deviation" of the distribution of the difference of two independent and identically distributed normal random variables with standard deviation o, A. VUAYA RAo Research Triangle Institute Center for Medical, Environmental and Energy Statistics Research Triangle Park, NC
From the Authors: We appreciate Dr. Rao's attention to our article and his desire to improve our usage of statistical terms and abbreviations. After additional statistical consultation, we conclude that we correctly identified and computed the unbiased estimate of sigma by multiplying the SD of each of three samples by the factor 1.128 (1-2). (The factor for two samples is 1.253 and decreases towards 1.00 as the number of samples increases [1-2]). As Rao correctly points out, the mean difference of Gini can also be related to the SD by multiplying by the factor 1.128 (3). It is a fascinating coincidence that the same constant gives an unbiased estimate of these two measures of dispersion when the number of samples is three. Kendall and Stuart (3) also point out that "Gini's mean difference (is) not to be confused with mean deviation ... which is about 80070 of the standard deviation." Thus, we doubt that we would have promoted clarity by introducing this infrequently used term and another abbreviation (MD) in our manuscript. 498
l. Dixon WJ, Massey FJ, Jr. Introduction to statistical analysis. 3rd ed. New York: McGraw-Hill, 1969; 135. 2. Johnson NL, Kotz S. Distributions in statistics. Boston: Houghton Mifflin, 1970; 63. 3. Kendall MG, Stuart A. The advanced theory of statistics, vol 1, 3rd ed. New York: Hafner, 1969; 45-7, 243.
ANTIASTHMA DRUGS AND AIRWAY HYPERRESPONSIVENESS
To the Editor: Drs. Morley and Chapman have raised the issue of the effects of drug therapy on bronchial hyperresponsiveness (BHR), and we presume they questioned whether prior use of bronchodilators and cromoglycate may have decreased the point prevalence of BHR in relation to asthma symptoms and diagnosis in our recently published study (1).The fact that certain asthma medications have acute effects on bronchial responsiveness is well documented and not disputed. However,wehavespecificallyexamined the question ofwhether medications taken before the test affected our results by considering the association of BHR with use of specific medications. At the time of challenge, children were shown a display of all inhalers and asthma medications available and were asked about medications taken in the previous 48 hours. Ninety-three children reported recent use of a bronchodilator (inhaled or oral Bsagonist or theophylline) of whom 68 (73%) had BHR (PD20 ~ 7.8l1mol histamine), and 47 children reported recent use of a prophylactic (inhaled cromoglycate or inhaled or oral steroids), 0 f whom 34 (72%) had BHR. Bronchodilator use before the test gave a relative risk of having BHR of 5.55 (95% CI 4.70,6.57) and prophylactic use gave a relative risk of 4.97 (95% CI 4.04, 6.11). These relative risks were very similar to those associated with current maintenance bronchodilator (relative risk 6.16;95% CI 5.21, 7.28) and prophylactic (relative risk 5.15; 95% CI 4.29, 6.18) use (as reported either by parents in the questionnaire or by children at the time of the test) suggesting that the increased risk of BHR was associated with the regular medication and not just pretest medication. Because selecting for medication use also selects for symptomatic subjects, maintenance bronchodilator and prophylactic use were included in a multiple logistic model in which the diagnosis and recent symptoms of asthma, other atopic conditions, ethnic group, area of residence, ambient climatic conditions, gender, height, and baseline spirometry were also controlled for. In this model maintenance prophylactic use had no significant effect on risk of BHR while the risk associated with maintenance bronchodilator use remained high (odds ratio 4.04; 95%
To the Editor: The purpose of this letter is to bring to the attention 0 f the authors, Hansen and colleagues (Assessing precision and accuracy in blood gas proficiency testing. Am Rev Respir Dis 1990; 11:1190-1193), an error that appears in the parenthetical remark on page 1190,column 8, sentence 1 under the paragraph Precision Assessment: "the customary standard deviation of three measures by each instrument multipled by 1.128 to give an unbiased estimate of the SD." The number 1.128 is the approximation for
Regardless of the term or abbreviation used, there should be no disagreement regarding the validity of the correlation coefficients, the statistical significance levels derived from the data, the finding that precision of analyte measurement in proficiencytesting materials correlates positively with other measures of analyte precision and accuracy, and the suggested conclusion that features unique to each model significantly affect precision. JAMES E. HANSEN, M.D. RICHARD CASABURI, PH.D., M.D. UCLA School of Medicine Torrance, CA ROBERT O. CRAPO, M.D. ROBERT L. JENSEN, PH.D. University of Utah College of Medicine Salt Lake City, UT
2
V'fC Therefore, the authors are actually estimating 2
-.[1t 0 which is the mean difference and not the SD, as the authors state. Hence, "SD" in the statement should replace with "MD (mean difference.)" There are several erroneous references to SD in the article. If the true intention of the authors is, as stated in the paragraph referenced above, to use the MD as the measure of precision, then these references ought to be the MD (mean difference). This parameter is known in the statistical literature as Gini's mean difference (Kendall MG and Stuart A, The advanced theory of statistics. Vol. 1, 1963, London: Charles Griffin and Company Limited, 42, 43, 47, and 241). It is the average (mean) absolute difference between pairs of measurements generated under identical conditions. When the measurements have a normal distribution with standard deviation 0, the parameter has the value 2
-.[1t
0
This parameter is also the "mean deviation" of the distribution of the difference of two independent and identically distributed normal random variables with standard deviation o, A. VUAYA RAo Research Triangle Institute Center for Medical, Environmental and Energy Statistics Research Triangle Park, NC
From the Authors: We appreciate Dr. Rao's attention to our article and his desire to improve our usage of statistical terms and abbreviations. After additional statistical consultation, we conclude that we correctly identified and computed the unbiased estimate of sigma by multiplying the SD of each of three samples by the factor 1.128 (1-2). (The factor for two samples is 1.253 and decreases towards 1.00 as the number of samples increases [1-2]). As Rao correctly points out, the mean difference of Gini can also be related to the SD by multiplying by the factor 1.128 (3). It is a fascinating coincidence that the same constant gives an unbiased estimate of these two measures of dispersion when the number of samples is three. Kendall and Stuart (3) also point out that "Gini's mean difference (is) not to be confused with mean deviation ... which is about 80070 of the standard deviation." Thus, we doubt that we would have promoted clarity by introducing this infrequently used term and another abbreviation (MD) in our manuscript. 498
l. Dixon WJ, Massey FJ, Jr. Introduction to statistical analysis. 3rd ed. New York: McGraw-Hill, 1969; 135. 2. Johnson NL, Kotz S. Distributions in statistics. Boston: Houghton Mifflin, 1970; 63. 3. Kendall MG, Stuart A. The advanced theory of statistics, vol 1, 3rd ed. New York: Hafner, 1969; 45-7, 243.
ANTIASTHMA DRUGS AND AIRWAY HYPERRESPONSIVENESS
To the Editor: Drs. Morley and Chapman have raised the issue of the effects of drug therapy on bronchial hyperresponsiveness (BHR), and we presume they questioned whether prior use of bronchodilators and cromoglycate may have decreased the point prevalence of BHR in relation to asthma symptoms and diagnosis in our recently published study (1).The fact that certain asthma medications have acute effects on bronchial responsiveness is well documented and not disputed. However,wehavespecificallyexamined the question ofwhether medications taken before the test affected our results by considering the association of BHR with use of specific medications. At the time of challenge, children were shown a display of all inhalers and asthma medications available and were asked about medications taken in the previous 48 hours. Ninety-three children reported recent use of a bronchodilator (inhaled or oral Bsagonist or theophylline) of whom 68 (73%) had BHR (PD20 ~ 7.8l1mol histamine), and 47 children reported recent use of a prophylactic (inhaled cromoglycate or inhaled or oral steroids), 0 f whom 34 (72%) had BHR. Bronchodilator use before the test gave a relative risk of having BHR of 5.55 (95% CI 4.70,6.57) and prophylactic use gave a relative risk of 4.97 (95% CI 4.04, 6.11). These relative risks were very similar to those associated with current maintenance bronchodilator (relative risk 6.16;95% CI 5.21, 7.28) and prophylactic (relative risk 5.15; 95% CI 4.29, 6.18) use (as reported either by parents in the questionnaire or by children at the time of the test) suggesting that the increased risk of BHR was associated with the regular medication and not just pretest medication. Because selecting for medication use also selects for symptomatic subjects, maintenance bronchodilator and prophylactic use were included in a multiple logistic model in which the diagnosis and recent symptoms of asthma, other atopic conditions, ethnic group, area of residence, ambient climatic conditions, gender, height, and baseline spirometry were also controlled for. In this model maintenance prophylactic use had no significant effect on risk of BHR while the risk associated with maintenance bronchodilator use remained high (odds ratio 4.04; 95%
