Correspondence BODY MASS INDEX AND NECK CIRCUMFERENCE IN OBSTRUCTIVE SLEEP APNEA
Variable Entered
To the Editor: Katz and colleagues (Am Rev Respir Dis 1990; 141:1228-31) show that patients with obstructive sleep apnea (OSA) have thicker necks than nonapneic subjects. The conclusions about the relative importance of body mass index (BMI) and neck circumference are, however, not clear. They base their conclusions on a multiple linear regression analysis. According to the authors, "external neck circumference was a more important determinant of apnea/hypopnea index (AHI) than BMI, accounting for 29070 of the variability in AHI, as opposed to only 4070 variability in AHI contributed by BMI." The correlation between AHI and BMI was 0.51, which is very close to the correlation between AHI and external neck circumference (0.53). The correlation between BMI and neck circumference was 0.68. Magnitude of partial R 2depends on the order of entering variables to a multiple linear regression model. I would like to see another analysis, where BMI had been entered to the model as the first variable before neck circumference (entered as the second variable). What happens to the partial R2values? I suspect that the difference is smaller than 29070 against 4070. This is important so that we know how much more external neck circumference adds to the information given by BMI. If the partial R2 of neck circumference is still significant, neck circumference should be measured in addition to BMI in future studies about OSA. It is easy to understand, as the authors write, that obesity produces much of its effect via fat in the neck. An estimate of neck circumference can be used in large scale epidemiologic studies as well. People usually know their collar size (or they can easily measure it), which correlates well with the external neck circumference. Neck circumference probably is important in the pathway of developing OSA, but solving the problem of obesity is more important in the prevention of OSA-and of many other diseases. MARKKU PARTINEN, M.D. Department of Neurology University oj Helsinki SF-00290 Helsinki, Finland
From the Author: Dr. Partinen wonders if our results depend on the order in which we enter the variables into our model. They do not. Our model is that of multiple linear regression (forward and stepwise). Weused SAS version 6.03 (one of the most powerful statistical packages) to set up the model (1). The model statements used in PROC REG were:MODEL AHI= BMI NECK CIRC3PH AGE/SELECTION= FORWARD, MODEL AHI = NECK BMI CIRC3PH AGE/SELEC-
NECK 8MI AGE
Partial
Model
R*"2
R"·2
F
0.2696 0.2797 0.2864
247.3146 9.3690 6.3082
0.2696 0.0101 0.0067
Prob
0.0001 0.0023 0.0123
TION = FORWARD, and two other MODEL statements identical to the above, except for SELECTION = STEPWISE; (CIRC3PH is the distal pharyngeal circumference). The statistical results were identical in each case. Furthermore, we now have a set of 672 patients in whom we also measured neck circumference and set up the following models: MODELAHI = BMINECKAGE/SELECTION = FORWARD, MODEL AHI = NECK BMI AGE/SELECTION = FORWARD, and two other models identical to above but with SELECTION = STEPWISE. The output, identical for each model, is shown below. Note that the neck circumference is a more important determinant of apnea index than BMI; this result is independent of the order in which the variables BMI, NECK, and AGE are entered into the model. Finally, I would not expect the results of forward stepwise regression to depend on the order of data entry into the model. This type of regression first puts.into the model the single independent variable that explains most of the variability in AHI (independently of the order in which the variables appear in the MODEL statement), and then successively at each step inserts the variable that explains most of the remaining (residual) variability in AHI. The procedure is terminated when none of the remaining independent variables explains a significant additional amount of variability in AHI at"a predetermined level of significance. The importance of the contribution of each independent variable depends on Nand on the degree of correlation between the "independent" variables. Perhaps Dr. Partinen's finding that regression coefficients depend on how the variables are entered into the model is due to the particular software package he is using for statistical analysis.
HOFFSTEIN, M.D. St. Michael's Hospital 30 Bond Street Toronto, Ontario, Canada M5B lW8 VIC10R
t SAS Institute Inc. SAS/STAT guide for personal computers. Version 6 ed. Gary, NC; SAS Institute Inc, 1987. 1028 pp.
ERRATUM Please note that table 5 in "Diagnosis and Treatment of Disease Caused by Nontuberculous Mycobacteria" (Am Rev Respir Dis 1990; 142:940-53) contains an error. The reference to increased serum levels of Dilantin should be listed under Isoniazid, not under Ethambutol as printed. 204
>F
Variable Entered
To the Editor: Katz and colleagues (Am Rev Respir Dis 1990; 141:1228-31) show that patients with obstructive sleep apnea (OSA) have thicker necks than nonapneic subjects. The conclusions about the relative importance of body mass index (BMI) and neck circumference are, however, not clear. They base their conclusions on a multiple linear regression analysis. According to the authors, "external neck circumference was a more important determinant of apnea/hypopnea index (AHI) than BMI, accounting for 29070 of the variability in AHI, as opposed to only 4070 variability in AHI contributed by BMI." The correlation between AHI and BMI was 0.51, which is very close to the correlation between AHI and external neck circumference (0.53). The correlation between BMI and neck circumference was 0.68. Magnitude of partial R 2depends on the order of entering variables to a multiple linear regression model. I would like to see another analysis, where BMI had been entered to the model as the first variable before neck circumference (entered as the second variable). What happens to the partial R2values? I suspect that the difference is smaller than 29070 against 4070. This is important so that we know how much more external neck circumference adds to the information given by BMI. If the partial R2 of neck circumference is still significant, neck circumference should be measured in addition to BMI in future studies about OSA. It is easy to understand, as the authors write, that obesity produces much of its effect via fat in the neck. An estimate of neck circumference can be used in large scale epidemiologic studies as well. People usually know their collar size (or they can easily measure it), which correlates well with the external neck circumference. Neck circumference probably is important in the pathway of developing OSA, but solving the problem of obesity is more important in the prevention of OSA-and of many other diseases. MARKKU PARTINEN, M.D. Department of Neurology University oj Helsinki SF-00290 Helsinki, Finland
From the Author: Dr. Partinen wonders if our results depend on the order in which we enter the variables into our model. They do not. Our model is that of multiple linear regression (forward and stepwise). Weused SAS version 6.03 (one of the most powerful statistical packages) to set up the model (1). The model statements used in PROC REG were:MODEL AHI= BMI NECK CIRC3PH AGE/SELECTION= FORWARD, MODEL AHI = NECK BMI CIRC3PH AGE/SELEC-
NECK 8MI AGE
Partial
Model
R*"2
R"·2
F
0.2696 0.2797 0.2864
247.3146 9.3690 6.3082
0.2696 0.0101 0.0067
Prob
0.0001 0.0023 0.0123
TION = FORWARD, and two other MODEL statements identical to the above, except for SELECTION = STEPWISE; (CIRC3PH is the distal pharyngeal circumference). The statistical results were identical in each case. Furthermore, we now have a set of 672 patients in whom we also measured neck circumference and set up the following models: MODELAHI = BMINECKAGE/SELECTION = FORWARD, MODEL AHI = NECK BMI AGE/SELECTION = FORWARD, and two other models identical to above but with SELECTION = STEPWISE. The output, identical for each model, is shown below. Note that the neck circumference is a more important determinant of apnea index than BMI; this result is independent of the order in which the variables BMI, NECK, and AGE are entered into the model. Finally, I would not expect the results of forward stepwise regression to depend on the order of data entry into the model. This type of regression first puts.into the model the single independent variable that explains most of the variability in AHI (independently of the order in which the variables appear in the MODEL statement), and then successively at each step inserts the variable that explains most of the remaining (residual) variability in AHI. The procedure is terminated when none of the remaining independent variables explains a significant additional amount of variability in AHI at"a predetermined level of significance. The importance of the contribution of each independent variable depends on Nand on the degree of correlation between the "independent" variables. Perhaps Dr. Partinen's finding that regression coefficients depend on how the variables are entered into the model is due to the particular software package he is using for statistical analysis.
HOFFSTEIN, M.D. St. Michael's Hospital 30 Bond Street Toronto, Ontario, Canada M5B lW8 VIC10R
t SAS Institute Inc. SAS/STAT guide for personal computers. Version 6 ed. Gary, NC; SAS Institute Inc, 1987. 1028 pp.
ERRATUM Please note that table 5 in "Diagnosis and Treatment of Disease Caused by Nontuberculous Mycobacteria" (Am Rev Respir Dis 1990; 142:940-53) contains an error. The reference to increased serum levels of Dilantin should be listed under Isoniazid, not under Ethambutol as printed. 204
>F
