DISEASE-SPECIFIC REFERENCE EQUATIONS FOR LUNG FUNCTION IN PATIENTS WITH CYSTIC FIBROSIS

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1 DISEASE-SPECIFIC REFERENCE EQUATIONS FOR LUNG FUNCTION IN PATIENTS WITH CYSTIC FIBROSIS Michal Kulich, PhD, Margaret Rosenfeld, MD, MPH, Jonathan Campbell, MS, Richard Kronmal, PhD, Ron L. Gibson, MD, Christopher H. Goss, MD, MPH, Bonnie Ramsey, MD ONLINE DATA SUPPLEMENT

2 METHODS Exclusions of suspected errors in height measurements. We excluded (1) all patients whose height decreased by more than 5 cm between two successive height measurements; (2) all patients under 20 years of age whose height increased by over 5 cm between two successive height measurements and the implied rate of growth exceeded 20 cm per year; (3) all patients over 20 years of age whose height increased by over 5 cm between two successive height measurements and the implied rate of growth exceeded 5 cm per year. Spline modeling of age and height effects on. Main effects of age and height were modeled using cubic B-spline bases. The knots for age were placed at 6, 8, 12 (11 in females), 15, 18, 22, 30, and 40 years. The knots for height were placed at 105, 115, 130, 145, 160, 175, and 190 cm in males and 105, 115, 130, 145, 155, 165, and 180 cm in females. The B-spline bases provide piecewise-polynomial bell-shaped curves that spanned 1 4 intervals between adjacent knots. Excluding the intercept, there were 9 linearly independent basis functions for age over the range 6 40 years and 8 linearly independent basis functions for height over the range cm ( cm in females). In bivariate models, which adjusted for both age and height, we included all pairwise interactions between the age and height bases such that both age and height bases were above 0.25 for at least 4,500 observations. This procedure assured that no interactions were fitted for regions that included too few observations. The total number of interaction parameters in the bivariate models was 25 for men and 26 for women. No significance testing was done for the interaction terms included in the models. Given the sample size, overfitting was not expected to be a serious problem. 1

3 Impact of repeated measurements on the estimated percentiles. The percentiles were estimated by quantile regression methods using an estimating equation designed for independent observations. Even though the observations are correlated within subjects, this procedure correctly estimates the percentiles provided that the number of independent subjects is sufficiently large. The presence of correlations would matter only if tests and confidence intervals were calculated. This approach has been used in generalized estimating equations models with working independence structure, where the correlations are ignored when estimating regression parameters. AGE-SPECIFIC -FOR-HEIGHT PERCENTILE CHARTS The remaining pages of this supplement present age-specific percentile reference charts for males (Figures E1 through E6) and females (Figures E7 through E12). The charts show - for-height percentiles calculated at ages 6 25 (in one-year increments), 30, 35, and 40. The calculations are based on a single reference equation for all ages in males and another equation for all ages in females. Because the two equations were evaluated only at specified ages the percentile charts exhibit certain jumps as a patient progresses from one age group to the next. In fact, the percentile for a patient who is 6 years and 6 months old is somewhere between the percentiles for ages 6 and 7. Percentiles for fractional ages with no jumps can be determined from the web calculator at which allows up to two decimal places for age. 2

4 FIGURE LEGENDS Figure E1: Age specific -for-height percentile reference charts. Males, age 6 9. Figure E2: Age specific -for-height percentile reference charts. Males, age Figure E3: Age specific -for-height percentile reference charts. Males, age Figure E4: Age specific -for-height percentile reference charts. Males, age Figure E5: Age specific -for-height percentile reference charts. Males, age Figure E6: Age specific -for-height percentile reference charts. Males, age Figure E7: Age specific -for-height percentile reference charts. Females, age 6 9. Figure E8: Age specific -for-height percentile reference charts. Females, age Figure E9: Age specific -for-height percentile reference charts. Females, age Figure E10: Age specific -for-height percentile reference charts. Females, age Figure E11: Age specific -for-height percentile reference charts. Females, age Figure E12: Age specific -for-height percentile reference charts. Females, age

5 Figure E1 Males, 6 years Males, 7 years Males, 8 years Males, 9 years

6 Figure E2 Males, 10 years Males, 11 years Males, 12 years Males, 13 years

7 Figure E Males, 14 years Males, 15 years Males, 16 years Males, 17 years

8 Figure E4 Males, 18 years Males, 19 years Males, 20 years Males, 21 years

9 Figure E5 Males, 22 years Males, 23 years Males, 24 years Males, 25 years

10 Figure E6 Males, 30 years Males, 35 years Males, 40 years

11 Figure E7 Females, 6 years Females, 7 years Females, 8 years Females, 9 years

12 Figure E Females, 10 years Females, 11 years Females, 12 years Females, 13 years

13 Figure E9 Females, 14 years Females, 15 years Females, 16 years Females, 17 years

14 Figure E10 Females, 18 years Females, 19 years Females, 20 years Females, 21 years 13

15 Figure E11 Females, 22 years Females, 23 years Females, 24 years Females, 25 years

16 Figure E Females, 30 years Females, 35 years Females, 40 years