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Published ahead of print on June 23, 2005, doi:10.1164/rccm.200410-1335OC
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American Journal of Respiratory and Critical Care Medicine Vol 172. pp. 885-891, (2005)
© 2005 American Thoracic Society
doi: 10.1164/rccm.200410-1335OC

Original Article

Disease-specific Reference Equations for Lung Function in Patients with Cystic Fibrosis

Michal Kulich, Margaret Rosenfeld, Jonathan Campbell, Richard Kronmal, Ron L. Gibson, Christopher H. Goss and Bonnie Ramsey

Department of Probability and Statistics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic; Division of Pulmonary Medicine, Department of Pediatrics; Departments of Pharmacy and Biostatistics; Division of Pulmonary and Critical Care Medicine, Department of Medicine, University of Washington; and Cystic Fibrosis Therapeutic Development Network Coordinating Center, Children's Hospital and Regional Medical Center, Seattle, Washington

Correspondence and requests for reprints should be addressed to Michal Kulich, Ph.D., Department of Probability and Mathematical Statistics, Charles University, Sokolovska 83, CZ-186 75 Praha 8, Czech Republic. E-mail: kulich{at}karlin.mff.cuni.cz


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Rationale: Forced expiratory volume in one second (FEV1), an important measure of pulmonary disease severity in patients with cystic fibrosis (CF), is frequently expressed as a percentage of a predicted value derived from a healthy reference population. There are limitations to comparing the lung function of a patient with CF to that of healthy control subjects, and potential advantages to comparing it to that of other patients with CF.

Objective: To estimate CF-specific percentiles of FEV1 as functions of height, age, and sex.

Methods: We used 287,108 FEV1 observations among more than 21,000 patients with CF in the CF Foundation National Patient Registry between 1994 and 2001. The percentiles were estimated using quantile regression methods.

Results: FEV1 percentile "growth grids" are presented, allowing comparison of an individual's FEV1 to that of patients with CF of the same sex, age, and height. Their potential uses in clinical practice and research are illustrated.

Conclusions: CF-specific reference equations allow individual patients' FEV1 to be placed in the context of the distribution of lung function of their peers with CF, and should improve generalizability of CF clinical trials by setting entry criteria that are equitable across sex and age ranges. They may serve as a useful adjunct to conventional reference equations.

Key Words: cystic fibrosis • lung function • percentile • reference equations

The hallmark of cystic fibrosis (CF) is chronic, progressive obstructive lung disease. Pulmonary function, specifically the FEV1, is an important marker of CF lung disease severity (1, 2), widely employed in both the clinical and research arenas. Serial monitoring of lung function at clinic visits is used to assess disease progression, inform clinical management, and aid in lung transplant referral decisions (3, 4). FEV1 has served as the primary outcome measure in most clinical trials of therapies for CF pulmonary disease (5–8), and entry criteria for CF clinical trials generally include a range of FEV1 values.

Pulmonary function is generally expressed as a percentage of a predicted value based on sex, age, and height, calculated from regression equations derived from a healthy reference population. Expressing pulmonary function in relation to a predicted value facilitates the comparison of values over time in an individual growing subject, and allows comparison of lung function between subjects. However, there are important limitations to comparing the lung function of patients with CF to that of a healthy reference population. First, in order for percent-predicted values to be valid in a given population, the reference population must be similar with respect to age and height (9, 10). This criterion is frequently not met for patients with CF, who, on average, have markedly lower height-for-age values than those of the general population: between 6 and 20 years of age, the median height of patients with CF is between the 20th and 30th percentiles for the general population (11). Thus, for patients with CF with low height-for-age values, reference equations must be extrapolated beyond the data that generated them, a practice discouraged by the American Thoracic Society because it substantially decreases accuracy (9, 10). In addition, patients with CF frequently have delayed puberty, altering the relationship between height and lung function and rendering comparison with normal control subjects particularly problematic during adolescence (12–14).

A number of reference equations are widely employed (15–17), without consensus as to the most appropriate equation. The choice of reference equation applied to patients with CF has been shown to have important effects on the value of percent-predicted FEV1, the apparent change in lung function over time, and the classification of lung function as normal or abnormal; this is due, in part, to the poor comparability of height-for-age between patients with CF and normal subjects (14, 18). The reference equations (15) most widely employed by the CF research community, and currently used in the Cystic Fibrosis Foundation National Patient Registry, have relatively low predictive accuracy in short and young children due to the modeling of FEV1 as a linear function of height, resulting in underestimation of the true normal predicted values in this age range (19).

Despite its widespread use, the percent-predicted method of comparing an individual's lung function to that of a reference population has drawbacks. In expressing lung function as a percent of a predicted value, two assumptions are made, both of which have been shown to be invalid (20, 21). First, it is assumed that a given percent-predicted value is comparable in terms of the degree of abnormality (i.e., deviation from the mean) across multiple lung function indices (e.g., FEV1, FVC). Second, it is assumed that, for each lung function index, a given percent-predicted value indicates the same degree of abnormality for persons of different sex, ages, and heights. The use of percentiles or Z scores, such as are employed in National Center for Health Statistics growth curves for height and weight (22), avoids both these limitations. The American Thoracic Society has recommended that normal ranges for lung function be calculated based on percentiles (9, 10).

We propose an alternative paradigm for evaluating the lung function of patients with CF: CF-specific reference equations, by which the FEV1 of an individual with CF is compared not to that of a healthy reference population but rather to that of a CF population. These equations describe the distribution of FEV1 among patients with CF in terms of percentiles of FEV1 for a given sex, age, and height. In both the clinical and research arenas, CF-specific reference equations may serve as a useful adjunct to conventional reference equations derived from a healthy control population. The primary aim of this study was to develop percentiles for FEV1 among patients with CF, and to provide a simple tool for the calculation of CF-specific FEV1 percentiles. The secondary aim was to demonstrate the utility of CF-specific FEV1 percentiles in clinical practice and research. Part of this work has previously been presented in abstract form (23).


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Study Population
The Cystic Fibrosis Foundation has maintained a registry of U.S. patients with CF since 1966 (11). From 1994 to 2001, the registry included over 28,000 subjects. For each quarter, CF care centers were instructed to record the best prebronchodilator raw pulmonary function tests available, reported in liters. Although not specified, it was presumed that sites would record the best FEV1 per quarter. We extracted quarterly data on patients with CF who were older than 6 years of age in 2001, had at least one quarterly measurement of pulmonary function between 1994 and 2001, and had a recorded height between 105 and 190 cm for males and between 105 and 180 cm for females. To improve the quality of height data, we compared successive height measurements for each patient, searching for major inconsistencies in recorded heights, such as implausible, sudden positive changes or large negative changes. Patients who had inconsistencies in height measurements that were likely to result in errors exceeding 5 cm were excluded from all analyses. The details on height data quality checks are provided in the online supplement. Patients of all races were included in the study. Percent-predicted FEV1 values were calculated using the reference equations of Knudson and colleagues (15). The study was approved by the Children's Hospital and Regional Medical Center Human Subjects Review Board. Permission to use CF registry data was obtained from the Cystic Fibrosis Foundation.

Statistical Methods
All analyses were done separately by sex. Quantile regression methods (24) were used to estimate percentiles for FEV1 given height and/or age. This method models a given percentile of the outcome variable as a linear function of independent variables, allowing fitting and smoothing of the percentiles in one step without assuming normality of the outcome. Cubic B-spline bases for height and age were used as independent variables in the quantile regression model. The bases are piecewise cubic functions; the model combines them linearly to obtain best fitting smooth curves. We fitted 99 separate models for the 1st–99th percentiles and interpolated linearly between them. No adjustments were made for correlations between multiple FEV1 measurements on the same subject. This lack of adjustment for repeated measures does not affect the estimated percentiles. Data manipulations were performed using SAS (SAS Institute, Cary, NC) and the analyses were performed in R (R Foundation for Statistical Computing, Vienna, Austria), an open-source statistical package (25). Details are provided in the online supplement.


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Reference curves for FEV1 were calculated from 287,108 FEV1 measurements made among 21,646 subjects (53.1% male) between 1994 and 2001. The average number of FEV1 measurements per subject was 13.3 (range, 1–47). Approximately 0.7% of all measurements (~ 2,000) were excluded due to inconsistencies in height. The size of the study population decreased with increasing age (Table 1), due, primarily, to attrition through mortality. Similarly, the increasing male/female ratio with age reflects the greater mortality of females. Figure 1 displays selected CF-specific FEV1-for-age percentile curves. Among patients with CF, FEV1 (L) increases throughout childhood, peaks during adolescence, and steadily declines in subjects of greater age. Until about 12 years of age, the difference in pulmonary function between boys and girls is relatively small. During the teenage years, boys' FEV1 increases more rapidly and peaks later, at 17–18 years of age, compared with 15–16 years of age in girls. At ages 18–25 years, the percentile curves for males decrease more steeply than those for females.


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  		TABLE 1. Characteristics of study population

 


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  		Figure 1. Selected cystic fibrosis (CF)–specific FEV1 percentile reference curves by age in years: (A) male patients with CF; (B) female patients with CF.

 
CF-specific FEV1-for-height percentiles for male and female patients with CF are shown in Figure 2. Curves for males and females have similar shapes. All FEV1 percentiles increase with height, but the increase in the lowest percentiles is rather slow. The variability in FEV1, demonstrated by the spread between the highest and lowest percentiles, is much larger among taller patients than among shorter patients, and among males than among females.



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  		Figure 2. Selected CF-specific FEV1 percentile reference curves by height: (A) male patients with CF; (B) female patients with CF.

 
Figure 3 displays four examples of CF-specific FEV1-for-height percentile charts for specific ages; CF-specific FEV1 percentile curves are plotted against height separately for males and females ages 12 and 18. These charts allow comparison of a given patient's FEV1 measurement to that of patients with CF of the same sex, height, and age. For example, an FEV1 of 3.0 L in a boy who is 18 years old and 180 cm tall is at the 35th CF-specific percentile for sex, height, and age. Thus, approximately 65% of male patients with CF of the same height and age have an FEV1 greater than this patient. The complete set of 50 charts of age-specific FEV1 percentiles (25 for males and 25 for females) is included in the online supplement. A tool for converting FEV1 (L) into CF-specific FEV1 percentiles given sex, age, and/or height is available online at http://www.karlin.mff.cuni.cz/~kulich/fevref/cfref.html.



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  		Figure 3. Examples of CF-specific FEV1 percentile reference curves for specific ages for male patients with CF ([A] 12 years and [B] 18 years) and female patients with CF ([C] 12 years and [D] 18 years).

 
CF-specific FEV1 percentiles may be especially useful in monitoring changes in lung function in an individual patient over time. Note that the curves are by necessity based on data from subjects alive at each age. Thus, the change in individuals' CF-specific percentiles with advancing age reflects their status relative to others surviving to each of these ages, not to patients who may have had steeper declines in lung function and then died. Figure 4 shows examples of pulmonary function trends for four patients selected from the CF registry, in terms of both percent-predicted FEV1 relative to a healthy control population (15) and CF-specific FEV1 percentiles. Patient shown in Figure 4A, a girl, had similar trends in her percent-predicted FEV1 and CF-specific FEV1 percentiles between 6 and 10 years of age. At age 6 years, her FEV1 was 120% predicted compared with a reference population and at the 82nd percentile among patients with CF of her height, age and sex. By age 7.5 years, her percent-predicted FEV1 dropped markedly to 77% predicted, at the 30th CF-specific percentile. Between ages 8 and 10 years, her percent-predicted FEV1 hovered around 80% and the CF-specific percentile recovered slightly, to the 40th percentile. Figures 4B through 4D illustrate patients in whom the CF-specific FEV1 percentile reveals information about the patient's lung function relative to that of other patients with CF—information that cannot be gleaned from the percent-predicted FEV1 relative to a healthy population. Whereas the FEV1 of Patient B declined from 117% predicted at the age of 7 years to 80–90% predicted at ages 12–14 years, the CF-specific percentiles, after an initial decline, show overall improvement from ages 9 to 14 years. Similarly, the CF-specific percentiles of Patient C improved from the lower quartile to about the median over 7 years, despite a modest decline in percent-predicted FEV1 during that same period. Patient D, a boy, presents a potentially worrisome fall in FEV1 percentile relative to other patients with CF, which could not be discerned from evaluation of percent-predicted FEV1 relative to a healthy population.



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  		Figure 4. Trends in pulmonary function of four selected patients. (A and B): females; (C and D): males. Solid lines represent percent-predicted FEV1 compared with a healthy reference population, based on the reference equations of Knudson and coworkers (15). Dashed lines indicate CF-specific FEV1 percentiles; dotted lines indicate fitted linear trends.

 
Although the linear modeling of the Knudson reference equations (15) is known to produce inaccuracies in the slopes of percent-predicted FEV1 as children grow in height (19), these inaccuracies do not explain the observed discrepancies between the CF-specific percentiles and percent-predicted FEV1. Use of the Lebecque equations (26) (which employ a log-linear model of the association between FEV1 and height) to generate percent-predicted FEV1 resulted in plots for these four subjects with very similar trends (data not shown).

Because lung function generally declines with increasing age in patients with CF, the frequency of a particular value of percent-predicted FEV1 among patients with CF varies with age. CF-specific FEV1 percentiles can be applied to calculate frequencies of percent-predicted FEV1 among patients with CF. Figure 5 shows percentages of patients with CF who exceed a given threshold of percent-predicted FEV1 for both sexes and four specific ages. Height is fixed at the median for patients with CF of each age and sex. For example, the median (50th percentile) percent-predicted FEV1 at ages 6, 12, 18, and 24 years are, respectively, 95, 90, 72, and 50% for male patients, and 97, 80, 67, and 58% for female patients. The percentage of patients with CF who have an FEV1 at least 80% predicted at ages 6, 12, 18, and 24 years are, respectively, 76, 67, 41, and 14% for male patients and 76, 52, 32, and 22% for female patients.



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  		Figure 5. Percentages of male (A) and female (B) patients with CF whose FEV1 exceeds a given percent-predicted FEV1 (based on Knudson equations [15]) at four selected ages. The intersections of the horizontal and vertical grid lines at each age-specific curve identify the proportion of patients of that age whose FEV1 % predicted exceeds a given threshold. For example, for males, the 50th percentile (median) horizontal grid line intersects the 6-year-old curve at 97% predicted and the 12-year-old curve at 90% predicted. Thus, the median FEV1 among 6-year-old males is 97% predicted and among 12-year-old males is 90% predicted. Similarly, for males, the 80% predicted FEV1 vertical grid line intersects with the 6-year-old age curve at the 76th percentile and with the 12-year-old age curve at the 67th percentile. Thus, 76% of 6-year-old males with CF and 67% of 12-year-old males with CF have an FEV1 of at least 80% predicted.

 
In Figure 5, the shift of the curves to the left with increasing age reflects the decline of pulmonary function in patients with CF compared with that in healthy subjects. The figure reveals a large difference in the rate of percent-predicted FEV1 decline between male and female patients with CF. Female patients have a large drop in percent-predicted FEV1 between ages 6 and 12 years, followed by much smaller drops between ages 12, 18, and 24 years. In male patients, the decline between ages 6 and 12 years is much smaller, but is followed by much larger drops between ages 12, 18, and 24 years. The large shift in the male curve between ages 18 and 24 years, and the lower percentages of males than females above any threshold, at least partly reflect the larger number of females who have died before age 24. Taken together, these curves suggest that males are more likely to survive for extended periods when they reach a critically low level of FEV1.

Most CF clinical trials include eligibility criteria based on FEV1, almost always defined in terms of the range of percent-predicted FEV1 (e.g., 30–80% predicted). Because the proportion of patients that falls within a given range of percent-predicted FEV1 varies markedly by sex, age, and height, entry criteria based on percent-predicted FEV1 can result in highly variable representation of groups of patients with CF depending on their sex, age, and height. For example, in a trial that enrolls subjects between 6 and 12 years of age, an entry criterion of an FEV1 30 to 80% predicted will result in an unequal representation of patients in different sex, age, and height categories (Table 2). Eligibility rates for this hypothetical trial vary widely, especially due to the upper limit of 80% predicted for FEV1—few 6-year-old patients will be eligible at all. Among older patients, more girls than boys will satisfy the criteria. The eligibility rates also depend strongly on height—subjects sampled for this hypothetical trial will be disproportionately taller in the younger age group and shorter in the older age group. Entry criteria based on CF-specific FEV1 percentiles would be more equitable, assuring that the same proportion of patients is eligible regardless of sex, age, and height and thereby improving the applicability of results.


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  		TABLE 2. Percentages of patients with cystic fibrosis eligible for a hypothetical clinical trial, by age, height, and sex

 

   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
We have developed CF-specific reference equations for FEV1 that, for the first time, allow comparison of lung function of an individual patient with CF with that of his or her peers with CF. We hope that, in both the clinical and research arenas, these novel CF-specific reference equations may serve as a useful adjunct to conventional reference equations. CF-specific reference equations: (1) allow an individual patient's lung function to be placed in the context of the average lung function for patients with CF of a given sex, age, and height; (2) overcome the limitations of comparing patients with CF to a reference population that has a very different distribution of height-for-age; and (3) describe lung function in terms of percentiles, as recommended by the American Thoracic Society (9, 10), rather than percent-predicted values, as is typical for established reference equations (15–17). In addition, the use of CF-specific reference equations avoids the inconsistencies introduced by switching from pediatric to adult reference equations as patients mature.

CF-specific reference equations account for the fact that the lung function of patients with CF generally declines with age. Thus, an FEV1 at the 50th CF-specific percentile always means that half of patients with CF of the same age, sex, and height have an FEV1 greater than this individual's and half have an FEV1 that is less. On the other hand, an FEV1 of 80% predicted corresponds to the average FEV1 for a 12-year-old female with CF, but only 30% of 18-year-old females with CF have an FEV1 of at least 80% predicted (Figure 5). Clearly, the ultimate goal for our patients is to maintain normal lung function throughout their lives. Currently, however, patients with CF do generally lose lung function with advancing age. The objective of CF-specific reference equations is not to allow clinicians and patients to settle for less than normal health, but rather to provide an important additional context in which to better understand patients' lung function. CF-specific reference equations may be employed in clinical practice to aid in early identification of atypical declines in FEV1 that may warrant more aggressive evaluation or intervention, or alternatively to reassure an individual that his or her lung function is average or above-average for patients with CF of his/her age.

In the clinical trial arena, we hope that the use of CF-specific reference equations may improve the generalized applicability of results by ensuring a more equitable distribution of study subjects across ages and sex. Entry criteria that include a range of percent-predicted FEV1 values relative to a reference population can result in an uneven distribution of study subjects, with one sex or certain age ranges likely to be over- or underrepresented. If, instead, the entry criteria are based on CF-specific percentiles of FEV1, an equitable sex and age distribution is much more likely to be achieved. In addition, because our FEV1 percentiles were developed specifically for the population with CF, their use as outcome measures in both clinical trials and observational studies may improve the reliability of sample size calculations and power to detect significant effects.

Fortunately, therapeutic advances result in ongoing improvements in lung function and survival (11) among patients with CF. Our current analysis provides a snapshot of lung function in U.S. patients with CF between 1994 and 2001. These CF-specific reference equations will need to be updated regularly (perhaps every 5–10 years) using newly available data. A change in the CF-specific FEV1 percentiles over time will help to quantify improvements in pulmonary function and survival achieved by new therapies. Ultimately, as therapies continue to improve, CF-specific curves may no longer be necessary.

Lung function data, of course, can only be obtained from subjects surviving to a given age. Thus, particularly at the greatest ages, the population from which the CF-specific percentile data are derived is relatively enriched for those with "mild" mutations and other risk factors associated with above-average survival. This survivor bias, inherent in any comparison of a patient with CF to his or her living peers, should be kept in mind when utilizing the CF-specific reference curves. Although mortality attrition also leads to a declining number of subjects available for the analyses with increasing age (Table 1), the sample sizes in the current analysis (n = 21,000) nevertheless compare favorably with those of widely employed standard reference equations (n = 7,429) (27).

We derived CF-specific reference equations using data from patients of all races and ethnicities. In the 2002 registry, 96% of patients were white, 3% were African American, and 4% were Hispanic (black or white). Because CF is rare in non-white populations, the data did not allow development of race-specific FEV1 percentiles. Thus caution should be used in applying our reference equations to non-white patients with CF. Similarly, as for any reference equations, caution should be exercised when interpreting percentiles for patients at the extremes of age (< 6 years or > 35 years), height (very short or very tall for age among patients with CF), or FEV1 (the lowest and the highest percentiles are estimated with more error).

To our knowledge, we have developed the first disease-specific lung function reference equations. Potentially, such reference equations could also be useful for other chronic pulmonary diseases, such as Duchenne muscular dystrophy, in which lung function relative to a healthy control population is anticipated to slowly decline with advancing age.


   Acknowledgments
 
The authors thank Preston Campbell, III, M.D., Executive Vice President of Medical Affairs, and Bruce Marshall, M.D., Director of Clinical Affairs, Cystic Fibrosis Foundation (CFF), for their support of this project and for making the CFF National Patient Registry data available to us.


   FOOTNOTES
 
This article has an online supplement, which is accessible from this issue's table of contents at www.atsjournals.org

Conflict of Interest Statement: M.K. does not have a financial relationship with a commercial entity that has an interest in the subject of this manuscript. M.R. does not have a financial relationship with a commercial entity that has an interest in the subject of this manuscript. J.C. does not have a financial relationship with a commercial entity that has an interest in the subject of this manuscript. R.K. does not have a financial relationship with a commercial entity that has an interest in the subject of this manuscript. R.L.G. does not have a financial relationship with a commercial entity that has an interest in the subject of this manuscript. C.H.G. does not have a financial relationship with a commercial entity that has an interest in the subject of this manuscript. B.R. serves as the Director for the CF Therapeutics Development Network (TDN) Coordinating Center, which is a cystic fibrosis clinical trials network, composed of 18 research sites in the United States. The TDN is involved in preclinical services and the conduct of clinical trials with industry partners. As the Director of the TDN, B.R. signs all grants/contracts with companies conducting studies at TDN sites. The TDN is not a freestanding entity and all contracts/grants are through the Office of Research Administration at Children's Hospital and Regional Medical Center. She does not receive separate consultant fees or hold stock/equity in any of the companies relevant to this manuscript.

Received in original form October 8, 2004; accepted in final form June 19, 2005


   REFERENCES
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 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
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