_{1}decline in patients with cystic fibrosis: a longitudinal study

RLS and PJD are joint senior authors.

Forced expiratory volume in 1 s as a percentage of predicted (%FEV_{1}) is a key outcome in cystic fibrosis (CF) and other lung diseases. As people with CF survive for longer periods, new methods are required to understand the way %FEV_{1} changes over time. An up to date approach for longitudinal modelling of %FEV_{1} is presented and applied to a unique CF dataset to demonstrate its utility at the clinical and population level.

The Danish CF register contains 70 448 %FEV_{1} measures on 479 patients seen monthly between 1969 and 2010. The variability in the data is partitioned into three components (between patient, within patient and measurement error) using the empirical variogram. Then a linear mixed effects model is developed to explore factors influencing %FEV_{1} in this population. Lung function measures are correlated for over 15 years. A baseline %FEV_{1} value explains 63% of the variability in %FEV_{1} at 1 year, 40% at 3 years, and about 30% at 5 years. The model output smooths out the short-term variability in %FEV_{1} (SD 6.3%), aiding clinical interpretation of changes in %FEV_{1}. At the population level significant effects of birth cohort, pancreatic status and _{1} are shown over time.

This approach provides a more realistic estimate of the %FEV_{1} trajectory of people with chronic lung disease by acknowledging the imprecision in individual measurements and the correlation structure of repeated measurements on the same individual over time. This method has applications for clinicians in assessing prognosis and the need for treatment intensification, and for use in clinical trials.

_{1}

Now that people with cystic fibrosis are living much longer, how can we optimally describe the changes in forced expiratory volume in 1 s as a percentage of predicted (%FEV_{1}) over time in a way that is useful for clinicians at the individual and the population level?

We describe a novel modelling approach for analysing changes in %FEV_{1} over time that can be applied at the individual level to interpret the clinical significance of sudden changes in %FEV_{1}, and at the population level to quantify the effect of factors such as

Lung function measures are correlated for over 15 years, and a baseline %FEV_{1} value explains 63% of the variability in %FEV_{1} at 1 year, 40% at 3 years and about 30% at 5 years.

Understanding the long-term natural history of changes in lung function in people with lung diseases is a research priority._{1}) is commonly used to monitor lung function, and to describe disease severity in cystic fibrosis (CF)_{1} is used to inform clinical decisions about changing or intensifying treatment, and as an outcome measure in clinical studies._{1} has been shown to be related to survival in CF. Kerem _{1} <30 had a 2-year mortality over 50%,

Interpreting the significance of changes in %FEV_{1} in CF to inform patient management and to counsel patients regarding prognosis requires an understanding of the inherent variability of %FEV_{1} measures within individuals, to determine what constitutes a clinically significant deterioration in %FEV_{1}, rather than a change due to measurement error, or recoverable day-to-day fluctuation in lung function._{1} in observational studies.

As survival in CF improves with successive cohorts, there are many more people surviving into late adulthood. An implication of this, coupled with the availability of long-term follow-up data in CF registers, is that up to date methods should be adopted to interpret the long-term dynamics of lung function in CF. Statistical techniques for longitudinal data analysis have been the subject of much methodological development over the past 20 years, and the random intercept and slope model has become a popular analysis framework._{1} increases as a quadratic function over time (in proportion to time squared), which leads to estimates that diverge unrealistically over longer time periods. Methods for undertaking these analyses over longer time periods have been described,

In this study we analyse a unique population-level dataset of people with CF that includes longitudinal %FEV_{1} measures taken monthly for up to 30 years. We apply these methods to develop a general model for %FEV_{1} decline that goes beyond the popular random-intercept and slope approach, and explicitly describes the variability in %FEV_{1} within individuals over time. We show how this could be applied clinically to help interpret the significance of changes in lung function, and at a population level to explore the association of covariates (eg, _{1} decline.

All patients aged over 5 years whose %FEV_{1} data were entered on the Danish CF database between 1969 and 2010 were eligible. Post-transplant data from patients who had received a lung transplant were excluded. Patients attending the two Danish CF centres (Copenhagen and Aarhus) are seen routinely every month in the outpatient clinic for evaluation of clinical status, pulmonary function and microbiology of lower respiratory tract secretions. It is estimated that coverage of people with CF resident in Denmark is almost complete from 1990 when CF care was centralised. This coverage and the unparallelled frequency of measurement make this a unique dataset for epidemiological research. The study was approved by the Danish Data Inspectorate (Datatilsynet).

The primary outcome for this analysis was %FEV_{1}. Pulmonary function tests were performed according to international recommendations,_{1}, expressed as a percentage of predicted values for sex and height using reference equations from Wang or Hankinson.

Covariates in the analysis were age, sex, genotype coded as the number of Delta F508 alleles (0, 1 or 2), onset of chronic

A detailed explanation is given in the online appendix. Repeated %FEV_{1} measures on individuals are correlated, and this must be accommodated to obtain valid inferences. We used a linear mixed effects model with longitudinally structured correlation,_{1} over time for an individual subject so that the strength of the correlation of the random variation between two values depends on the corresponding time separation. The model decomposed the overall random variation in the data into three components: between subjects, between times within subjects, and measurement error.

First, we fit a provisional model for the mean response by ordinary least squares and used the empirical variogram of the residuals (see figure E1 in the online appendix) to provide initial estimates for the three components of variation, and for the shape of the correlation function of the between-times-within-subjects component. We then re-estimated all of the model parameters by maximum likelihood estimation, and used generalised likelihood ratio statistics to compare nested models, and Wald statistics to test hypotheses about model parameters. We assessed associations between single or multiple covariates and the population mean %FEV_{1} over time, and explored alternatives to a linear function for the population-averaged time trend.

The dataset contained 70 448 lung function measures on 479 patients seen between 1969 and 2010 in Denmark (_{1} measures per person was 101 (range 2–597). The median follow-up period was 10.5 years (range 0.1–31.5), with a total of 6500 person-years of follow-up. Forty-two patients were followed up for more than 30 years (see also figures E2 and E3 in the online appendix).

Baseline characteristics of the Danish cystic fibrosis (CF) population

Birth cohort | |||||||

≥1948 | ≥1958 | ≥1968 | ≥1978 | ≥1988 | ≥1998 | Total | |

N (%) | 7 (1.5) | 42 (8.8) | 110 (23) | 105 (21.9) | 141 (29.4) | 74 (15.4) | 479 (100) |

Women | 1 (14.3) | 19 (45.2) | 48 (43.6) | 52 (49.5) | 74 (52.5) | 42 (56.8) | 236 (49.3) |

No. Delta F508 = 0 | 0 (0) | 0 (0) | 1 (0.9) | 4 (3.8) | 5 (3.5) | 5 (6.8) | 15 (3.1) |

No. Delta F508 = 1 | 2 (28.6) | 14 (33.3) | 26 (23.6) | 24 (22.9) | 42 (29.8) | 19 (25.7) | 127 (26.5) |

No. Delta F508 = 2 | 5 (71.4) | 28 (66.7) | 83 (75.5) | 77 (73.3) | 94 (66.7) | 50 (67.6) | 337 (70.4) |

Developed chronic | 6 (85.7) | 31 (73.8) | 84 (76.4) | 55 (52.4) | 20 (14.2) | 5 (6.8) | 201 (42) |

Missing infection information | 0 (0) | 5 (11.9) | 2 (1.8) | 2 (1.9) | 1 (0.7) | 0 (0) | 10 (2.1) |

Pancreatic insufficient | 7 (100) | 42 (100) | 105 (95.5) | 99 (94.3) | 133 (94.3) | 73 (98.6) | 459 (95.8) |

Copenhagen | 7 (100) | 38 (90.5) | 83 (75.5) | 72 (68.6) | 79 (56) | 50 (67.6) | 329 (68.7) |

Alive | 4 (57.1) | 27 (64.3) | 79 (71.8) | 77 (73.3) | 132 (93.6) | 74 (100) | 393 (82) |

Developed CFRD | 3 (42.9) | 21 (50) | 41 (37.3) | 31 (29.5) | 22 (15.6) | 1 (1.4) | 119 (24.8) |

CFRD, cystic fibrosis related diabetes.

The high degree of short-term and long-term variation in predicted %FEV_{1} is illustrated in _{1} over time.

Comparison of conventional random intercept and slope model over short and long follow-up periods, versus our proposed Gaussian process model. (A) Data for a single individual, illustrating that a linear trend fits reasonably well over short time periods, but gives a very poor fit to this individual's complete data; linear trends are fitted by ordinary least squares. (B) The same data with the fitted trajectory of the stationary Gaussian process model. The smoothed fitted trace is a better representation of the ‘true’ underlying lung function, and could be used in real time to guide the interpretation of sudden changes in lung function. For instance, the sudden drop to under 30% indicated by the arrow is not mirrored in the model trace, suggesting that this may be recoverable random fluctuation. (C, D) Corresponding plots for a second individual. %FEV_{1}, forced expiratory volume in 1 s as a percentage of predicted.

The empirical variogram quantifies the variability in the dataset (_{1} at follow-up time (t), which can be explained by their %FEV_{1} value at baseline. For example, about 50% of the within-patient variability at t=2.5 years is explained by the baseline measurement, and about 30% at t=5 years. Overall, the dependence on baseline measures gradually decays and is negligible at 15 years.

Quantifying the variability in forced expiratory volume in 1 s as a percentage of predicted (%FEV_{1}) with the variogram approach. (A) Scaled empirical variogram for the Danish data. The solid line (variogram function) represents the variance of the difference between residual errors within individuals at time lags from 0 to 30 years. The variogram function increases up to about 15 years, corresponding to a decreasing correlation between paired lung function measures with increasing time separation. The variogram partitions the variability in the data into three components: within person, between person, and error. (B) Proportion of variability in an individual's %FEV_{1} at follow-up time t that is explained by their %FEV_{1} at baseline. This shows that the variogram can predict 63% of the variability from the population average at 1 year, which decreases to around 60%, 40%, 30% and 10% at 2, 3, 5 and 10 years respectively.

The model can be used to guide interpretation of sudden changes in lung function. Consider seeing the person in _{1} of around 50%. We suggest that this estimate provides a more realistic assessment of underlying lung function by smoothing out the short-term variability. This could be a useful adjunct to clinical decision-making. As well as providing information about the significance of a sudden change in lung function, _{1} measure. In terms of counselling patients, this means that a higher %FEV_{1} today is associated with a higher %FEV_{1} at subsequent time points, but the predictive value deteriorates over time as illustrated in the figure.

We explored the effect of covariates that have been associated with %FEV_{1} in previous studies to demonstrate how this model can be used to answer questions at the population level (see table E1 online appendix for univariate associations)._{1} for sub-populations of individuals sharing the same explanatory characteristics, rather than for any one individual. The most prominent effects are associated with birth cohort, pancreatic function and the onset of

Estimates from final multivariate model

Point estimate | Lower 95% CI | Upper 95% CI | p Value | |

Intercept at age 5 years | 66.02 | 61.13 | 70.92 | <0.001 |

CFRD | −2.47 | −3.58 | −1.37 | <0.001 |

Age | −0.26 | −0.49 | −0.03 | 0.025 |

Cohort≥1948 (reference 1968) | 1.20 | −25.50 | 27.90 | 0.930 |

Cohort≥1958 | −0.75 | −10.01 | 8.51 | 0.874 |

Cohort≥1978 | 16.60 | 10.15 | 23.05 | <0.001 |

Cohort≥1988 | 25.19 | 19.11 | 31.27 | <0.001 |

Cohort≥1998 | 29.81 | 22.85 | 36.78 | <0.001 |

Pancreatic sufficiency | 2.78 | −10.43 | 15.99 | 0.679 |

| −0.51 | −0.72 | −0.29 | <0.001 |

Age×cohort≥1948 | −0.03 | −0.67 | 0.61 | 0.920 |

Age×cohort≥1958 | 0.06 | −0.23 | 0.34 | 0.699 |

Age×cohort≥1978 | −0.72 | −1.00 | −0.44 | <0.001 |

Age×cohort≥1988 | −0.72 | −1.09 | −0.35 | <0.001 |

Age×cohort≥1998 | 0.50 | −0.41 | 1.42 | 0.280 |

Age×pancreatic sufficiency | 0.98 | 0.29 | 1.67 | 0.005 |

CFRD, cystic fibrosis related diabetes.

Effect of covariates on forced expiratory volume in 1 s as a percentage of predicted (%FEV_{1}). (A) Birth cohort effect in the final model. There is clear separation between the three most recent birth cohorts, with a successive increase in the intercept term at age 5 years. (B) Effect of pancreatic insufficiency and

We describe a novel longitudinal modelling technique specifically aimed at analysing long sequences of repeated measurements, and apply this to %FEV_{1} from a CF population. We show how this approach could be used to inform patient management, by aiding the interpretation of sudden changes in lung function, and by quantifying the predictive value of a baseline %FEV_{1} measure up to 15 years later. At the population level, we show how our model can be used to quantify the effect of covariates on populations or sub-populations. Translation of these methods into clinical practice is important because people with CF are living longer, and we have shown how commonly applied approaches are unhelpful over long follow-up periods.

This study quantifies the short-term variability in %FEV_{1} in this population (SD 6.3%), and demonstrates that %FEV_{1} measures within individuals are correlated over time lags of 15 years or more. We have also explored the effect of previously studied risk factors for lung function decline in the Danish CF population, and have demonstrated significant effects of birth cohort, pancreatic status and

The findings from this study have a number of clinical applications. Quantifying the variability in lung function measures is essential to make correct clinical interpretation._{1} of >13% (ie, twice the error SD, to give a 95% confidence range) is likely to represent true within-patient variation over time (disease progression), whereas anything less than this could be due to short-term fluctuation, which may recover. Stanbrook _{1} SD of 4.5% when measured over a 9-day period in 21 stable adults with CF. This population is different to the population in our study, who were measured regardless of clinical status, and one would therefore expect greater variability. Other studies have shown that people with CF, asthma and COPD have more short-term variability in lung function tests

Our model can be used to generate an underlying representation of an individual's ‘true’ lung function trajectory (_{1} measures. These smoothed traces could be used to inform clinical decision-making—the model fit curves in

We have generated, for the first time to our knowledge, the variogram function for %FEV_{1} in people with CF over long follow-up periods. This precisely quantifies how %FEV_{1} measures are correlated over time. Furthermore we have done this for the whole CF population of Denmark. This quantifies the degree to which a baseline %FEV_{1} measure can be used to predict subsequent %FEV_{1} measures over long follow-up periods, and is likely to be of interest to clinicians and patients. We demonstrate a long-term correlation between levels of %FEV_{1} within an individual. This suggests that there is long-term predictive value in a high %FEV_{1} measure—people with CF with a high %FEV_{1} at baseline are more likely to have a high %FEV_{1} up to 15 years later than individuals with a lower baseline %FEV_{1} (_{1} measure drops away rapidly over this period. We can say that on average a %FEV_{1} reading today explains about 63% of the variability in %FEV_{1} at 1 year, 40% at 3 years, and about 30% at 5 years.

This corroborates Rosenthal's study,_{1} explains 66% of the variability in %FEV_{1} at 1 year, and Mastella _{1} for a given age can be used to characterise the aggressiveness of lung disease._{1} to be an independent risk factor for a greater rate of decline of %FEV_{1} over the next few years._{1} can be a risk factor for greater decline in the short term, while still being associated with a relatively higher %FEV_{1} over the longer term.

At the population level we show how our approach can be applied to quantify the effect of covariates on changes in lung function. Furthermore, the partitioning of the variability in %FEV_{1} and the precise description of the correlation structure captured in the model provide important information for sample size calculations in longitudinal clinical studies with %FEV_{1} as an outcome. Increasingly longitudinal outcomes are being used in randomised control trials, and to undertake an a priori sample size calculation it is essential to have information on the correlation structure. Furthermore, our modelled %FEV_{1} trace could be used as an outcome in its own right.

As with other studies of patients with CF,

Our approach to modelling changes in %FEV_{1} can be applied over long follow-up periods. This is in contrast to the widely used random intercept and slope approach that has been applied in studies of CF and COPD over short-term_{1} over time, and to better understand how this might inform clinical decision making. Future research could explore the utility of our proposed model in other diseases such as COPD.

A limitation of this study is the likely influence of survivor bias on lung function estimates in the earlier birth cohorts. In the 1948–1978 period, the intercept at age 5 appears significantly lower than in the other cohorts, but there is also a shallower rate of decline of lung function. This is likely to be due to the incomplete capture of patients in earlier cohorts, with censoring due to death leaving only the more stable survivors. This is a common problem in datasets of this type.

Pancreatic sufficiency had an important effect on the overall rate of decline of lung function (+0.9% per year). In Konstan's study_{1} of −0.31% per year in the 6–8-year-old age group, and −0.22 in the 9–12-year-old age group.

In conclusion, our modelling approach provides a more realistic estimate of the %FEV_{1} trajectory in CF, which could be applied in real time to help clinicians interpret the significance of changes in %FEV_{1}. Furthermore, our approach quantifies the predictive value of a baseline %FEV_{1} measure, over three decades. This method is equally applicable to the longitudinal assessment of %FEV_{1} in other lung diseases, and can enable more robust comparisons of populations, including groups studied in clinical trials. As people are now living for many decades with these diseases, the development of tools to better understand the natural history of this important outcome will be essential for improved clinical care, as well as being a key research priority.

We thank Professor Peter Oluf Schiøtz for his support in accessing the data for this analysis.

DTR, MMW, FD, TP, RLS and PD conceived and designed the study. TP and HVO collected the data. DTR undertook the analysis and PD supervised analysis. DTR, MMW, RLS and PD interpreted the results and drafted the paper. All authors contributed to and approved the final draft for publication.

This work was supported by an MRC Population Health Scientist Fellowship to DTR (G0802448). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

None.

The study was approved by the Danish Data inspectorate (Datatilsynet). Danish CF registry data were used, analysed anonymously.

Not commissioned; externally peer reviewed.