Relevant and Redundant Lung Function Parameters in Discriminating Asthma from COPD

Abstract

A relevant set of lung function parameters, derived from spirometry, flow-volume curves, diffusion capacity and bodyplethysmography, to discriminate asthma from COPD was established via logistic regression analysis. All new patients, referred to the outpatient clinic and later defined as asthma or COPD, underwent extensive lung function testing with reversibility testing. Logistic regression was used to calculate the probability to be a COPD or asthma patient. Selection of relevant parameters was done via 1] forward-, 2] backward-, 3] stepwise selection and 4] the best score method. All four methods were supplemented by bootstrapping to obtain a validated selection and estimation of the logistic regression parameters. The area under the ROC curve (mean ± sd) for respectively the forward, backward, stepwise and best score selection method is 0.9348 ± 0.0115, 0.9346 ± 0.0115, 0.9348 ± 0.0115 and 0.9296 ± 0.0121. The TL_CO, V_A and the postdilator MEF₅₀, VC and PEF were selected as the most relevant parameters in discriminating asthma from COPD: they appeared most often as relevant discriminators in 500 bootstrapped samples: TL_CO was present in all bootstrapped samples and V_A, postdilator MEF₅₀, VC and PEF in resp. 70.8%, 46.2%, 42.8% and 36.8%. Bodyplethysmography derived parameters turned out to be of limited value. Diffusion capacity testing and spirometry/flow-volume curve after administration of bronchodilators are the methods of choice when having to chose between asthma or COPD.

Key words:

• Asthma
• COPD
• Diagnosis
• Logistic regression.
• ROC
• curve
• Age.

INTRODUCTION

Nowadays, lung function laboratories are able to generate a wealth of information, such as spirometry, flow-volume curves, diffusion capacity, body plethysmography, etc are widely available and became standard techniques. That wealth of information does not automatically mean that each (new) parameter is a valuable or useful addition. When so many parameters are available, the probability that the same patho-physiological process influences these is conceivable, as such parameters share information and thus are correlated. A high degree of correlation between two parameters means that the second one does not supply much new information and could be skipped. Ideally all parameters measured and available should not, or only weakly, be correlated because such independent parameters deliver the highest quality of information. The remaining parameters can therefore be excluded from analysis or assessment.

As far as we know this aspect of lung function testing has not received much attention in the past. We wanted to examine the relevance of parameters derived from spirometry, flow-volume curves, diffusion capacity and bodyplethysmography to define a parsimonious set of lung function parameters, while loss of information must be minimal. Redundant parameters are defined via logistic regression analysis and because patients with asthma or COPD constitute the bulk of a pulmonologist's daily work, we restrict ourselves to these two entities.

METHODS

Subjects

The subjects included were all patients referred to the outpatient clinic of the pulmonology department of University Medical Centre, Utrecht, the Netherlands (UMCU). Patients reporting attacks of breathlessness and wheeze without cough or sputum production were labelled as asthmatics. Current or former smokers without a history of asthmatic attacks, but with chronic cough with or without sputum production or with dyspnoea or both were labelled as chronic obstructive lung disease. Patients reporting both attacks of breathlessness and wheeze and cough and sputum production were labelled as asthmatic bronchitis. For this study the asthmatic bronchitis and the chronic obstructive lung disease patients were pooled and labelled as COPD [[1]]. History taking was supplemented by physical examinations, elaborate lung function testing, X-thorax, HRCT scans or every other diagnostic test one thought fit to arrive at the correct diagnosis. Other diagnoses were not part of the resulting database.

Lung function measurements

Only tests taken on the same day were used. Total lung capacity and residual volume (TLC, RV) were determined by whole body plethysmography (Erich Jaeger GmbH, Wurzburg, Germany) and spirometry or flow-volume curves via pneumotachography (Materscreen, Erich Jaeger GmbH, Wurzburg, Germany). The V_A, determined by single breath helium dilution, was measured as part of the determination of the TL_CO (Masterscreen, Erich Jaeger GmbH, Wurzburg, Germany). TL_CO was corrected for haemoglobin levels.

Measurement of the bronchodilator response was done on a protocol basis [[2]]. Patients refrained from using short-acting and long-acting bronchodilators 8 or 12 hours prior to testing, respectively. At arrival, they first rested for approximately fifteen minutes after which the baseline lung function was determined. Three consecutive measurements were done and the flow-volume loop with the highest value of the FEV₁ was selected. Subsequently, 400 μ g salbutamol via MDI plus a spacer device was administrated. Fifteen minutes after the administration of the bronchodilator the lung function was determined again in the same way at the baseline. Patients without any bronchodilation do exist. ‘No change’ was defined as changes from 0 to –200 ml FEV₁, because due to random error, the post-bronchodilator FEV₁ can be lower than the pre-bronchodilator value while the airway diameter did not change [[3]]. Larger negative changes were rejected because of the distinct possibility of technical errors.

Parameters

Chosen parameters were

1. the pre-and post-bronchodilator VC, FVC, FEV₁, PEF and MEF_50/25

2. TLC and RV

3. R_0.5, R_in/ex, R_tot and R_eff (R_in/ex is the ratio of inspiratory over expiratory resistance)

4. TL_CO and V_A

5. airtrapping (TLC minus V_A)

All parameters were ln-transformed (most biological parameters are log-normal distributed), the latter, however, means that ratio parameters such as the FEV₁ over VC and T_LCO over V_A are no longer needed or useful in the analysis. After transformation they become a simple linear combination of the FEV₁ and VC (ln FEV₁ over VC = lnFEV₁ − lnVC) and, as logistic regression seeks for linear combinations of the included parameters, inclusion of the FEV₁ over VC would mean including FEV₁ and VC twice. For T_LCO over V_A the same reasoning applies. Age and height were included in the calculations as correction factors.

Statistical methods

The basic statistical method used is logistic regression, which calculates the probability to be a COPD or asthma patient. Selection of relevant or redundant parameters was done via four approaches 1] forward selection, 2] backward selection, 3] stepwise selection and 4] the best score method [[4]]. Forward selection starts with the most significant parameter and keeps on adding parameters until the chi-square statistic does not increase significantly anymore. Backward selection starts with a full set parameters and keeps on removing parameters until the chi-square statistic starts to change significantly. The stepwise selection uses the same procedure as the forward selection, but each time a new parameter is added to the model the method checks whether a previously included one can be removed from the model. The best score method is a computer intensive method which starts with (in this case, 21) sets of only one parameter and for each set the chi-square statistic is calculated. The next step is that all the possible sets of two parameters are formed, for each set again the chi-square statistic is calculated. The difference between the chi-square statistic of the best “two parameter set” and that of the best “one parameter set” must be significant (i.e., delta chi-square ≥ 3.84) for the “two parameter set” to be a better choice. The next step now is that all possible set of three parameters are formed and this process goes on until at last the combination of 21 parameters is formed.

We used these four approaches in order to assess whether the outcome in terms of relevant or redundant parameters is sample-and method-dependent. In order to even further minimise the probability of a sample or method dependent outcome we used bootstrapping [[5], [6]]. Bootstrapping is a resampling technique designed to investigate the stability of the outcome of estimates. Bootstrapping draws a random samples (with replacement) from the total data-base. This procedure is repeated here 500 times, resulting in 500 (bootstrapped) data-sets of 478 observations each, however, some subjects can be drawn more than once in the dataset, whereas others will no be drawn at all. On average 63% of the subjects will be drawn in a single data set, each data set, however, has a different combination of subjects. In each of the 500 data sets the four logistic regression selection procedure, described previously, were repeated. This results in 500 sets of suitable parameters and the more frequent a lung function parameter is present in these relevant parameters sets, the more valuable it is for the discrimination between asthma and COPD. This is assessed as the percentage presence in the 500 bootstrap sets of relevant parameters, 100% presence means that the parameter is always chosen, 50% presence in half the cases. The above-described procedure was repeated for each of the four model selection procedures.

For final model building, we selected the five most frequently emerging parameters, but allowed ourselves to skip one if that one parameter would lead to implementing a different lung function method. So, if the six best ones encompassed five flow-volume curve parameters and only one bodyplethysmograph parameter as the fourth of fifth ranking parameter, we ignored the latter and selected the sixth one. The discriminatory quality of each of the four models was assessed and compared via the area under the ROC curve, which is a curve in which the sensitivity of the discriminating method is plotted against one minus the specificity. The area under this curve is a measure for the discriminatory power of the logistic regression model.

RESULTS

In this study 478 subjects were included, 243 males (89 asthmatics and 154 COPD) and 235 females (156 asthmatics and 79 COPD). The demographics are shown in Table 1. Table 2 shows the AUC's of the most relevant ROC curves. In Table 3, the first 10 most relevant asthma-COPD discriminating lung function parameters are listed. In the 500 bootstrapped forward selection logistic regression analysis, e.g. the V_A appeared 438 times (= 87.6%) as a relevant or significant factor, etc. The first five parameters of each method were subsequently selected as the best discriminators. For the four methods this means that determination of the diffusion capacity and pre-or post-bronchodilator spirometry or flow-volume curve should suffice. Bodyplethysmography derived parameters turned out to be of limited additional value.

Table 1 Demography of subjects in this study

Sex	Disease		Age	FEV1	FEV1 over VC	VCmax	TLCO	VA	TLC	RV
Male	Asthma	Mean	46.7	87.3	89.5	97.6	91.0	94.0	101.9	111.9
		Sd	15.5	18.6	14.3	16.0	19.1	14.1	12.8	35.0
	COPD	Mean	63.7	66.7	75.8	88.2	59.0	87.4	104.8	134.0
		Sd	12.0	19.0	15.9	17.2	20.6	15.7	17.8	40.4
Female	Asthma	mean	42.3	90.1	95.0	103.2	76.4	93.2	103.7	111.8
		Sd	16.9	17.7	13.6	14.7	13.7	12.0	12.0	25.7
	COPD	Mean	58.8	69.6	79.2	96.9	52.4	89.1	109.9	141.2
		Sd	11.8	17.4	14.5	17.9	18.1	14.6	16.8	37.9

The lung function data were expressed as percent of the predicted value [[2]].

Table 2 Individual areas under the ROC curve for the most relevant parameters listed in Table 3

	AUC ROC	sd
TLco	0.8328	0.4226
VA	0.6169	0.5747
Post-bronchodilator MEF25	0.8262	0.4226
Post-bronchodilator VC	0.6337	0.5679
Post-bronchodilator PEF	0.7141	0.5229
Pre-bronchodilator MEF50	0.8443	0.4047
Pre-bronchodilator MEF25	0.8443	0.4092

Table 3 The presence of lung function parameters in the four selection methods as significant asthma-COPD discriminators in 500 bootstrapped logistic regression analyses

Forward selection	%	Backward selection	%	Stepwise selection	%	Best score	%
method	presence	method	presence	method	presence	method	presence
TLCO	100.0	TLCO	100.0	TLCO	100.0	TLCO	100.0
VA	70.8	VA	83.6	VA	69.4	Pre-bd MEF25	78.0
Post-bd MEF50	46.2	Post-bd VC	82.2	Post-bd MEF50	42.6	Pre-bd MEF50	73.2
Post-bd VC	41.8	Post-bd MEF50	65.8	Post-bd VC	41.2	VA	69.0
Post-bd PEF	36.8	Pre-bd PEF	51.8	Post-bd PEF	32.8	Post-bd MEF50	67.8
TLCbb	34.6	pre-bd VC	45.2	Pre-bd PEF	29.8	Pre-bd PEF	55.4
Pre-bd PEF	31.0	R0.5	35.4	Post-bd FEV1	27.8	Post-bd VC	54.2
Post-bd FEV1	30.8	Rinex	34.2	Post-bd MEF50	27.0	Post-bd MEF25	43.4
Post-bd MEF25	30.0	Post-bd FVC	33.8	TLCbb	25.2	Pre-bd FVC	40.4
Rinex	24.4	Post-bd FEV1	33.0	Rinex	21.4	Post-bd FVC	34.2

The presence is reported as the percentage a parameter appeared as a significant discriminator. (post-bd stands for post-bronchodilation, pre-db stands for pre-bronchodilation).

The next step compares the discriminatory power of the outcome of these four logistic regression methods. The area under the ROC curve (AUC ROC; mean ± sd) for respectively the forward, backward, stepwise and best score method is 0.9339 ± 0.0111, 0.9342 ± 0.0110, 0.9339 ± 0.0111 and 0.9287 ± 0.0116 (the differences between these values were not significant[7]) and for sake of comparison we list in Table 2 the AUC ROC for the individual lung function parameters.

Having found that the AUC ROC of the parameter set selected via the best score method does not differ from that of the other three methods, one could decide that determination of the diffusion capacity and listed post-bronchodilator spirometry or flow-volume curve parameters suffice. The full logistic regression equations to calculate the probability to diagnose a patient as asthmatic are listed in Appendix 1

DISCUSSION

This study was done in patients referred by general practitioners to the pulmonologist and which means that the patients in the database are selected to a degree, therefore it is conceivable that they were referred because their disease status required so and one may expect that these patients constituted a more difficult patient to treat by a general practitioner. Extrapolation of this outcome to other groups of asthmatics and COPD patients, i.e., within a general practitioner environment may be hazardous.

The fact that the patients were referred to a university hospital does not mean that a second type of selection bias is present as our hospital does not function as an exclusive third-line hospital for specialised cases only. The bulk of patients referred are “run-off-the mill” patients directly referred by general practitioners. Extrapolation of these results to outpatient clinic of non-university hospitals should be possible.

The diagnosis of asthma or COPD does, of course, plays an important role in this study, because that distinction forms the basis of the logistic regression analysis. We like to emphasize that the clinical diagnosis was made by the pulmonologists, and was based on an array of methods (X-thorax and HRCT-scans, thorough physical examinations and interviews, smoking behavior, allergy testing, etc.). It is realized that despite this extensive test battery, mistakes are possible since there is no accepted, easy to use, gold standard for the diagnosis of asthma. All studies, where asthma is contrasted versus COPD, did and will in the future suffer from that diagnostic problem [[8], [9]]. The size of this database offers some degree of protection against the influence of incorrect diagnosis as we can safely assume that these form a minority and hence their influence in this large database is proportionally. Moreover, if a large number of diagnostic mistakes were present, many COPD subjects would incorrectly be labeled as asthmatics and visa versa. The group distinction would be blurred because the groups grow more alike; however, the demographics in Table 1 show otherwise.

Two further arguments center on the statistical approach to this so-called imperfect standard bias, the general result is a lowered sensitivity and specificity of new tests [[7]]. A low sensitivity and specificity translates in a low AUC ROC closer to 0.5. This has the same diagnostic value as tossing a coin. The fact that we here report AUC ROC of about 0.928 must mean that misclassification due to imperfect standard bias was minimized. To add to this, the doctor-based diagnoses asthma or COPD behave in the same way as any other (chemical, pathological or radiological) test, since the errors in diagnosis are reflected in a lowered sensitivity and specificity. This problem is called the imperfect standard bias. When the sensitivity and specificity of the imperfect standard are known, a correction of the new test sensitivity and specificity is possible [[7]]. The correction is a multiplication by a factor of the sensitivity and specificity of the new test. Here, the imperfect standard sensitivity and specificity are of course not known. We however compared the four logistic regression approaches within the same database with the same imperfect standard bias for all approaches, so the correction factor will be exactly the same for all approaches and the resulting ranking of the relevant parameters cannot change. The differences we found in discriminatory power are hence valid despite diagnostic error being present.

The choice of parameters was, of course, straightforward as we included standard lung function parameters and methods. As said in the methods section inclusion of ratio parameters like FEV₁ over VC and T_LCO over V_A is not required from a mathematical point of view. From a clinical point of view there are also arguments to exclude these parameters because they serve as guides in the determination of a type of disease. A proportionally small FEV₁ over VC denotes obstructive disease and a high ratio restrictive disease; the severity of both types of diseases is charted via the FEV₁ sec. In obstructive disease a low FEV₁ will also mean a low FEV₁ over VC and so these two parameters share information and one of the two is superfluous. In restrictive disease the severity can only be assessed via the FEV₁: the FEV₁ over VC can not rise above unity. In the list of parameters the PC_20,histamine does not occur. We found that, due to its obstructive character, many pulmonologists use the PC₂₀ only when they are almost sure that asthma is present. The test is hence not applied to all subjects and this selection bias makes inclusion of the PC₂₀ in the model undesirable. Moreover, according to García-Río the positive predictive value can be as low as 39%, depending on the pre-test probability for a patient to be an asthmatic, making it a less suitable diagnostic tool in our situation [[10]]. Logistic regression was used as the principal statistical method to select relevant lung function parameters. Model building or selection of relevant parameters in logistic regression is a complicated and sometimes hazardous task, extrapolation is frequently jeopardized. To ensure extrapolation, we took care to obtain a sufficiently large database. In general a ratio of 1 out of 20 (one parameter included in the model needs 20 subjects) is advocated and we had a ratio of 1 out of 40.

Mathematical selection procedures (forward, backward, stepwise, or best score method) are known to render different outcomes, sometimes hard to reconcile [[11]]. Some researchers even reject these mathematical selection procedures and turn to pathophysiology for an a-priori selection of parameters, which can be even a more hazardous approach when pathophysiology is only partially understood. Differences in outcome are due to the way these procedures select their parameters, slight differences in e.g., not yet selected parameter significance levels can easily lead to different choices. One different choice early in the process will affect the subsequent choices heavily. However, this disadvantage of different outcomes can turn into an advantage when there is agreement.

When comparable sets are found, an influence of the selection procedure must be minimal. To validate selections, it is often advised to split databases into a learning and validation part, which is difficult for smaller databases. Bootstrapping can be considered as an extension of this splitting approach. The procedure draws a random sample from the database with replacement, (i.e. the subject is ‘tossed back’ into the database) and performs all calculations on that sample and the outcome is stored. In a next cycle, a new sample is drawn and the outcome is again stored, which procedure is repeated over and over. When much variability between all outcomes is present, a conclusion of instable and “not so useful” parameters is reached. In our way of working, ‘not so useful’ parameters would not appear often and their percentage presence would be low. Direct estimation of the model parameters in a logistic regression can produce biased estimators as part of the noise may be modelled as well. To overcome this problem cross-validation, bootstrapping or parameter shrinkage can be used, within each option a number of different techniques can be used. We chose parameter shrinkage using the formula of van Houwelingen and Le Cessie [[12]].

The best validation of the outcome of a statistical approach, however, is a pathophysiological sound explanation. In this study the T_LCO and V_A proved to be relevant asthma-COPD discriminators and one must acknowledge that damage of the alveolar membrane and the resulting low T_LCO is not an entity supposed to be present with asthma and is prominent with COPD [[13]]. Here pathophysiology and logistic regression coincide. The alveolar volume (V_A), determined via single breath helium dilution, is very sensitive to ventilation inhomogeneities, better said influenced by the presence of ill ventilated parts of the lungs. The loss of elasticity and destruction of tissue makes it very probable that ventilation inhomogeneities are a prominent COPD phenomenon.

The fact that only post-bronchodilator flow-volume parameters did emerge as useful discriminators may come as a surprise. One must realise that, because asthma is advocated as a reversible disease, high asthma post-bronchodilator functions are expected and in COPD this is less probable and so post-bronchodilator function behaviour can function as a discriminator. The pre-bronchodilator function will differ less by definition since only after bronchodilator administration the asthma-COPD differences get clearer. For assessing that phenomenon one could turn to the difference between pre-and post-bronchodilator function but equally well to post-bronchodilator function sec.

Bodyplethysmography derived TLC, RV and resistance measurements did not emerge as relevant discriminators. In general terms this can be caused by a lack of difference between the groups or high inter-or intra-individual variability. From Table 1, one can conclude that the RV differences between asthma and COPD are quite large on the average, but the standard deviations are too. The strong differences in RV are consistent with the pathophysiology, but the strong variability reduces the discriminatory power due to a considerable overlap. The TLC differences are much smaller as an increase in TLC in COPD is very common, but large increases not and also here the overlap of values will be strong. The fact that resistance measures do not constitute a useful diagnostic will not surprise many. This is most likely because the variability in this parameter is known to be high. The difference in inspiratory and expiratory resistance (R_inex) ranked rather high and such is not illogical. In COPD the expiratory resistance frequently is high due to the collapse of diseased tissue, where in asthma collapse should not occur. In theory this would make the R_inex a suitable diagnostic, but the variability exerts its negative effects.

The first consequence of the outcome of this study is that one, when faced with the question asthma or COPD, rather straightforward function testing will suffice, since diffusion capacity testing and spirometry or flow-volume curve will do. This will have a positive bearing on workload and costs. Secondly and may be as important is the fact that, because post-and not pre-bronchodilator function is a valuable discriminator, patients could be spared the bronchodilator-free period. For many this is a less comfortable situation, especially in the case of long-acting bronchodilators. Patients should be able to use their regular bronchodilators at home, while at the function laboratory one could opt for a next administration to ensure full bronchodilation and to deal with those who do use bronchodilators incorrectly and experience a suboptimal effect.

The fact that diffusion capacity takes such a prominent role in the asthma-COPD discrimination may lead to a change in the attitude towards guidelines. Many now advocate the GOLD criteria as the standard approach to COPD diagnosis, however, only incorporating spirometry can and will lead to a higher number of diagnostic mistakes than necessary. Adding diffusion capacity to the diagnostic tests would certainly improve diagnostic quality. At the same time we can confirm that the emphasis of the GOLD approach on post-bronchodilator lung function is justified [[14]].

We could conclude that discrimination between asthma and COPD, based on lung function testing, is served well when a combination of only the T_LCO, V_A and post-bronchodilator VC, PEF and MEF₅₀ are considered. Other parameters do not contribute much.

LIST OF ABBREVIATIONS

HRCT:	=	High Resolution Computer Tomography
TLC:	=	Total Lung Capacity
RV:	=	Residual Volume
TLCO:	=	Diffusion Capacity for Carbon Monoxide
FEV1:	=	Forced Expiratory Volume in one second
MDI:	=	Metered Dose Inhaler
VC:	=	Vital Capacity
FVC:	=	Forced Vital Capacity
PEF:	=	Peak Expiratory Flow
MEF50/25:	=	Maximum Expiratory Flow at 50 or 25 % of vital capacity
TLC:	=	Total Lung Capacity
Rin/ex,:	=	Ratio inspiratory over expiratory resistance
Rtot:	=	Total Resistance
Reff:	=	Effective Resistance
VA:	=	Alveolar Volume
ROC:	=	Receiver-Operator Curve
AUC:	=	Area Under the Curve

APPENDIX

Combining the best five parameters of each model selection procedure gives the results shown in Table 3. T_LCO, V_A, and post-bronchodilator MEF₅₀ are present in all four selection methods within the five highest ranking parameters. The post-bronchodilator VC is not ranked high in the “best score” method and post-bronchodilator PEF is not so in backward and “best score” method.

The final model choice of lung function parameters are the highest ranking parameters of the forward selection method. This choice is made both the highest scores with respect to the occurrence in the bootstrapping approach and on the fact that these five are all post-bronchodilator spirometry values. This means that a patient does not need to refrain from his or her bronchodilator treatment. Other approaches including pre-bronchodilator values may show a slightly higher discriminatory power, but we feel that that gain in information does not outweigh the patients discomfort. To calculate the probability to be an asthma patient, one should use the following formulaewhere for malesand for females

In the above equations, the measured lung function values should be used and not a “percentage of predicted.”

These parameter estimates were obtained from the logistic regression calculation on the data and shrunken, using the formula Model χ² − k/Model χ² with k the number of parameters in the model [[12]].

See calculation example in Table A.1.

Table A. 1 Calculation examples: two patients

	Units	A Measured	B = Ln(A) Ln(measured)	C Regression factor	D = B*C Result
Female diagnosed with asthma
TLCO	mmol/min/kPa	7.8	2.0541	3.56	7.313
Alveolar volume	L	4.9	1.5892	−5.87	−9.329
MEF50 post-dilator	L/sec	6.8	1.9169	2.02	3.872
VCmax post-dilator	L	4.2	1.4351	5.00	7.176
PEF post-dilator	L/sec	10.17	2.3191	−2.56	−5.937
Intercept				1.29	1.29
Sum of all terms (= t)					4.385
Predicted probability for asthma = (exp(t)/(1 + exp(t)))					0.988
Male diagnosed with COPD
TLCO	mmol/min/kPa	4.4	1.4816	5.45	8.075
Alveolar volume	L	6.6	1.8871	−8.14	−15.361
MEF50 post-dilator	L/sec	0.8	−0.2201	0.64	−0.141
VCmax post-dilator	L	4.4	1.4816	2.87	4.252
PEF post-dilator	L/sec	5.18	1.6448	1.31	8.520
Intercept				−1.23	−1.23
Sum of all terms (= t)					−2.250
Predicted probability for asthma = (exp(t)/(1 + exp(t)))					0.095