USE OF FACTOR ANALYSIS TO CONSOLIDATE MULTIPLE OUTCOME MEASURES IN CHRONIC OBSTRUCTIVE PULMONARY DISEASE

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1 J ClinEpidemiolVol.44,No. 6,pp , /91$ Printedin GreatBritain.All rightsreserved Copyright 1991PergamonPresspie USE OF FACTOR ANALYSIS TO CONSOLIDATE MULTIPLE OUTCOME MEASURES IN CHRONIC OBSTRUCTIVE PULMONARY DISEASE ANDREW L. RIES, l* ROBERT M. KAPLAN 2and ELAINE BLUMBERG1'2 _Division of Pulmonary and Critical Care Medicine, Department of Medicine and 2Division of Health Care Sciences, Department of Community and Family Medicine, University of California, San Diego, CA 92103, U.S.A. (Received in revised form 9 November 1990) Abstract--Multiple outcome measures are often used in clinical research and practice. However, the use of multiple measures inflates the probability of a type I error. In this paper, we used factor analysis techniques to reduce multiple outcome measures to a lesser number of orthogonal dimensions. The data were obtained from 119 patients with chronic obstructive pulmonary disease. Each patient had measurements made of 28 variables, including multiple parameters of pulmonary function, exercise tolerance and gas exchange. Factor analysis using a maximum likelihood iterative solution was performed. The factors were then rotated to a varimax solution. The analysis yielded four meaningful factors: exercise tolerance, disease severity, lung volumes and flow rates. Exercise tolerance and disease severity were the most important factors accounting, respectively, for 44 and 13% of the common variance. For further analyses, these composite factors could be used or a representative clinical measure from each factor might be chosen. We conclude that many physiologic measures provide highly correlated information about chronic obstructive pulmonary disease patients. Factor analysis may help reduce these measures into a smaller number of reliable composites. Factor analysis Chronic obstructive pulmonary disease Pulmonary function tests Exercise tests Pulmonary rehabilitation INTRODUCTION In clinical research, multiple outcome measures are also used commonly. However, In the practice of medicine, clinicians frequently the use of multiple measures and multiple statuse multiple pieces of information in evaluating istical tests in evaluating the effects of a clinical individual patients. In many instances, measure- trial increases the probability of a type I error ments are made of several related variables (detecting spurious significant differences). In a that characterize different aspects of a patient's study with a large number of variables or tasks, disease process. For instance, in pulmonary it is often desirable to reduce this large amount medicine, multiple related parameters may be of information into more manageable commeasured in pulmonary function testing to ponents. The statistical task in correlation and characterize changes in airway and parenchymal linear regression involving two variables is to lung function related to lung disease. find the best fitting line through the points created by a 2-D scatter diagram. As more *All correspondence should be addressed to: Andrew L. Ries, M.D. UCSD Medical Center H772-E, 225 variables are added in multivariate analysis, the Dickinson Street, San Diego, CA 92103, USA. number of dimensions increases, 497

2 498 ANDREWL. RIE$et al. Factor analysis is used to study the inter- Factor analysis relationship among a set of variables without Twenty-eight variables that are commonly reference to a specific criterion. Factor analysis reported from these standard tests of pulmonary may be considered a data reduction technique, function, exercise performance, and arterial In factor analysis a matrix of correlations be- blood gases were selected to be included in the tween variables is created. Then, data are trans- factor analysis. The initial step in the factor formed into linear combinations of variables analysis was the creation of a correlation matrix that share common variance between measures, of all 28 variables (with unit values on the In this paper, we describe the use of factor diagonal). Then, an iterative maximum likelianalysis to reduce multiple outcome measures to hood procedure was used to obtain a residuala fewer number of related variables in a clinical ized matrix with only common variance between trial of pulmonary rehabilitation for patients variables. with chronic obstructive pulmonary disease The residualized matrix was then subjected to (COPD). This technique may also be useful in factor analysis using a maximum likelihood clinical research involving other diseases, algorithm available in the BMDP package (routine BMPD-4M). Factors are combinations of METHOD variables; the goal in creating them is to simplify " Patients and measurements or reduce a complex array of information. There may be as many factors extracted as there are The data used in this analysis include baseline variables. However, the factors are created measurements of pulmonary function, exercise using mathematical rules that make each one performance, and gas exchange in 119 patients independent or uncorrelated with all other with COPD. All of the patients were participat- factors. Typically, only a few factors that ing in a clinical trial of pulmonary rehabilita- account for large proportions of the common tion. The sample included 32 females and 87 variance are extracted for further study. Once males with stable obstructive lung disease, the linear combinations or factors were found, All patients underwent pulmonary function the correlations between the original items and tests including spirometry, lung volumes and the factors were obtained. These correlations airway resistance (RAw) by body plethysmogra- are called factor loadings. By examining which phy, single-breath diffusing capacity (DLCO), variables loaded highly on each factor, the maximum voluntary ventilation, and maximum factors were then interpreted and named [5]. inspiratory and expiratory pressures. Spirome- Factor analysis is a complex and technical try, lung volumes, and RAWtests were repeated method, and there are many options the user after bronchodilation with two puffs or inhaled must consider. For example, investigators fremetaproterenol. Testing and quality-control quently use methods to help get a clearer picture procedures followed standard and rec- of the meaning of components by rotating the ommended methods [1, 2]. Normal values used axes in the space created by the factors. These were those of Morris and coworkers for spiro- transformations have been labeled "rotation metric data [3]. methods." In this application, we used the : On a separate day, each patient performed an varimax rotation method. incremental, symptom-limited exercise test to the maximal tolerablelevel on a treadmill. A RESULTS radial arterial catheter was inserted percutaneously for arterial blood gas measurements at Table 1 lists the means, standard deviations rest and during exercise. Expired gases were and coefficients of variation for the 28 variables analyzed for measurement of minute ventilation included in the factor analysis. One index of the (VE), oxygen uptake (VO2), carbon dioxide extent to which there was overlap between elimination (VCO2), and dead space/tidal variables is the squared multiple correlation of volume ratio (VD/VT). Electrocardiogram was each variable with all other variables. A variable monitored during the test to measure heart rate with a high squared multiple correlation is one and to detect significant arrhythmias or is- that shares repetitive information with many chemic changes. Ratings of perceived symptoms other variables. Table 2 summarizes the squared of breathlessness and muscle fatigue were multiple correlations for each variable. As the obtained at maximum exercise using scales table suggests, some variables share high permodified from Borg [4]. centages of their variation with other variables.

3 Factor Analysis in COPD 499 Table I. Means, standard deviations and coefficients of variation Standard Coefficient Variable Mean deviation of variation 1.HT(cm) Age(years) FEVI(1) FEVI/FVC (%) FEV 1(% predicted) _ FEF2s_75o/o (% predicted) PIFR (l/s) Raw (cmh_o/1/sec) DLCO (ml/min/mmhg) MIP(cmH20) RV(1) FRC (I) TLC(1) RV/TLC FEFso (1/sec) P,O 2 rest (mmhg) METSmaximum exercise PaO2 exercise (mmhg) PaCO2 exercise (mmhg) VEmax (1/min) VO2 max (1/min) VOzmax (ml/kg/min) Vo/Vx exercise (%) HRmax (beats/min) MVV (l/min) 26PF PB FEV_ postbd-fev_prebd Definitions: HT=height; FEV_ =forced expiratory volume in 1 sec; FVC = forced vital capacity; FEF25_750/o = forced expiratory flow rate over midportion of FVC; PIFR = peak inspiratory flow rate; RAw=airway resistance; DLCO=diffusing capacity (single-breath); MIP = maximal inspiratory pressure; RV = residual volume; FRC = functional residual capacity; TLC = total lung capacity; FEFs0 = forced expiratory flow rate at 50% of FVC; PaO2=partial pressure of O2 in arterial blood; METS = metabolic equivalent at maximum exercise; (I MET=oxygen consumption of 3.5ml/kg/min); P_CO2=partial pressure of COs in arterial blood; VEmax = minute ventilation (expired) at maximum exercise; VO 2max = oxygen uptake at maximum exercise; VD/Vr = dead space/tidal volume ratio at maximum exercise; HR max = heart rate at maximum exercise; MVV = maximum voluntary ventilation; PF = perceived fatigue at maximum exercise; PB = perceived breathlessness at maximum exercise; PostBD = postbronchodilator; PreBD = pre-bronchodilator. FEV1, residual volume, and total each accounting for approximately 5% of the almost entirely represented by variance. the data set. Conversely, Table 3 provides a summary of the varimax (PF) and perceived breathless- rotation of the factor analysis. Factor 1 appears maximum exercise are not as well to be an exercise and gas exchange factor. variables. Variables with high loadings on this factor provide an index of the pro- included VO2 max (ml/kg/min and l/min), maxivariance explained by successive mum metabolic equivalents of exercise (METS), of thumb, eigenvalues greater maximum minute ventilation, maximum heart studied further. Factor 1 had an rate, DLCO, PaO2 at maximum exercise, and and explained about 44% of VD/VT at maximum exercise. Thus, the factor variation in the entire data set. conceptually integrates maximum exercise tolereigenvalue of 3.66 (accounting ance measurements with parameters of pulmoncommon variance) while ary gas exchange. eigenvalue of 1.99 (or about The second factor appears to be related to the common variance). The fourth and severity of obstructive lung disease. The factor eigenvalues of 1.43 and 1.37, includes forced expiratory volume in one second

4 500 ANDREWL. RIESet al. Table2. of each Squaredmultiplecorrelations(SMC) variable with all other variables patients with multiple interrelated outcome measures used to characterize the disease pro- Item Variable SMC cess. As expected, there were high intercorrela- 11 RV (1) 0.99 tions between several measures of pulmonary 13 3 TLC(1) FEV_(1) function, exercise performance, and gas ex- 5 FEV_ (% predicted) 0.98 change for these patients. The use of data 12 FRC (1) 0.98 reduction procedures such as factor analysis 14 6 FEF25_75O/o RV/TLC (% predicted) 0.97 may have substantial benefits in clinical studies 15 FEFs0(l/see) 0.97 of this sort. 21 VO2max (1/min) 0.97 In many cases, measures taken in clinical 20 4 FEVJFVC(%) VEmax(l/min) studies overlap greatly. Examination of the 22 VO2max (ml/kg/min) 0.93 squared multiple correlations (Table 2) suggests 25 MVV(l/rain) 0.89 that there is considerable redundancy in these METS PaO2exercise(mmHg) maximumexercise 0.88 physiological measurements typical for pulmon- 23 VD/VTexercise(%) 0.88 ary patients. One of the problems in analyzing 1 HT (cm) 0.87 data from clinical studies of this sort is that 9 DLCO (ml/min/mmhg) PaC02 exercise(mmhg) 0.80 there are often many possible independent and _' 8 RAW(cmH20/1/sec) 0.70 dependent measures to select in evaluating out- 16 PaO2rest (mmhg) 0.70 come. If an investigator assumes these multiple 2 Age(years) MIP(cmH20) 0.63 outcome measures are independent, downward 7 PIFR (1/see) 0.60 adjustments of alpha levels are required. Ulti- 28 FEV 1 postbd-fevi prebd 0.60 mately, this may result in a very stringent test of HRmax PB (beats/min) the null hypothesis. As a result, the investigator 26 PF 0.40 may be required to bias the investigation See Table 1 for definitionsof variables, against the experimental effect. On the other hand, arbitrarily selecting single measures for analysis may mask important relationships. (FEVI), maximum voluntary ventilation Factor analysis can produce composite (MVV), airway resistance (RAw), RV/TLC measures that simplify this problem by taking ratio, and PaCO2 at maximum exercise. This into consideration the redundancy in a data set. factor conceptually integrates expiratory flow Factor anlaysis may also contribute insights obstruction, lung volume hyperinflation and into possible interrelationships among variventilatory reserve, ables. Certain variables measured in clinical The third factor appears related to lung vol- settings are known to be highly correlated. For ume and includes total lung capacity, functional example, maximum voluntary ventilation residual capacity, residual volume and height. A (MVV) is highly correlated with FEVI (r = 0.90) fourth factor may represent expiratory flow andis often approximated as a multiple of FEV_ rates and includes FEFs0, FEF25_750/0% pre- (e.g. MVV=35 FEV1). On the other hand, dicted, FEV_/FVC ratio and FEVI % predicted, certain intercorrelations between variables may The fifth factor (not shown in the table) includes not be so obvious. For instance, in this study, only two variables: age and maximal inspiratory Factor 1, the "exercise" factor, appears to inpressure, clude variables of gas exchange (DLCO, PaO2 One product of a factor analysis is a vector of and VD/liT) in addition to the expected indices factor score transformation coefficients. These of maximum exercise tolerance for these coefficients allow the creation of new composite patients ( VO2 max, METSmax, HRmax, VE. variables that represent the factors. Table 4 max). This suggests that exercise performance summarizes these transformations. The table in these patients with COPD is related more to uses standardized coefficients that are applied to indices of gas exchange than to measures of standardized (or Z) scores for the variables, ventilatory lung function. Therefore, significant portions of the variation in exercise perform- DISCUSSION ance in these patients were not explained by the more standard indices of pulmonary function. The results of this analysis demonstrate that Factor 2, the "obstructive lung disease" factor analysis can be used successfully as a data factor, also illustrates an interesting potential reduction technique in a clinical study of COPD advantage of this type of analysis. It includes

5 FactorAnalysis incopd 501 Table 3. Sorted rotated factor loadings (pattern) Factor 1 Factor 2 Factor 3 Factor 4 Factor l--exercise-gas exchange VO2 max (ml/kg/min) METS maximum exercise) VO_max (1/min) VD/VT exercise (%) DLCO (ml/min/mmhg) VEmax (l/min) HRmax (beats/min) PaO2 exercise (mmhg) Factor 2--Disease severity RAw (cmh2o/l/see) RV/TLC FEVI 0) _ MVV (l/rain) PaCO2 exercise (mmhg) Factor 3--Lung volume TLC(1) FRC (1) RV(1) HT(cm) I Factor 4--Expiratory flow rates FEFs0 (1/see) FEF2s_75,/o(% predicted) FEVzFVC(%) FEV_(% predicted) Other factors Age(years) MIP(cmH20) PIFR (l/s) P_O2rest (mrnhg) PF PB FEVl postbd-feviprebd See Table 1 for definitions of variables. variables which appear to characterize different In using the results of the factor analysis, physiological aspects of disease severity for ob- investigators might have two options. First, the structive lung disease: reduction in expiratory new derived composite variables might be used flow (FEV_), airway caliber (RAw), lung volume directly in the analysis. However, preliminary hyperinflation (RV/TLC ratio), ventilatory analyses from this study suggest that the comreserve (MVV), and CO2 retention with exercise posites perform no better than selected clinical (exercise PaCO2). Thus, this factor may be measures as correlates of health outcomes. In useful as a proxy for general severity of obstruc- addition, use of a composite variable has the tive lung disease incorporating a bit of each distinct disadvantage that the derived variable, of these different, but related, aspects of the although made up of conceptually related corndisease, ponents, does not result in a quantitative Insight may also be gained from variables measure with clinical or intrinsic meaning. that do not appear to be significantly related An alternative approach would be to utilize to others in the analysis. In this study, the the derived factors to select individual variables ratings of perceived symptoms (breathlessness which might represent most closely the concepand fatigue) were not well clustered with tual meaning of the composite variable. Since other variables. Dyspnea on exertion is a there is a high level of intercorrelations within hallmark symptom for patients with chronic factors, selection of one variable from each obstructive pulmonary disease and the major factor might provide a statistically based and symptom limiting exercise tolerance. How- rational means of reducing the number of cliniever, dyspnea is complex and, although cal measures. This selection might be based on related to lung function, is also a subjective factor loading (high correlation with composite symptom unrelated to many other variables redundancy with other measures--table 2) measured, and establishedclinicalvalue of the measure.

6 502 ANDREW L. Rms et al. Utilizing this approach for the factor analysis in measurements of outcome. Some of these correthis study, we selected the following single vari- lations for Factors 1 and 2 are presented in ables as the best (statistically valid) represen- Table 5 for changes in exercise performance in tation of each of the derived factors: VO2max the rehabilitation group immediately after com- (ml/kg/min) for Factor 1 (exercise tolerance/gas pleting the treatment program. These data indiexchange); FEVI for Factor 2 (disease severity); cate that the correlations for both Factor 1 and TLC for Factor 3 (lung volume); and FEF25_75% VO2max, its primary component, with these (% predicted) for Factor 4 (expiratory flow), outcome measurements are similar. Although The other measures provide largely redundant Factor I does slightly better in predicting change information for these patients with COPD. The in exercise endurance, the correlation is not advantage of using representative measures statistically significant. Likewise, when Factor 2 from each factor is that the total number of and FEVi, its primary component, are used to measures is reduced, When several measures predict changes in other variables the differences had equivalent high loadings, we selected the are similar but not identical. However, correone believed to be the most meaningful clini- lations at baseline between these variables (also, cally, presentedin Table 5) show that the factorsdo One possible concern in using the derived contain information independent of the selected factors for subsequent analysis is the question of individual variables. As expected, Factors 1 and whether the factors do, in fact accurately rep- 2 do not correlate with each other (as with resent the conceptual meaning attached to them. Factors 3 and 4). Nevertheless, the single In an attempt to evaluate the validity of the selected variables (VOzmax and FEV1)do corfactors derived in this study, we correlated each relate with the "other" factor, indicating that factor, along with its primary component when taken alone, these variables do contain a variable, with selected important preliminary certain amount of redundant information which Table 4. Standardized factor score coefficients for transformations of Z units Factor 1 Factor 2 Factor 3 Factor 4 Factor l--exercise-gas exchange 22 VO 2 max (ml/kg/min) METS maximum exercise VO2 max (l/min) Vo/V x exercise (%) DLCO (ml/min/mmhg) VE max (l/min) HRmax (beats/min) PaO2 exercise (mmhg) Factor 2--Disease severity 8 RAW (cmh20/1/sec) RV/TLC FEVt (1) I MVV (l/min) PaCO 2 exercise (mmhg) Factor 3--Lung volume 13 TLC(1) FRC (1) RV (1) HT(cm) Factor 4--Expiratory.[tow rates 15 FEFs0 (1/sec) FEF25_75o/0(% predicted) FEVI/FVC (%) FEV1(% predicted) Other factors 2 Age(years) MIP (cmh20) PIFR (l/sec) PaO2 rest (mmhg) PF PB FEV I postbd-fev t prebd *These coefficients are for the standardized variables, mean zero and standard deviation one. See Table 1 for definitions of variables.

7 Factor Analysis in COPD 503 Table 5. Correlations with selected outcome measurements VO2max FEV l Factor 1 (ml/kg/min) Factor 2 (1) Change at 2 months: rehabilitation group only (n = 49) METS maximum exercise VO 2max (ml/kg/min) Treadmill Endurance (min) Baseline: all subjects (n = 112) Factor VO 2 max (ml/kg/min) See Table 1 for definitions of variables. is eliminated in the factor analysis. As used here, comes. The major disadvantage of this apfactor analysis might be used to identify which proach is that it tranforms variables that measures to select for study from among many are intuitively meaningful to the clinician into alternatives. Ultimately, whether these factors multivariate composites. The multivariate do represent the conceptual labels indicated in composites may not give specific diagnostic this analysis may depend upon important information. longer-term associations with morbidity and In summary, we conclude that factor analysis mortality, is a usefulstatistical tool to reduce the number There have been relatively few applications of of multiple interrelated measures in evaluating multivariate statistical procedures in the assess- outcome in clinical studies such as this one in ment of pulmonary disease. Kanner el al. [6] patients with COPD. used multivariate cluster analysis to identify patient subgroups in the chronic obstructive pulmonary disease population that were charac- REFERENCES terized by the alphal-antitrypsin phenotype. 1 American Thoracic Society, ATS statement--snow- Spinaci and colleagues [7] also used cluster bird workshop on standardization of spirometry.am Rev Resp Dis 1979; 119: analysis to stratify chronic lung disease patients 2. Clausen JL, Zarins LP, Eds. Pulmonary Function into homogeneous subgroups for further Testing Guidelines and Controversies. New York: studies. However, most reports consider mul- Academic Press; tiple pulmonary function measures as though 3. dards MorrisforJF, healthy Koskinonsmoking A, Johnson adults. LC. Spirometric Am Rev Respstan- Dis they were independent of one another. 1979; 103: The approach discussed in this study con- 4. Borg tion. GAV. Psychophysical Med Sci Sports Exert bases of perceived 1982; 14: exer- siders clustering of outcome variables rather 5. Harman HH. Modern Factor Analysis, 2rid edn. than clustering of patients. This methodology Chicago: University of Chicago Press; may yield reliable composite variables that 6. Kanner RE, Klauber MR, Watanabe S, Renzetti AD, Bigler A. Pathologic patterns of chronic obstructive can be considered for prospective follow-up, pulmonary disease in patients with normal and deft- The advantage of this approach is that it cient levels of alpha_ antitrypsin. Am JMed 1973; 54: reduces the number of variables and, there Spinaci S, Bugiani M, Arossa W, Bucca C, Rolla G. fore, decreases the probability of type I errors A multivariate analysis of the risk in chronic obstrucassociated with the comparison of multiple out- tive lung disease. J Chron Dis 1985; 5: