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Factor analysis of the interrelationships between clinical variables in horses with colic
Preventive Veterinary Medicine 48 (2001) 201±214
Factor analysis of the interrelationships between clinical variables in horses with colic M.B. Thoefnera,*, A.K. Ersbùllb, A.L. Jensenc, M. Hesselholta a
Department of Large Animal Surgery, University of Copenhagen, BuÈlowsvej 17, DK-1870 Frederiksberg C, Denmark b Department of Animal Science and Animal Health, University of Copenhagen, BuÈlowsvej 17, DK-1870 Frederiksberg C, Denmark c Central Laboratory, Royal Veterinary and Agricultural University of Copenhagen, BuÈlowsvej 17, DK-1870 Frederiksberg C, Denmark Received 7 September 1999; accepted 26 October 2000
Abstract A prospective survey of horses with colic referred to the Large Animal Hospital at the Royal Veterinary and Agricultural University of Copenhagen, Denmark, was undertaken between August 1994 and December 1997. The interrelationships between 17 clinical variables were analysed using factor analysis. Factor analysis uncovers the structure of the variability in data and therefore detects multicollinearity. A total of 528 horses were admitted in the study period. Of these, 16 were excluded from the analysis as a result of miscellaneous conditions. Only 205 horses had observations for all 17 variables. Because no major change occurred in the main diagnostic categories, this population was considered as a representative subset. Factor analysis confirmed the clinical impression of correlation between variables, but the multicollinearity turned out not to be strong. Four factors were extracted, and these accounted for 51% of the total variance. The retained factors were interpreted by integrating previously reported clinical research. The first factor, which was interpreted as endotoxaemia, had high loadings on capillary refill time, mucous-membrane colour, degree of pain, heart rate, packed-cell volume and abdominal sounds. In the second factor, cecal decompression, admission month and gastric reflux had the predominant influence, and this factor was explained as cecal tympany. The third factor was simply interpreted as age because it had high loadings on gender, age and temperature. In the fourth factor, the interpretation was not straightforward, although breed had the greatest influence in the formation of this factor. Subsequently, the extracted factors were used in a logistic-regression analysis to determine their
* Corresponding author. Present address: Royal Veterinary and Agricultural University of Copenhagen, BuÈlowsvej 17, DK-1870 Frederiksberg C, Denmark. Tel.: 45-35-28-28-60; fax: 45-35-28-28-80. E-mail address: [email protected] (M.B. Thoefner).
0167-5877/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 8 7 7 ( 0 0 ) 0 0 1 9 3 - 8
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association with outcome (survival/death). The two factors interpreted as endotoxaemia and age were related to the outcome. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Horse; Colic; Optimal scaling; Multicollinearity; Factor analysis
1. Introduction In a large health-monitoring study of horses, equine colic was one of the most-common causes of death (Kaneene et al., 1997). Colic is multifactorial and complex in nature. It ranges from a harmless temporary large-intestinal impaction to severe strangulation or colitis together with multi-organ failure as a consequence of circulatory collapse (Saville et al., 1996; Dabareiner, 1998). To improve diagnosis and prognosis, some studies have identified variables associated with specific conditions, such as grass sickness (Doxey et al., 1991) and peritonitis (Gollard et al., 1994; Hillyer and Wright, 1997). Others have focused on the clinical decision-making process and the reliability of diagnostic tools (Pascoe et al., 1990; Reeves et al., 1991; Sandholm et al., 1995; Freden et al., 1998). Only a few papers have examined the correlations between variables measured in colic horses. If several variables were highly correlated (i.e. were found to be related by a linear function and thus to display `multicollinearity'), the information they represent could be `expressed' with fewer variables. This would simplify the clinical-decision process. Parry et al. (1983) reported strong bivariable correlation coefficients r > 0:65 between packed-cell volume, haemoglobin concentration and blood erythrocyte count, between packed-cell volume and plasma-protein concentration, between blood and peritoneal-fluid glucose concentrations and between blood and peritoneal-fluid lactate concentrations. Gosset et al. (1987) found a close linear relationship between anion gap and blood lactate r 0:91. Sandholm et al. (1995) published a bivariable correlation matrix of 15 variables measured in 105 horses with severe colic as part of an exploratory data analysis. However, the authors did not attempt to explain the variability in the data. Topper and Prasse (1998) reported bivariable correlations between selected coagulation proteins in colic horses. The object of our study was to examine patterns of variation in commonly recorded clinical variables in colic horses; we used a multivariable exploratory analysis. Additionally, we attempted to explain any emerging patterns pathophysiologically. Finally, the association between the patterns of variation and the risk of death was assessed by regression analysis. 2. Materials and methods 2.1. Data Data were collected prospectively from all colic horses admitted to the Large Animal Hospital at the Royal Veterinary and Agricultural University of Copenhagen, Denmark, between August 1994 and December 1997. The university hospital is the only referral centre in the region and it is therefore very probably that it receives almost all local horses
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Table 1 Variables measured in 512 colic horses (Copenhagen, Denmark, 1994±1997) Variable type
Measurement levels or mean
Number of observations available
January, February, March, . . ., December Day, evening, night Mare, stallion, gelding Coldblood ponies, coldblood horses, warmblood horses
512 512 503 423 458 510 460 475 449
Gastric reflux volume >51 Cecal decompression Capillary refill time (s)
None, spasmolytics only, opioids, flunixin None, mild, moderate, severe, lethargic Normal, red, white/cyanotic Normal, abnormal but present, absent Normal, impaction/coprostasis, other abnormal, distended small intestines No, yes No, yes 1; 2; 3; . . . ; 10
Continuous variables Age (years) Heart rate (beats/min) Rectal temperature (8C) Packed-cell volume (%) Standard base excess (mmol/l)
8.1 60.2 38.0 39.5 ÿ2.2
501 498 455 449 454
Nominal variables Admission month Admission time Gender Breed Ordinal variables Prehospital analgesic medicationa Degree of pain Mucous-membrane colour Abdominal sounds Rectal examination
383 512 477
a A range of analgesic combinations were used by practitioners. The grouping are somewhat arbitrary, based on the analgesic thought to be the most powerful one in the combination given to the horse.
referred with colic. A physical examination was performed on each horse at admission and variables of interest were recorded (Table 1). Horses with peritonitis were included in the study where the primary cause of the peritonitis was believed to be enteric; those with other extra-enteric conditions, such as uterine torsion and urolithiasis, were excluded. Simple bivariable correlation coefficients were calculated using all the observations available for both variables. Prior to multivariable analysis, cases with missing values were deleted. The impact of this was examined by comparing the distribution of horses in the main diagnostic categories before and after deletion. In assessing the association between outcome of the colic episode (survival/death) and variance patterns, a horse was classified as a survivor if it was discharged from hospital. Horses subjected to euthanasia to prevent unnecessary suffering and those that died naturally were classified as `dead'. Horses destroyed other than on humane grounds were excluded from analysis. 2.2. Statistical analysis Simple bivariable associations among the collected variables were reported as Spearman rank-order correlation coefficients. Factor analysis was used to describe the
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interrelationships of multiple variables. This kind of analysis is a multivariable analytic technique that uses variables (with unknown correlations) to create a new set of variables called `factors' (Sharma, 1996). The factors considered here are orthogonal linear combinations of the original variables. They are therefore not correlated. The extent of variation between variables in each factor is expressed by the so-called `eigenvalue'. If there is a strong relationship between variables, the first few factors explain a high proportion of the total variance and the last factors contain very little additional information (Dohoo et al., 1996). Eigenvalues were calculated using the correlation matrix. The factor-analysis model is: yc lc1 F1 lc2 F2 lc3 F3 lcn Fn ec where yc is the cth original variable, c 1; . . . ; p, p the number of original variables, lc1 ; lc2 ; lc3 ; . . . ; lcn are the factor loadings, F1 ; F2 ; F3 ; . . . ; Fn are the (new) factors, n the number of factors, and ec the error term related to yc (Sharma, 1996). The number of factors to be extracted largely depends on the amount of information (or unexplained variance) one is willing to sacrifice, although a more-objective decision can be made using scree plots or Horn's parallel procedure (Sharma, 1996). In the present study, the different criteria governing the number of factors to be retained will be further discussed. In interpreting the retained factors we only used variables with loadings above 0.5 or below ÿ0.5 (i.e. variables with high influence). Further, we looked for a logical connection (also called a `latent factor') between the magnitude and direction of the loadings of these variables. Before factor analysis, an optimal scaling of data was performed, because the variables were recorded on different measurement scales (nominal, ordinal, interval Ð see Table 1). Optimal scaling is an iterative, data-driven process in which data are transformed to obtain linear relationships between variables. The maximum-total-variance method (which attempts to maximise the sum of the covariance matrix) was used. This maximises the total variance for the number of components selected. The number of components selected for optimal scaling was similar to the number of factors selected for the factor analysis. The nominal variables (admission time and date, gender, breed) were transformed by the scoring and subsequent ranking of the categories. Ordinal variables (pre-hospital analgesic medication, degree of pain, mucous-membrane colour, abdominal sounds, rectal examination, gastric reflux, cecal decompression and capillary refill time) were transformed monotomically so that the order of the measurement levels was weakly preserved. Interval variables (age, heart rate, rectal temperature, packed-cell volume and standard base excess) were not transformed (SAS Institute, 1989b). Finally, the retained factors were subjected to logistic-regression analysis to determine any significant association (p < 0:05, 2-tailed) with outcome (survival/death). For all analysis and data management the SAS computer package release 6.12 was used.1 The SAS procedure `PROC PRINQUAL' was used to obtain an optimal scaling of variables (SAS Institute, 1989b) and the `PROC FACTOR' procedure with orthogonal `VARIMAX' rotation was used for subsequent factor analysis (SAS Institute, 1989a). 1
Statistical Analysis System1, Release 6.12, SAS Institute Inc., SAS Campus Drive, Cary, NC 27513, USA.
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3. Results In total, 528 colic horses were admitted between August 1994 and December 1997. Sixteen horses had miscellaneous conditions considered to be primarily extra-enteric, and thus 512 horses with colic remained for analysis. In these 512 horses, mortality was 28% (145 horses). Twenty-nine horses died spontaneously and 116 horses were subjected to euthanasia. Surgery was performed in 19% of cases (95 horses). The simple bivariable correlation coefficients are displayed in Table 2. When all variables were considered together, observations from only 205 horses were available for factor analysis. This sample was considered a representative subset, because the distribution of horses in the main diagnostic categories exhibited only minor changes (Table 3). In Fig. 1, the changes in nominal and ordinal variable scales resulting from optimal scaling are shown. The eigenvalues of the 17 factors are depicted in a scree plot (Fig. 2), together with the eigenvalues resulting from Horn's parallel procedure. Horn's parallel procedure generates a reference curve which represents the expected eigenvalues of a similar data set (205 observations, 17 variables) if no correlation exists between variables (Sharma, 1996). Only four factors had eigenvalues above the reference curve. The results of the factor analysis and suggested interpretation are shown in Table 4. From the cumulative proportions, it is evident that no single factor explained a major part of the variance between the variables. The first factor accounted for only 24% of the total variability in the data and 13 factors were necessary to explain 90% of variability (not shown). Logistic-regression analysis was used to determine the association between outcome (survival/death) and the extracted factors. Only two of the factors showed a significant relationship p < 0:05 in the multivariable assessment (all four factors were in the model). Factor one had a strong relation to outcome p < 0:001, whereas factor three showed a weak association p 0:020. The p-values for factors two and four were 0.236 and 0.088, respectively. 4. Discussion As indicated by the number of variables with high loadings participating in the formation of the first factors (Table 4), multicollinearity was present to some extent. However, the number of factors needing to be generated to account for 90% of the variance was surprisingly high to us. Further, because no single factor explained a major proportion of the total variance, it is difficult to draw any conclusions regarding variable redundancy. Thus, in the present data no strong correlation exists between variables. This was also evidenced by the small-to-moderate bivariable correlation coefficients shown in Table 2. The reason for this might be the heterogeneity of the equine colic syndrome. In a veterinary teaching book on equine colic, more than 50 specific diagnoses are listed (White, 1990b). Although the pathophysiological mechanisms behind the different diagnoses are less numerous, a considerable variety in the way the syndrome manifests itself still exists.
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Prehospital analgesic medication Prehospital analgesic 1.00 medication Degree of pain 0.17 Mucous-membrane colour 0.14 Abdominal sounds 0.18 Rectal examination 0.18 Gastric reflux 0.09 Cecal decompression 0.09 Capillary refill time 0.10 Age 0.01 Heart rate 0.17 Temperature ÿ0.04 Packed-cell volume 0.17 Standard base excess 0.01 a
Degree of pain
1.00 0.42 0.45 0.33 0.24 0.21 0.38 ÿ0.04 0.49 ÿ0.04 0.30 ÿ0.12
Mucousmembrane colour
1.00 0.32 0.26 0.20 0.03 0.52 ÿ0.01 0.52 0.06 0.42 ÿ0.26
Abdominal sounds
Rectal examination
Gastric reflux
1.00 0.36 0.29 0.17 0.41 0.07 0.45 0.02 0.27 ÿ0.17
1.00 0.29 0.10 0.24 0.04 0.35 ÿ0.02 0.16 ÿ0.08
1.00 0.21 0.19 0.13 0.34 0.03 0.22 ÿ0.01
Cecal decompression
1.00 0.09 ÿ0.01 0.14 0.01 ÿ0.01 ÿ0.06
Capillary refill time
1.00 0.08 0.52 0.05 0.44 ÿ0.36
Age
Heart rate
1.00 ÿ0.03 1.00 ÿ0.14 0.18 0.16 0.48 ÿ0.09 ÿ0.38
Nominal variables were excluded from this analysis. Number in italic indicates coefficients above |0.40| (Copenhagen, Denmark, 1994±1997).
Temperature
1.00 0.06 ÿ0.05
Packed-cell Standard volume base excess
1.00 ÿ0.26
1.00
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Table 2 Spearman correlation coefficients for original variablesa
Diagnostic category
Number of horses in original population
Proportion
Strangulation obstruction or infarction Intestinal or peritoneal inflammation Intestinal rupture Non-strangulation, non-inflammatory Could not be classifiedb
80 43 17 367 5
Total
512
a
95% confidence interval
Number of horses after deletion
Proportion
Lower
Upper
0.156 0.084 0.033 0.717 0.010
0.128 0.060 0.018 0.678 0.001
0.187 0.108 0.048 0.756 0.019
30 19 9 145 2
0.146 0.093 0.044 0.707 0.010
1.000
±
±
205
1.000
528 colic horses were admitted to the university hospital (Copenhagen, Denmark) in the study period (1994±1997). Sixteen horses with miscellaneous extra-enteric conditions were excluded. b Horses for which post-mortem records were insufficient for classification.
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Table 3 Distribution of horses in the main diagnostic categories before and after deletion of cases with missing valuesa
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Fig. 1. Transformation of the original variables (nominal and ordinal) using optimal scaling. Abbreviations: in `breed' CP, CH and WH designate coldblood ponies, coldblood horses and warmblood horses. In `prehospital analgesic medication', spas. only is spasmolytics only. In `rectal examination', N, I/C, OA and DSI designate the findings: normal, impaction/coprostasis, other abnormal and distended small intestines.
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Fig. 1. (Continued ).
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Fig. 2. Scree plot depicting the eigenvalues of factors (solid line). The dotted line is the reference line generated by Horn's parallel procedure.
4.1. Extraction of factors Several methods have been used to determine the number of meaningful factors that should be extracted. Commonly, as a rule of thumb, factors with an eigenvalue greater than 1.0 are retained. The rationale for this rule is that, for standardised data, the amount of variance accounted for by each factor should be at least equal to the variance of one variable (Sharma, 1996). According to this criterion, six factors should be extracted in the present study (not shown). Alternatively, depending on the object of the study (and on how much variance the scientist is willing to leave unexplained), the `proportion of variance accounted for' can be used as an extraction rule. Factors are retained until the cumulative proportion reaches a certain value, e.g. 90% (Pfeiffer, 1999). Because the objective of the present study is merely exploratory, this rule was not considered. The scree plot was developed as a visual method for assessing the abrupt change in relative size of eigenvalues. Its `elbow' indicates the number of factors that should be extracted. The elbow in Fig. 2 indicates that only two factors should be extracted. Horn's parallel procedure is a less-subjective method. It takes into account that, through sampling error in data where variables are not correlated among themselves, some eigenvalues of factors will automatically be >1.0, and some will be <1.0. From the number of observations and variables in the data, a reference curve can be generated (Sharma, 1996). The number of factors to be extracted appears where the two curves intersect. In Fig. 2, the curves intersect close to factor four. Finally, Pfeiffer (1999) emphasises the importance of the
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Table 4 Results of factor analysis after optimal scaling and `varimax' rotationa Variable
Factor 1
Factor 2
Factor 3
Factor 4
Capillary-refill time Mucous-membrane colour Degree of pain Heart rate Packed-cell volume Abdominal sounds Cecal decompression Gastric reflux Admission month Gender Age Admission time (in day) Rectal examination Temperature Breed Standard base excess Prehospital analgesic medication
0.812 0.797 0.786 0.769 0.704 0.616 0.012 0.267 0.106 0.033 ÿ0.065 0.032 0.397 0.224 ÿ0.024 ÿ0.314 0.283
ÿ0.144 ÿ0.009 0.027 0.237 ÿ0.036 0.339 0.750 0.500 ÿ0.673 ÿ0.164 ÿ0.028 ÿ0.003 0.158 ÿ0.070 ÿ0.050 ÿ0.200 0.272
ÿ0.062 ÿ0.015 ÿ0.045 0.066 0.047 0.216 ÿ0.051 0.330 0.239 0.616 0.592 0.454 0.424 ÿ0.483 0.055 ÿ0.008 0.090
ÿ0.165 0.000 0.077 ÿ0.300 0.070 ÿ0.123 0.060 ÿ0.046 0.143 0.134 ÿ0.406 0.059 ÿ0.077 ÿ0.416 0.759 0.567 0.393
4.120 0.242
1.691 0.342
1.522 0.431
1.332 0.510
Eigenvalue Cumulative proportionb Suggested interpretation
Endotoxaemia
Cecal tympany
Age
Breed ?
a Loadings, eigenvalues, cumulative proportion of the total variance and a suggested interpretation are given for four factors. Only variables with loadings above 0.5 or below ÿ0.5 were used in interpretation (displayed in italic). b The cumulative proportion is the cumulative proportion of the total variance in data. Since the variables are standardised to a variance of 1, the total eigenvalue 17 (number of variables).
interpretability criterion. The retained factors should be meaningful. If more than four factors had been extracted in the present study, the additional factors would simply have consisted of lone variables with very high loadings. Difficulties affecting the interpretability of the former four factors also arose. On this background, it seemed appropriate to extract four factors in the present study. 4.2. Interpretation of factors Endotoxaemia occurs in a substantial proportion of horses referred to veterinary hospitals with gastrointestinal disease. Alterations in the colour of the mucous membranes, prolongation of capillary refill time, increased heart and respiratory rates, reduced gastrointestinal sounds and evidence of dehydration are some of its morecommon clinical effects (Moore and Barton, 1998). Putting aside the fact that degree of pain also correlated with the variables reflecting endotoxaemia, these variables were the very combination of variables with the greatest influence on the first factor. The high loading on degree of pain was not surprising to us, because the severity of gastrointestinal disease is in general associated with the intensity of colic signs (White, 1990a). A morecentral estimate of endotoxaemia could probably replace the variables in the first factor.
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Steverink et al. (1995) showed, by the use of bivariable comparisons, that interleukin-6 (a mediator of endotoxaemia) was superior to platelet count, base excess, packed-cell volume and heart rate in the prediction of unfavourable outcome in horses with acute abdomen. In experimentally induced endotoxaemia, Morris et al. (1990) reported significant bivariable correlations between tumor necrosis factor activity and temperature, demeanour, white blood-cell count and heart rate. The second factor was formed largely by cecal decompression, gastric reflux and admission month. Fig. 1 shows that when admission month is transformed by optimal scaling; the location of the various months in the scale is changed. The last seven months of the year are located almost identically in the uppermost part of the new scale. January has the smallest value, followed by April, May, March and February. The locations of the measurement levels in cecal decompression and gastric reflux are unchanged. The loadings on cecal decompression and gastric reflux are positive, whereas the loading on admission month is negative (Table 4). This means that a change in cecal decompression from `no' to `yes' would parallel a change in gastric reflux from <5 to >5 l. Further, because the loading on month is negative, this change would be followed by a decrease in the new scale of month-corresponding to a spring month. Cecal decompression was included as a variable indicating severe cecal tympany. This factor could be explained by a severe tympany creating ileus. A small-intestinal obstruction could probably be involved, given the anatomical relation of the duodenum to the cecal base (Allen and Tyler, 1990). Severe cecal distension can be due primarily to a rapid cecal fermentation of carbohydrates, or secondarily to a large-intestinal obstruction. A sudden exposure to lush green grass in the spring months is believed to carry an increased risk of colic caused by primary cecal tympani. However, a specific diagnosis or cause is rarely obtained (Dart et al., 1999). Although this interpretation of the second factor is both tempting and clinically reasonable, factors need to be interpreted with care because no statistical procedure exists to test their reliability. Indeed, in January (the month with the smallest value in the new scale), we have no lush green grass at all in Denmark. Some of the loadings might be attributable to sources of variation other than the latent factor. The third factor had high positive loadings on age and gender. Gender was originally measured on a nominal scale: the categories were mare, stallion and gelding. The transformation by optimal scaling resulted in a low score to stallion, an intermediate score to mare and a high score to gelding (Fig. 1). Thus, a change from early to later age parallels a change from stallion to gelding. The straightforward explanation of this is that most stallions are castrated at a young age. The third factor is therefore interpreted as age. Further, temperature has a negative loading just below ÿ0.5, indicating an inverse association with age (Table 4). Temperatures in foals and yearlings are higher than those in adult horses. Although other causes of temperature change are likely to occur in horses with colic (e.g. poor cardiovascular function, inflammation and pain), the effect of age can still be seen in a small part of the data. In the formation of the fourth factor, breed had the predominant influence, followed by standard base excess. At present, the connection between the main breed categories and variation in acid±base balance is not clear to us. If the latent factor is a specific diagnosis mainly encountered in, e.g. coldblood ponies, such a connection is probable. However, conflicting reports on the association between breed and the various types of colic appear
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in the literature. Because the loading on breed is relatively higher than the loading on standard base excess, we therefore suggest that factor four simply be interpreted as breed. 4.3. Association with outcome A further application of factor analysis uses the factors in a regression analysis. The regression coefficients obtained hereby would be more stable than the regression coefficients in the original variables. The first factor interpreted as endotoxaemia was strongly associated with outcome. This finding accords with reports on pro-inflammatory mediators of endotoxaemia in horses with colic. In horses where the tumor-necrosis factor or interleukin-6 activity was increased, an unfavourable outcome was likely (MacKay, 1992; Steverink et al., 1995; Barton and Collatos, 1999). Factor three (interpreted as age) also was related to outcome. In studies on prognostic indicators, age was identified as a risk factor in fatality (Orsini et al., 1988; Reeves et al., 1989; Ebert, 1994). Although these factors were associated with outcome, factors as such are impractical as predictors, because the `feeling' with the original variables is lost. Alternative multivariable predictive methods that are more suitable for the clinical situation should be applied in prognostication of disease. 5. Conclusions The present exploration of the variance structure in a subset of horses with colic confirmed the clinical impression of correlation between variables. The number of factors that needed to be generated to account for a substantial proportion of the total variance was, however, surprisingly high and we therefore considered the multicollinearity to be less than strong. Four factors explained 51% of the variability in data and these were interpreted as effects of endotoxaemia, cecal tympany, age and breed. Endotoxaemia and age were significantly associated with outcome. Acknowledgements We are grateful to members of staff at the Large Animal Hospital in the Royal Veterinary and Agricultural University of Copenhagen who helped to collect samples during day and night hours. References Allen, D., Tyler, D.E., 1990. Pathophysiology of acute abdominal disease. In: White, N.A. (Ed.), The Equine Acute Abdomen. Lea Febiger, Philadelphia, PA, pp. 66±67. Barton, M.H., Collatos, C., 1999. Tumor necrosis factor and interleukin-6 activity and endotoxin concentration in peritoneal fluid and blood of horses with acute abdominal disease. J. Vet. Intern. Med. 13, 457±464. Dabareiner, R.M., 1998. Impaction of the ascending colon and cecum. In: White, N.A., Moore, J.N. (Eds.), Current Techniques in Equine Surgery and Lameness, 2nd Edition. Saunders, London, pp. 270±272. Dart, A.J., Dowling, B.A., Hodgson, D.R., 1999. Caecal disease. Equine Vet. Educ. 11, 182±188. Dohoo, I.R., Ducrot, C., Fourichon, C., Donald, A., Hurnik, D., 1996. An overview of techniques for dealing with large numbers of independent variables in epidemiologic studies. Prev. Vet. Med. 29, 221±239.
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Doxey, D.L., Milne, E.M., Gilmour, J.S., Pogson, D.M., 1991. Clinical and biochemical features of grass sickness (equine dysautonomia). Equine Vet. J. 23, 360±364. Ebert, R., 1994. Prognostische parameter bei der kolik des pferdes. TieraÈrztl. Prax. 22, 256±263. Freden, G.O., Provost, P.J., Rand, W.M., 1998. Reliability of using results of abdominal fluid analysis to determine treatment and predict lesion type and outcome for horses with colic: 218 cases (1991±1994). J. Am. Vet. Med. Assoc. 213, 1012±1015. Gollard, L.C., Hodgson, D.R., Hodgson, J.L., Brownlow, M.A., Hutchins, D.R., Rawlinson, R.J., Collins, M.B., McClintock, S.A., Raisis, A.L., 1994. Peritonitis associated with Actinobacillus equuli in horses: 15 cases (1982±1992). J. Am. Vet. Med. Assoc. 205, 340±343. Gosset, K.A., Cleghorn, B., Martin, G.S., 1987. Correlation between anion gap, blood L-lactate concentration and survival in horses. Equine Vet. J. 19, 29±30. Hillyer, M.H., Wright, C.J., 1997. Peritonitis in the horse. Equine Vet. Educ. 9, 136±142. Kaneene, J.B., Ross, W.A., Miller, R., 1997. The Michigan equine monitoring system. II. Frequencies and impact of selected health problems. Prev. Vet. Med. 29, 277±292. MacKay, R.J., 1992. Association between serum cytotoxicity and selected clinical variables in 240 horses admitted to a veterinary hospital. Am. J. Vet. Res. 53, 748±752. Moore, J.N., Barton, M.H., 1998. An update on endotoxaemia. Part 1. Mechanisms and pathways. Equine Vet. Educ. 10, 300±306. Morris, D.D., Crowe, N., Moore, J.N., 1990. Correlation of clinical and laboratory data with serum tumor necrosis factor activity in horses with experimentally induced endotoxemia. Am. J. Vet. Res. 51, 1935±1940. Orsini, J.A., Elser, A.H., Galligan, D.T., Donawick, W.J., Kronfeld, D.S., 1988. Prognostic index for acute abdominal crisis (colic) in horses. Am. J. Vet. Res. 11, 1969±1971. Parry, B.W., Anderson, G.A., Gay, C.C., 1983. Prognosis in equine colic: a comparative study of variables used to assess individual cases. Equine Vet. J. 15, 211±215. Pascoe, P.J., Ducharme, N.G., Ducharme, G.R., Lumsden, J.H., 1990. A computer derived protocol using recursive partitioning to aid in estimating prognosis of horses with abdominal pain in referral hospitals. Can. J. Vet. Res. 54, 373±378. Pfeiffer, D.U., 1999. Analysis of high-dimensionality epidemiological data. Nordic Society of Veterinary Epidemiology, Copenhagen, November 11±13, personal communication. Reeves, M.J., Curtis, C.R., Salman, M.D., Hilbert, B.J., 1989. Prognosis in equine colic patients using mulitvariable analysis. Can. Vet. Res. 53, 87±94. Reeves, M.J., Curtis, C.R., Salman, M.D., Stashak, T.S., Reif, J.S., 1991. Multivariable prediction model for the need for surgery in horses with colic. Am. J. Vet. Res. 52, 1903±1907. Sandholm, M., Vidovic, A., Puotunen-Reinert, A., Sankari, S., Nyholm, K., Rita, H., 1995. D-dimer improves the prognostic value of combined clinical and laboratory data in equine gastrointestinal colic. Acta Vet. Scand. 36, 255±272. SAS Institute Inc., 1989a. SAS/STAT User's Guide, Vol. 1, 4th Edition, Version 6. SAS Institute, Cary, NC, USA, pp. 773±821. SAS Institute Inc., 1989b. SAS/STAT User's Guide, Vol. 2, 4th Edition, Version 6. SAS Institute, Cary, NC, USA, pp. 1265±1323. Saville, J.W., Hinchcliff, K.W., Moore, B.R., Kohn, C.W., Reed, S.M., Mitten, L.A., Rivas, L.J., 1996. Necrotizing enterocolitis in horses: a retrospective study. J. Vet. Intern. Med. 10, 265±270. Sharma, S. (Ed.), 1996. Applied Multivariate Techniques. Wiley, New York, pp. 77, 90±143. Steverink, P.J.G.M., Sturk, A., Rutten, W.P.M.G., Wagenaar-Hilbers, J.P.A., Klein, W.R., van der Velden, M.A., Nemeth, F., 1995. Endotoxin interleukin-6 and tumor necrosis factor concentrations in equine acute abdominal disease: relation to outcome. J. Endotoxin Res. 2, 289±298. Topper, M.J., Prasse, K.W., 1998. Analysis of coagulation proteins as acute-phase proteins in horses with colic. Am. J. Vet. Res. 59, 542±545. White, N.A. (Ed.), 1990a. Examination and diagnosis of the acute abdomen. In: The Equine Acute Abdomen. Lea and Febiger, Philadelphia, PA, pp. 104±111. White, N.A. (Ed.), 1990b. Diseases of the acute abdomen. In: The Equine Acute Abdomen. Lea and Febiger, Philadelphia, PA, pp. 337±418.
Factor analysis of the interrelationships between clinical variables in horses with colic M.B. Thoefnera,*, A.K. Ersbùllb, A.L. Jensenc, M. Hesselholta a
Department of Large Animal Surgery, University of Copenhagen, BuÈlowsvej 17, DK-1870 Frederiksberg C, Denmark b Department of Animal Science and Animal Health, University of Copenhagen, BuÈlowsvej 17, DK-1870 Frederiksberg C, Denmark c Central Laboratory, Royal Veterinary and Agricultural University of Copenhagen, BuÈlowsvej 17, DK-1870 Frederiksberg C, Denmark Received 7 September 1999; accepted 26 October 2000
Abstract A prospective survey of horses with colic referred to the Large Animal Hospital at the Royal Veterinary and Agricultural University of Copenhagen, Denmark, was undertaken between August 1994 and December 1997. The interrelationships between 17 clinical variables were analysed using factor analysis. Factor analysis uncovers the structure of the variability in data and therefore detects multicollinearity. A total of 528 horses were admitted in the study period. Of these, 16 were excluded from the analysis as a result of miscellaneous conditions. Only 205 horses had observations for all 17 variables. Because no major change occurred in the main diagnostic categories, this population was considered as a representative subset. Factor analysis confirmed the clinical impression of correlation between variables, but the multicollinearity turned out not to be strong. Four factors were extracted, and these accounted for 51% of the total variance. The retained factors were interpreted by integrating previously reported clinical research. The first factor, which was interpreted as endotoxaemia, had high loadings on capillary refill time, mucous-membrane colour, degree of pain, heart rate, packed-cell volume and abdominal sounds. In the second factor, cecal decompression, admission month and gastric reflux had the predominant influence, and this factor was explained as cecal tympany. The third factor was simply interpreted as age because it had high loadings on gender, age and temperature. In the fourth factor, the interpretation was not straightforward, although breed had the greatest influence in the formation of this factor. Subsequently, the extracted factors were used in a logistic-regression analysis to determine their
* Corresponding author. Present address: Royal Veterinary and Agricultural University of Copenhagen, BuÈlowsvej 17, DK-1870 Frederiksberg C, Denmark. Tel.: 45-35-28-28-60; fax: 45-35-28-28-80. E-mail address: [email protected] (M.B. Thoefner).
0167-5877/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 8 7 7 ( 0 0 ) 0 0 1 9 3 - 8
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association with outcome (survival/death). The two factors interpreted as endotoxaemia and age were related to the outcome. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Horse; Colic; Optimal scaling; Multicollinearity; Factor analysis
1. Introduction In a large health-monitoring study of horses, equine colic was one of the most-common causes of death (Kaneene et al., 1997). Colic is multifactorial and complex in nature. It ranges from a harmless temporary large-intestinal impaction to severe strangulation or colitis together with multi-organ failure as a consequence of circulatory collapse (Saville et al., 1996; Dabareiner, 1998). To improve diagnosis and prognosis, some studies have identified variables associated with specific conditions, such as grass sickness (Doxey et al., 1991) and peritonitis (Gollard et al., 1994; Hillyer and Wright, 1997). Others have focused on the clinical decision-making process and the reliability of diagnostic tools (Pascoe et al., 1990; Reeves et al., 1991; Sandholm et al., 1995; Freden et al., 1998). Only a few papers have examined the correlations between variables measured in colic horses. If several variables were highly correlated (i.e. were found to be related by a linear function and thus to display `multicollinearity'), the information they represent could be `expressed' with fewer variables. This would simplify the clinical-decision process. Parry et al. (1983) reported strong bivariable correlation coefficients r > 0:65 between packed-cell volume, haemoglobin concentration and blood erythrocyte count, between packed-cell volume and plasma-protein concentration, between blood and peritoneal-fluid glucose concentrations and between blood and peritoneal-fluid lactate concentrations. Gosset et al. (1987) found a close linear relationship between anion gap and blood lactate r 0:91. Sandholm et al. (1995) published a bivariable correlation matrix of 15 variables measured in 105 horses with severe colic as part of an exploratory data analysis. However, the authors did not attempt to explain the variability in the data. Topper and Prasse (1998) reported bivariable correlations between selected coagulation proteins in colic horses. The object of our study was to examine patterns of variation in commonly recorded clinical variables in colic horses; we used a multivariable exploratory analysis. Additionally, we attempted to explain any emerging patterns pathophysiologically. Finally, the association between the patterns of variation and the risk of death was assessed by regression analysis. 2. Materials and methods 2.1. Data Data were collected prospectively from all colic horses admitted to the Large Animal Hospital at the Royal Veterinary and Agricultural University of Copenhagen, Denmark, between August 1994 and December 1997. The university hospital is the only referral centre in the region and it is therefore very probably that it receives almost all local horses
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Table 1 Variables measured in 512 colic horses (Copenhagen, Denmark, 1994±1997) Variable type
Measurement levels or mean
Number of observations available
January, February, March, . . ., December Day, evening, night Mare, stallion, gelding Coldblood ponies, coldblood horses, warmblood horses
512 512 503 423 458 510 460 475 449
Gastric reflux volume >51 Cecal decompression Capillary refill time (s)
None, spasmolytics only, opioids, flunixin None, mild, moderate, severe, lethargic Normal, red, white/cyanotic Normal, abnormal but present, absent Normal, impaction/coprostasis, other abnormal, distended small intestines No, yes No, yes 1; 2; 3; . . . ; 10
Continuous variables Age (years) Heart rate (beats/min) Rectal temperature (8C) Packed-cell volume (%) Standard base excess (mmol/l)
8.1 60.2 38.0 39.5 ÿ2.2
501 498 455 449 454
Nominal variables Admission month Admission time Gender Breed Ordinal variables Prehospital analgesic medicationa Degree of pain Mucous-membrane colour Abdominal sounds Rectal examination
383 512 477
a A range of analgesic combinations were used by practitioners. The grouping are somewhat arbitrary, based on the analgesic thought to be the most powerful one in the combination given to the horse.
referred with colic. A physical examination was performed on each horse at admission and variables of interest were recorded (Table 1). Horses with peritonitis were included in the study where the primary cause of the peritonitis was believed to be enteric; those with other extra-enteric conditions, such as uterine torsion and urolithiasis, were excluded. Simple bivariable correlation coefficients were calculated using all the observations available for both variables. Prior to multivariable analysis, cases with missing values were deleted. The impact of this was examined by comparing the distribution of horses in the main diagnostic categories before and after deletion. In assessing the association between outcome of the colic episode (survival/death) and variance patterns, a horse was classified as a survivor if it was discharged from hospital. Horses subjected to euthanasia to prevent unnecessary suffering and those that died naturally were classified as `dead'. Horses destroyed other than on humane grounds were excluded from analysis. 2.2. Statistical analysis Simple bivariable associations among the collected variables were reported as Spearman rank-order correlation coefficients. Factor analysis was used to describe the
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interrelationships of multiple variables. This kind of analysis is a multivariable analytic technique that uses variables (with unknown correlations) to create a new set of variables called `factors' (Sharma, 1996). The factors considered here are orthogonal linear combinations of the original variables. They are therefore not correlated. The extent of variation between variables in each factor is expressed by the so-called `eigenvalue'. If there is a strong relationship between variables, the first few factors explain a high proportion of the total variance and the last factors contain very little additional information (Dohoo et al., 1996). Eigenvalues were calculated using the correlation matrix. The factor-analysis model is: yc lc1 F1 lc2 F2 lc3 F3 lcn Fn ec where yc is the cth original variable, c 1; . . . ; p, p the number of original variables, lc1 ; lc2 ; lc3 ; . . . ; lcn are the factor loadings, F1 ; F2 ; F3 ; . . . ; Fn are the (new) factors, n the number of factors, and ec the error term related to yc (Sharma, 1996). The number of factors to be extracted largely depends on the amount of information (or unexplained variance) one is willing to sacrifice, although a more-objective decision can be made using scree plots or Horn's parallel procedure (Sharma, 1996). In the present study, the different criteria governing the number of factors to be retained will be further discussed. In interpreting the retained factors we only used variables with loadings above 0.5 or below ÿ0.5 (i.e. variables with high influence). Further, we looked for a logical connection (also called a `latent factor') between the magnitude and direction of the loadings of these variables. Before factor analysis, an optimal scaling of data was performed, because the variables were recorded on different measurement scales (nominal, ordinal, interval Ð see Table 1). Optimal scaling is an iterative, data-driven process in which data are transformed to obtain linear relationships between variables. The maximum-total-variance method (which attempts to maximise the sum of the covariance matrix) was used. This maximises the total variance for the number of components selected. The number of components selected for optimal scaling was similar to the number of factors selected for the factor analysis. The nominal variables (admission time and date, gender, breed) were transformed by the scoring and subsequent ranking of the categories. Ordinal variables (pre-hospital analgesic medication, degree of pain, mucous-membrane colour, abdominal sounds, rectal examination, gastric reflux, cecal decompression and capillary refill time) were transformed monotomically so that the order of the measurement levels was weakly preserved. Interval variables (age, heart rate, rectal temperature, packed-cell volume and standard base excess) were not transformed (SAS Institute, 1989b). Finally, the retained factors were subjected to logistic-regression analysis to determine any significant association (p < 0:05, 2-tailed) with outcome (survival/death). For all analysis and data management the SAS computer package release 6.12 was used.1 The SAS procedure `PROC PRINQUAL' was used to obtain an optimal scaling of variables (SAS Institute, 1989b) and the `PROC FACTOR' procedure with orthogonal `VARIMAX' rotation was used for subsequent factor analysis (SAS Institute, 1989a). 1
Statistical Analysis System1, Release 6.12, SAS Institute Inc., SAS Campus Drive, Cary, NC 27513, USA.
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3. Results In total, 528 colic horses were admitted between August 1994 and December 1997. Sixteen horses had miscellaneous conditions considered to be primarily extra-enteric, and thus 512 horses with colic remained for analysis. In these 512 horses, mortality was 28% (145 horses). Twenty-nine horses died spontaneously and 116 horses were subjected to euthanasia. Surgery was performed in 19% of cases (95 horses). The simple bivariable correlation coefficients are displayed in Table 2. When all variables were considered together, observations from only 205 horses were available for factor analysis. This sample was considered a representative subset, because the distribution of horses in the main diagnostic categories exhibited only minor changes (Table 3). In Fig. 1, the changes in nominal and ordinal variable scales resulting from optimal scaling are shown. The eigenvalues of the 17 factors are depicted in a scree plot (Fig. 2), together with the eigenvalues resulting from Horn's parallel procedure. Horn's parallel procedure generates a reference curve which represents the expected eigenvalues of a similar data set (205 observations, 17 variables) if no correlation exists between variables (Sharma, 1996). Only four factors had eigenvalues above the reference curve. The results of the factor analysis and suggested interpretation are shown in Table 4. From the cumulative proportions, it is evident that no single factor explained a major part of the variance between the variables. The first factor accounted for only 24% of the total variability in the data and 13 factors were necessary to explain 90% of variability (not shown). Logistic-regression analysis was used to determine the association between outcome (survival/death) and the extracted factors. Only two of the factors showed a significant relationship p < 0:05 in the multivariable assessment (all four factors were in the model). Factor one had a strong relation to outcome p < 0:001, whereas factor three showed a weak association p 0:020. The p-values for factors two and four were 0.236 and 0.088, respectively. 4. Discussion As indicated by the number of variables with high loadings participating in the formation of the first factors (Table 4), multicollinearity was present to some extent. However, the number of factors needing to be generated to account for 90% of the variance was surprisingly high to us. Further, because no single factor explained a major proportion of the total variance, it is difficult to draw any conclusions regarding variable redundancy. Thus, in the present data no strong correlation exists between variables. This was also evidenced by the small-to-moderate bivariable correlation coefficients shown in Table 2. The reason for this might be the heterogeneity of the equine colic syndrome. In a veterinary teaching book on equine colic, more than 50 specific diagnoses are listed (White, 1990b). Although the pathophysiological mechanisms behind the different diagnoses are less numerous, a considerable variety in the way the syndrome manifests itself still exists.
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Prehospital analgesic medication Prehospital analgesic 1.00 medication Degree of pain 0.17 Mucous-membrane colour 0.14 Abdominal sounds 0.18 Rectal examination 0.18 Gastric reflux 0.09 Cecal decompression 0.09 Capillary refill time 0.10 Age 0.01 Heart rate 0.17 Temperature ÿ0.04 Packed-cell volume 0.17 Standard base excess 0.01 a
Degree of pain
1.00 0.42 0.45 0.33 0.24 0.21 0.38 ÿ0.04 0.49 ÿ0.04 0.30 ÿ0.12
Mucousmembrane colour
1.00 0.32 0.26 0.20 0.03 0.52 ÿ0.01 0.52 0.06 0.42 ÿ0.26
Abdominal sounds
Rectal examination
Gastric reflux
1.00 0.36 0.29 0.17 0.41 0.07 0.45 0.02 0.27 ÿ0.17
1.00 0.29 0.10 0.24 0.04 0.35 ÿ0.02 0.16 ÿ0.08
1.00 0.21 0.19 0.13 0.34 0.03 0.22 ÿ0.01
Cecal decompression
1.00 0.09 ÿ0.01 0.14 0.01 ÿ0.01 ÿ0.06
Capillary refill time
1.00 0.08 0.52 0.05 0.44 ÿ0.36
Age
Heart rate
1.00 ÿ0.03 1.00 ÿ0.14 0.18 0.16 0.48 ÿ0.09 ÿ0.38
Nominal variables were excluded from this analysis. Number in italic indicates coefficients above |0.40| (Copenhagen, Denmark, 1994±1997).
Temperature
1.00 0.06 ÿ0.05
Packed-cell Standard volume base excess
1.00 ÿ0.26
1.00
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Table 2 Spearman correlation coefficients for original variablesa
Diagnostic category
Number of horses in original population
Proportion
Strangulation obstruction or infarction Intestinal or peritoneal inflammation Intestinal rupture Non-strangulation, non-inflammatory Could not be classifiedb
80 43 17 367 5
Total
512
a
95% confidence interval
Number of horses after deletion
Proportion
Lower
Upper
0.156 0.084 0.033 0.717 0.010
0.128 0.060 0.018 0.678 0.001
0.187 0.108 0.048 0.756 0.019
30 19 9 145 2
0.146 0.093 0.044 0.707 0.010
1.000
±
±
205
1.000
528 colic horses were admitted to the university hospital (Copenhagen, Denmark) in the study period (1994±1997). Sixteen horses with miscellaneous extra-enteric conditions were excluded. b Horses for which post-mortem records were insufficient for classification.
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Table 3 Distribution of horses in the main diagnostic categories before and after deletion of cases with missing valuesa
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Fig. 1. Transformation of the original variables (nominal and ordinal) using optimal scaling. Abbreviations: in `breed' CP, CH and WH designate coldblood ponies, coldblood horses and warmblood horses. In `prehospital analgesic medication', spas. only is spasmolytics only. In `rectal examination', N, I/C, OA and DSI designate the findings: normal, impaction/coprostasis, other abnormal and distended small intestines.
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Fig. 1. (Continued ).
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Fig. 2. Scree plot depicting the eigenvalues of factors (solid line). The dotted line is the reference line generated by Horn's parallel procedure.
4.1. Extraction of factors Several methods have been used to determine the number of meaningful factors that should be extracted. Commonly, as a rule of thumb, factors with an eigenvalue greater than 1.0 are retained. The rationale for this rule is that, for standardised data, the amount of variance accounted for by each factor should be at least equal to the variance of one variable (Sharma, 1996). According to this criterion, six factors should be extracted in the present study (not shown). Alternatively, depending on the object of the study (and on how much variance the scientist is willing to leave unexplained), the `proportion of variance accounted for' can be used as an extraction rule. Factors are retained until the cumulative proportion reaches a certain value, e.g. 90% (Pfeiffer, 1999). Because the objective of the present study is merely exploratory, this rule was not considered. The scree plot was developed as a visual method for assessing the abrupt change in relative size of eigenvalues. Its `elbow' indicates the number of factors that should be extracted. The elbow in Fig. 2 indicates that only two factors should be extracted. Horn's parallel procedure is a less-subjective method. It takes into account that, through sampling error in data where variables are not correlated among themselves, some eigenvalues of factors will automatically be >1.0, and some will be <1.0. From the number of observations and variables in the data, a reference curve can be generated (Sharma, 1996). The number of factors to be extracted appears where the two curves intersect. In Fig. 2, the curves intersect close to factor four. Finally, Pfeiffer (1999) emphasises the importance of the
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Table 4 Results of factor analysis after optimal scaling and `varimax' rotationa Variable
Factor 1
Factor 2
Factor 3
Factor 4
Capillary-refill time Mucous-membrane colour Degree of pain Heart rate Packed-cell volume Abdominal sounds Cecal decompression Gastric reflux Admission month Gender Age Admission time (in day) Rectal examination Temperature Breed Standard base excess Prehospital analgesic medication
0.812 0.797 0.786 0.769 0.704 0.616 0.012 0.267 0.106 0.033 ÿ0.065 0.032 0.397 0.224 ÿ0.024 ÿ0.314 0.283
ÿ0.144 ÿ0.009 0.027 0.237 ÿ0.036 0.339 0.750 0.500 ÿ0.673 ÿ0.164 ÿ0.028 ÿ0.003 0.158 ÿ0.070 ÿ0.050 ÿ0.200 0.272
ÿ0.062 ÿ0.015 ÿ0.045 0.066 0.047 0.216 ÿ0.051 0.330 0.239 0.616 0.592 0.454 0.424 ÿ0.483 0.055 ÿ0.008 0.090
ÿ0.165 0.000 0.077 ÿ0.300 0.070 ÿ0.123 0.060 ÿ0.046 0.143 0.134 ÿ0.406 0.059 ÿ0.077 ÿ0.416 0.759 0.567 0.393
4.120 0.242
1.691 0.342
1.522 0.431
1.332 0.510
Eigenvalue Cumulative proportionb Suggested interpretation
Endotoxaemia
Cecal tympany
Age
Breed ?
a Loadings, eigenvalues, cumulative proportion of the total variance and a suggested interpretation are given for four factors. Only variables with loadings above 0.5 or below ÿ0.5 were used in interpretation (displayed in italic). b The cumulative proportion is the cumulative proportion of the total variance in data. Since the variables are standardised to a variance of 1, the total eigenvalue 17 (number of variables).
interpretability criterion. The retained factors should be meaningful. If more than four factors had been extracted in the present study, the additional factors would simply have consisted of lone variables with very high loadings. Difficulties affecting the interpretability of the former four factors also arose. On this background, it seemed appropriate to extract four factors in the present study. 4.2. Interpretation of factors Endotoxaemia occurs in a substantial proportion of horses referred to veterinary hospitals with gastrointestinal disease. Alterations in the colour of the mucous membranes, prolongation of capillary refill time, increased heart and respiratory rates, reduced gastrointestinal sounds and evidence of dehydration are some of its morecommon clinical effects (Moore and Barton, 1998). Putting aside the fact that degree of pain also correlated with the variables reflecting endotoxaemia, these variables were the very combination of variables with the greatest influence on the first factor. The high loading on degree of pain was not surprising to us, because the severity of gastrointestinal disease is in general associated with the intensity of colic signs (White, 1990a). A morecentral estimate of endotoxaemia could probably replace the variables in the first factor.
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Steverink et al. (1995) showed, by the use of bivariable comparisons, that interleukin-6 (a mediator of endotoxaemia) was superior to platelet count, base excess, packed-cell volume and heart rate in the prediction of unfavourable outcome in horses with acute abdomen. In experimentally induced endotoxaemia, Morris et al. (1990) reported significant bivariable correlations between tumor necrosis factor activity and temperature, demeanour, white blood-cell count and heart rate. The second factor was formed largely by cecal decompression, gastric reflux and admission month. Fig. 1 shows that when admission month is transformed by optimal scaling; the location of the various months in the scale is changed. The last seven months of the year are located almost identically in the uppermost part of the new scale. January has the smallest value, followed by April, May, March and February. The locations of the measurement levels in cecal decompression and gastric reflux are unchanged. The loadings on cecal decompression and gastric reflux are positive, whereas the loading on admission month is negative (Table 4). This means that a change in cecal decompression from `no' to `yes' would parallel a change in gastric reflux from <5 to >5 l. Further, because the loading on month is negative, this change would be followed by a decrease in the new scale of month-corresponding to a spring month. Cecal decompression was included as a variable indicating severe cecal tympany. This factor could be explained by a severe tympany creating ileus. A small-intestinal obstruction could probably be involved, given the anatomical relation of the duodenum to the cecal base (Allen and Tyler, 1990). Severe cecal distension can be due primarily to a rapid cecal fermentation of carbohydrates, or secondarily to a large-intestinal obstruction. A sudden exposure to lush green grass in the spring months is believed to carry an increased risk of colic caused by primary cecal tympani. However, a specific diagnosis or cause is rarely obtained (Dart et al., 1999). Although this interpretation of the second factor is both tempting and clinically reasonable, factors need to be interpreted with care because no statistical procedure exists to test their reliability. Indeed, in January (the month with the smallest value in the new scale), we have no lush green grass at all in Denmark. Some of the loadings might be attributable to sources of variation other than the latent factor. The third factor had high positive loadings on age and gender. Gender was originally measured on a nominal scale: the categories were mare, stallion and gelding. The transformation by optimal scaling resulted in a low score to stallion, an intermediate score to mare and a high score to gelding (Fig. 1). Thus, a change from early to later age parallels a change from stallion to gelding. The straightforward explanation of this is that most stallions are castrated at a young age. The third factor is therefore interpreted as age. Further, temperature has a negative loading just below ÿ0.5, indicating an inverse association with age (Table 4). Temperatures in foals and yearlings are higher than those in adult horses. Although other causes of temperature change are likely to occur in horses with colic (e.g. poor cardiovascular function, inflammation and pain), the effect of age can still be seen in a small part of the data. In the formation of the fourth factor, breed had the predominant influence, followed by standard base excess. At present, the connection between the main breed categories and variation in acid±base balance is not clear to us. If the latent factor is a specific diagnosis mainly encountered in, e.g. coldblood ponies, such a connection is probable. However, conflicting reports on the association between breed and the various types of colic appear
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in the literature. Because the loading on breed is relatively higher than the loading on standard base excess, we therefore suggest that factor four simply be interpreted as breed. 4.3. Association with outcome A further application of factor analysis uses the factors in a regression analysis. The regression coefficients obtained hereby would be more stable than the regression coefficients in the original variables. The first factor interpreted as endotoxaemia was strongly associated with outcome. This finding accords with reports on pro-inflammatory mediators of endotoxaemia in horses with colic. In horses where the tumor-necrosis factor or interleukin-6 activity was increased, an unfavourable outcome was likely (MacKay, 1992; Steverink et al., 1995; Barton and Collatos, 1999). Factor three (interpreted as age) also was related to outcome. In studies on prognostic indicators, age was identified as a risk factor in fatality (Orsini et al., 1988; Reeves et al., 1989; Ebert, 1994). Although these factors were associated with outcome, factors as such are impractical as predictors, because the `feeling' with the original variables is lost. Alternative multivariable predictive methods that are more suitable for the clinical situation should be applied in prognostication of disease. 5. Conclusions The present exploration of the variance structure in a subset of horses with colic confirmed the clinical impression of correlation between variables. The number of factors that needed to be generated to account for a substantial proportion of the total variance was, however, surprisingly high and we therefore considered the multicollinearity to be less than strong. Four factors explained 51% of the variability in data and these were interpreted as effects of endotoxaemia, cecal tympany, age and breed. Endotoxaemia and age were significantly associated with outcome. Acknowledgements We are grateful to members of staff at the Large Animal Hospital in the Royal Veterinary and Agricultural University of Copenhagen who helped to collect samples during day and night hours. References Allen, D., Tyler, D.E., 1990. Pathophysiology of acute abdominal disease. In: White, N.A. (Ed.), The Equine Acute Abdomen. Lea Febiger, Philadelphia, PA, pp. 66±67. Barton, M.H., Collatos, C., 1999. Tumor necrosis factor and interleukin-6 activity and endotoxin concentration in peritoneal fluid and blood of horses with acute abdominal disease. J. Vet. Intern. Med. 13, 457±464. Dabareiner, R.M., 1998. Impaction of the ascending colon and cecum. In: White, N.A., Moore, J.N. (Eds.), Current Techniques in Equine Surgery and Lameness, 2nd Edition. Saunders, London, pp. 270±272. Dart, A.J., Dowling, B.A., Hodgson, D.R., 1999. Caecal disease. Equine Vet. Educ. 11, 182±188. Dohoo, I.R., Ducrot, C., Fourichon, C., Donald, A., Hurnik, D., 1996. An overview of techniques for dealing with large numbers of independent variables in epidemiologic studies. Prev. Vet. Med. 29, 221±239.
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