PHYSIOLOGY AND REPRODUCTION

PHYSIOLOGY AND REPRODUCTION Evaluation of Logistic Versus Linear Regression Models for Predicting Pulmonary Hypertension Syndrome (Ascites) Using Cold Exposure or Pulmonary Artery Clamp Models in Broilers 1 YVONNE KOCHERA KIRBY,* RONALD W. MCNEW, JOHN D. KIRBY,* and ROBERT F. WIDEMAN JR.*,2 *Department of Poultry Science and Agriculture Statistics Laboratory, University of Arkansas, Fayetteville, Arkansas 72701 ABSTRACT Syndromes such as ascites (pulmonary hypertension syndrome) present difficulties both in the interpretation of associated physiological observations and in their analyses. The ability to predict which physiological variables have the greatest influence on survival or, more importantly, which individuals are most susceptible or resistant to ascites would be very useful selection tools. When addressed in this manner, ascites data become binary data sets (healthy or affected). Binary data can be problematic in that they do not meet all of the assumptions necessary for more traditional analyses such as ANOVA and linear regression. Binary data are discrete and do not have normally distributed errors, which violates a fundamental assumption of linear models. The predictive abilities of linear and logistic regression were evaluated in two replicated experiments using two methods to induce ascites, cold exposure (COLD) and surgical clamping of one pulmonary artery (PAC). The logistic and linear predictive models were derived using the same data and variables. The first data set from PAC and COLD were used to develop the predictive models and the replicate data sets of PAC and COLD were used as test data sets for the prediction of ascites. The linear models developed were complex, using four or five variables and requiring up to seven different measurements. On average, the linear models predicted ascites correctly 87.6% of the time. The logistic models were simple (single variable) models that predicted ascites correctly 92.0% of the time. The variables used in the logistic models were derivations of the ratio of right ventricular weight to total ventricular weight, either corrected for age or the body weight of the bird. Although linear regression predicted the incidence of ascites almost as well as logistic regression did, logistic regression is the more appropriate test statistic to use. (Key words: logistic regression, binary data, ascites, pulmonary hypertension syndrome, chicken) 1997 Poultry Science 76:392 399 INTRODUCTION Ascites, also known as pulmonary hypertension syndrome, is commonly encountered in fast-growing broilers. The ability to predict which individuals are most susceptible or resistant to ascites could be a very useful selection tool. Heritability estimates for susceptibility to ascites range from 0.11 to 0.44 depending on the line of broilers used (Huchzermeyer et al., 1988; Julian et al., 1989; Lubritz et al., 1995). Lubritz et al. (1995) clearly demonstrated that ascites mortality is strongly related to the ratio of right ventricular weight to total ventricular weight (RV:TV), and that phenotypic and genotypic Received for publication July 29, 1996. Accepted for publication October 27, 1996. 1Published as Arkansas Agricultural Experiment Station Manuscript Number 96078 with the approval of the Experiment Station Director. 2To whom correspondence should be addressed: Department of Poultry Science, O-402 Poultry Science Center, University of Arkansas, Fayetteville, AR 72701. correlation coefficients involving these two variables are significant (P < 0.0001), ranging from 0.43 to 0.54 and 0.46 to 0.78, respectively. Shlosberg et al. (1996) showed that broilers with high hematocrit values have an increased chance of developing ascites when exposed to cold temperatures and suggested that hematocrit values might be a useful selection tool. In addition to selection programs involving the RV:TV ratio and hematocrit, the electrocardiogram (ECG) lead II R-S wave amplitude has been identified by Odom et al. (1991) as a potential tool for identifying 1-wk-old birds that are predisposed to developing ascites. Wideman and Kirby (1996) likewise found a strong positive relationship between lead II S wave amplitude and the RV:TV ratio. Selection pressure for increased growth rate in broilers has produced a bird that has a greater oxygen demand and is more susceptible to ascites (Wideman, 1988; Julian et al., 1989). Ascitic birds have a lower percentage saturation of hemoglobin with oxygen than nonascitic birds (Peacock et al., 1990; Julian and Mirsalimi, 1992; Wideman and Kirby, 1995a). 392

PREDICTIVE MODEL FOR ASCITES 393 TABLE 1. Incidence of ascites by induction method and replicate trial (T). Ascites induced by pulmonary artery clamp (PAC) in T1 and T2 and by cold exposure (COLD) in T3 and T4 PAC 3Criticare Systems, Inc., Milwaukee, WI 53226. COLD Birds T1 T2 T3 T4 Total 37 58 55 41 Nonascites birds 12 4 40 36 Ascitic birds 25 54 15 5 Percentage ascites 67.6 93.1 27.3 12.2 A predictive model for assessing the susceptibility of individuals prone to developing ascites has not been developed. This is in part due to an incomplete understanding of the physiological changes that occur during the development of ascites as well as the difficulties associated with analyzing binary data sets (healthy or affected). Binary data can be problematic in that they typically do not meet all of the assumptions necessary of more familiar statistical analyses such as ANOVA and linear regression. Binary data are discrete and do not have normally distributed errors, which violates a fundamental assumption of linear models. Logistic regression provides a more appropriate method of statistically analyzing binary data sets. In the present study, the abilities of logistic and linear regression to predict susceptibility to ascites in subclinical individuals were evaluated using data obtained from broilers subjected to two experimental methods known to trigger ascites: cold stress (Lubritz and McPherson, 1994; Lubritz et al., 1995; Julian et al., 1989; Wideman et al., 1995a,b) and the surgical clamping of one pulmonary artery (Wideman and Kirby, 1995a). MATERIALS AND METHODS Male by-product chicks of a Hubbard breeder pullet line were used in replicated experiments designed to induce ascites. Two experiments (T1, n = 37 birds; T2, n = 58 birds) were conducted in which the left pulmonary artery was clamped (PAC) to induce ascites, and two experiments (T3, n = 55 birds; T4, n = 41 birds) were conducted in which cold exposure (COLD) was used to induce ascites. The birds were obtained from three hatches separated in time by approximately 1 yr. Chicks from the same hatch were used for T2 and T3. Birds were reared in environmental chambers on clean rice hull litter and brooded at 32 C for 1 wk. Between Days 7 and 15, the temperature was gradually reduced to 27 C. On Day 16, and until the end of each trial, COLD birds were maintained at 16 C whereas the PAC birds were kept at 24 C. The PAC surgery was performed at 15 to 19 d of age, as described by Wideman and Kirby (1995a). Briefly, birds were anesthetized to a surgical plane, the thoracic inlet was opened, and the left pulmonary artery was clamped. Birds recovered under a heat lamp for 2 to 4 h and then they were returned to the environmental chamber. Birds that died within the first 5 d following the PAC surgery were excluded from the experiment. All birds were fed commercial corn-soybean meal broiler starter (Days 1 to 20), grower (Days 21 to 41), and finisher (Days 42 to the end of experiment) diets that met or exceeded NRC (1984) standards. Feed and water were provided for ad libitum consumption. Within each trial, birds were weighed on Day 1 and at weekly intervals thereafter. Chicks were culled on Day 1 if they weighed less than 40 g or had wet navels. Birds with leg defects were culled throughout the experiment. The following initial (I) measurements were taken at either 15 or 21 d of age, depending on the experiment: hematocrit (HCTI), electrocardiogram (ECG) (lead II R-S wave amplitude: ECGI; lead II S wave amplitude: SI), and heart rate (beats per minute, HRI). A pulse oximeter3 was used for noninvasive measurements of percentage saturation of hemoglobin with oxygen (O2I) (Peacock et al., 1990; Julian and Mirsalimi, 1992; Wideman and Kirby 1995a). The last (L) oximetry readings (O2L), body weights (BWL), hematocrits (HCTL), heart rate (HRL), and electrocardiograms (lead II R-S wave amplitude: ECGL; lead II S wave amplitude: SL) were obtained from individual broilers as soon as clinical ascites became evident, or prior to the final necropsy for broilers that survived to the end of the experiment. All birds that died during an experiment were necropsied, as were birds that survived to the end of the experiment. The RV:TV ratios and the age of the bird (AGE) were recorded. Birds were categorized as ascitic only when they exhibited abdominal fluid accumulation (ascites). The nonascitic category included birds that died from sudden death syndrome or unknown causes, as well as birds that developed some of the symptoms associated with preascites (right ventricular hypertrophy and dilation, vascular congestion, hypoxemia) but did not have abdominal fluid accumulation. During necropsies of PAC broilers, the clamp was examined to determine whether its jaws tightly occluded the entire width of the pulmonary artery and could prevent a small probe from passing from the right ventricle through the artery. Only data from birds with a fully clamped pulmonary artery were included in the statistical analyses for T1 and T2. All data sets were analyzed using the regression, logistic, and frequency procedures in SAS (SAS Institute, 1994). Linear regression and logistic regression both with the stepwise option, were used in the first data set of PAC and COLD (T1 and T3) to derive a statistical equation that would be useful for predicting ascites. The a-levels of significance for including and excluding variables in the stepwise model-fitting procedure were set at 0.3 and 0.15, respectively. The necropsy result, nonascitic or ascitic (NEC = 0 or 1), was regressed on all possible variables. Using the derived models and the frequency procedure in SAS, ascites was predicted

394 KIRBY ET AL. TABLE 2. Variables considered for both logistic and linear regression analyses in creating a predictive model for ascites using data sets in which ascites was induced using pulmonary artery clamp or cold exposure treatments Acronym Variable considered BW1 Body weight (grams) at Day 1 BW7 Body weight (grams) at Day 7 BW14 Body weight (grams) at Day 14 BW21 Body weight (grams) at Day 21 BW28 Body weight (grams) at Day 28 BW35 Body weight (grams) at Day 35 BW42 Body weight (grams) at Day 42 BW49 Body weight (grams) at Day 49 BW56 Body weight (grams) at Day 56 BWL Last body weight (grams) available prior to death BW17 One-week weight gain (grams) BW114 Two-week weight gain (grams) (gain prior to surgery in PAC birds) BW121 Three-week weight gain (grams) BW128 Four-week weight gain (grams) BW1421 Weight gain (grams) from Day 14 through Day 21 (gain following surgery in PAC birds) HCTI Hematocrit at Day 15 or 21 (percentage) HCTL Last hematocrit taken prior to death (percentage) DHCT Change in hematocrit (HCTL HCTI) (percentage) ECGI Electrocardiogram, lead II R-S amplitude (millivolts) at Day 15 or 21 ECGL Last electrocardiogram, lead II R-S amplitude (millivolts) available prior to death DECG Change in electrocardiogram, lead II R-S amplitude (millivolts) (ECGL ECGI) SI Electrocardiogram, lead II S amplitude (millivolts) at Day 15 or 21 SL Last electrocardiogram, lead II S amplitude (millivolts) available prior to death DS Change in electrocardiogram, lead II S amplitude (millivolts) (SL SI) O21 Percentage saturation of hemoglobin with oxygen at Day 15 to 21 (percentage) O2L Last available measurement of percentage saturation of hemoglobin with oxygen prior to death (percentage) DO2 Change in percentage saturation of hemoglobin with oxygen (O2L O2I) HRI Heart rate (beats per minute) of bird at Day 15 to 21 HRL Last heart rate (beats per minute) of bird available prior to death DHR Change in heart rate (beats per minute, HRL HRI) AGE Age of bird (days) when necropsied RV:TV Ratio of right ventricular weight to total ventricular weight (no units) RVTVAGE Ratio of RV:TV divided by AGE (no units) RVTVBW Ratio of RV:TV divided by BWL (no units) where the predicted model value for a bird was greater than 0.5; conversely, values less than 0.5 were determined to be nonascitic. The second experiment of PAC and COLD (T2 and T4) was then used as a test data set for each of the linear and logistic models developed from T1 and T3. Differences between the predictive abilities of linear and logistic regression were analyzed using the McNemar test for significant changes along with William s correction factor (Sokal and Rohlf, 1995). RESULTS The incidence of ascites in each trial is presented in Table 1. The variables considered for both the logistic and linear analyses are shown in Table 2. The most promising variables or combinations thereof were the O2L, ECG lead II S wave variables SL and DS, HCTI, BWL, RV:TV, RVTVAGE, and RVTVBW. The best linear models derived from T1 and T3, LIN1 and LIN3, respectively, are shown in Table 3. The LIN1 and LIN3 account for 81.2 and 86.6% of the variation in the necropsy results, respectively. The best regression equations developed using logistic regression were single-variable models (Table 4). LOGAGE1 was developed using T1 and uses the variable RVTVAGE. LOGBW3 was derived using T3 and includes the variable RVTVBW. RVTVAGE and RVTVBW are highly correlated (Table 5); thus, both variables were taken into consideration for potential use in the models for T1 and T3. The two new models are referred to as LOGBW1 and LOGAGE3 (T1 using RVTVBW and T3 using RVTVAGE, respectively). The TABLE 3. Best linear models derived from trials T1 and T3 for the prediction of ascites 1 Data set Model Regression equation R 2 T1 LIN1 Y ijklm = 0.434 + 0.0263(HCTI) (0.0136(O2L) 1.331(DS) + 134.7(RVTVAGE) + 1.938(SL) 0.812 T3 LIN3 Y ijkl = 4.219 0.000349(BWL) 0.0029(HRL) 0.0139(HCTI) 0.078(O2L) 0.866 1HCTI = hematocrit at Day 15 or 21 (percentage); SL = last electrocardiogram, lead II S wave amplitude (millivolts) available prior to death; O2L = last percentage saturation of hemoglobin with oxygen available prior to death (percentage); RVTVAGE = ratio of right ventricular weight to total ventricular weight divided by the age of bird at time of necropsy (no units); DS = change in electrocardiogram, lead II S wave amplitude (millivolts) between SI and SL; BWL = last available body weight prior to death (grams); HRL = last heart rate available prior to death (beats per minute).

PREDICTIVE MODEL FOR ASCITES 395 TABLE 4. Best logistic models derived from trials T1 and T3 for the prediction of ascites 1 Data Predicted set Model Regression equation correctly (%) T1 LOGBW1 Y i = 11.626 + 45244.0(RVTVBW) 89.2 LOGAGE1 Y i = 13.165 + 1608.6(RVTVAGE) 89.2 T3 LOGBW3 Y i = 12.531 + 88716.6(RVTVBW) 94.5 LOGAGE3 Y i = 17.435 + 2107.5(RVTVAGE) 90.9 1RVTVAGE = ratio of right ventricular weight to total ventricular weight divided by the age of bird at time of necropsy (no units); RVTVBW = ratio of right ventricular weight to total ventricular weight divided by the last available body weight prior to death (no units). odds ratio for each of the four models were the same: 999.0 for the variable of interest. The percentage predicted correctly ranged from 89.2% in both of the T1 models to 90.9 and 94.5% in the T3 models. Given the similarity in results and the strong correlation between the variables on which the models are based (RVTVBW and RVTVAGE), both models were kept in this analysis. The mean value of each variable identified as a significant contributor to a bird s necropsy result, using either logistic or linear regression, is presented in Table 6. In T3, ascitic birds were significantly different from nonascitic birds for each variable (P < 0.002 for HCTI and P < 0.001 for all other variables). The SL, DS, and HRL in T1 are the only variables for which ascitic and nonascitic birds do not differ significantly, whereas significant differences were obtained for the remaining variables (P < 0.009 or greater). Each variable (O2L, BWL, HCTI, HRL, SL, DS, RVTVBW, and RVTVAGE) was subsequently used to develop two single-variable linear regression equations, one from T1 and the other from T3 (Table 7). The regression equations were then used to predict which birds were ascitic or nonascitic in all four data sets. RVTVAGE was able to predict the incidence of ascites correctly over 91.9% of the time. The comparisons of each linear model to the logistic models developed from T1 (PAC stressor) are shown in Figure 1. The predictive abilities for LIN1, LOGBW1, and LOGAGE1 ranged from 86.2 to 94.5%, 89.1 to 93.1%, and 91.9 to 98.3%, respectively. LOGAGE1 predicted ascites as well or better than LOGBW1 in all data sets. TABLE 5. Pearson correlation coefficient for RVTVBW and RVTVAGE in each data set 1 Pearson Data correlation P set coefficient value T1 0.8625 0.001 T2 0.8880 0.001 T3 0.9658 0.001 T4 0.9050 0.001 1T = trial; RVTVBW = ratio of right ventricular weight to total ventricular weight divided by the last available body weight prior to death (no units); RVTVAGE = ratio of right ventricular weight to total ventricular weight divided by the age of bird at time of necropsy (no units). The predictive ability of LOGAGE1 was equal to or better than LIN1 in three out of four trials, and LOGAGE1 did a significantly (P < 0.005) better job of predicting ascites or nonascites birds in T2. When data from the four trials were combined, LOGAGE1 did the best overall job (P < 0.062) of predicting ascites, 94.8% correct, compared to LIN1 at 90.6% correct. The models developed using T3, COLD exposure, (Figure 2) were more variable in their predictive abilities. LIN3 predicted 62.2 to 96.4% correctly. LOGBW3 predicted over 90% of the birds correctly in each trial with the exception of T1, in which it was correct 73% of the time. Again, the model using RVTVAGE, LOGAGE3, predicted greater than 90% correctly (91.9 to 98.3%) in all trials. LIN3, developed using COLD, tended to predict ascites in T3 and T4 more accurately (1.9 and 2.4%, respectively) than any of the logistic models; however, this difference was not statistically significant (P > 0.50). Across all trials, LOGAGE3 did the best overall job predicting, and LOGAGE3 was significantly better than LIN3 in T1, T2, and when the four trials were pooled (P < 0.005, P < 0.01, and P < 0.005, respectively). DISCUSSION The pathophysiological progression leading to terminal ascites typically has been monitored through sequential changes in individual diagnostic indices, such as those associated with primary cardiac changes triggered by pulmonary hypertension (ECG, RVTV, HR), the extent of blood oxygenation (HCT, O2), or growth dynamics (BW) (see Introduction). Most evidence indicates that these indices cannot reliably be used to predict subclinical ascites susceptibility unless broilers are subjected to an appropriate inducing challenge. For example, it was demonstrated that the ECG lead II S wave amplitude is not predictive of the RV:TV ratio until after pulmonary hypertension had been initiated using the PAC surgical protocol (Wideman and Kirby, 1996). In this context, data from control or shamoperated broilers maintained under optimal conditions are not considered useful for predicting ascites susceptibility (Wideman and Kirby, 1996). The present study

396 KIRBY ET AL. TABLE 6. Variables that were identified for use in either linear or logistic regression and their mean values for normal and ascitic birds with associated P values for differences between normal and ascitic birds 1 Mean value T1 Mean value Variable Ascitic Nonascitic P value Ascitic Nonascitic P value HCTI, % 39.1 34.3 0.009 39.1 36.4 0.002 SL, mv 0.30 0.23 0.116 0.32 0.13 0.001 DS, mv 0.17 0.17 0.980 0.28 0.09 0.001 O2L, % 62.9 70.1 0.005 62.0 80.0 0.001 BWL, g 1,032.3 2,009.9 0.001 1,919.5 3,158.8 0.001 HRL, bpm 378.0 375.0 0.816 353.6 393.1 0.001 RVTVAGE 0.01255 0.00614 0.001 0.01171 0.00554 0.001 (no units) RVTVBW 0.000488 0.0001822 0.001 0.000264 0.0000865 0.001 (no units) 1T = trial; HCTI = hematocrit at Day 15 to 21 (percentage); SL = last electrocardiogram, lead II S wave amplitude (millivolts) available prior to death; O2L = last percent saturation of hemoglobin with oxygen available prior to death (percentage); DS = change in electrocardiogram, lead II S wave amplitude (millivolts) between SI and SL; BWL = last available body weight prior to death (grams); HRL = last heart rate available prior to death (beats per minute); RVTVAGE = ratio of right ventricular weight to total ventricular weight divided by the age of bird at time of necropsy (no units); RVTVBW = ratio of right ventricular weight to total ventricular weight divided by the last available body weight prior to death (no units). T3 represents an original approach to simultaneously assessing multiple pathophysiological indices in broilers subjected to the PAC or COLD models. It is under these conditions, which trigger dynamic changes even in resistant broilers, that those independent and combined indices that are most highly predictive of ascites susceptibility are likely to be revealed. Initial examination of the six models (two linear and four logistic) revealed that the models developed using logistic regression were simple, single-variable models that correctly predicted ascites, on average, 92% of the time. The variables of interest in all four logistic models were derivations of RV:TV. This variable appears to have considerable biological relevance, in that an elevated RV:TV ratio results from hypertrophy of the right ventricle and is associated with primary pulmonary hypertension (Burton et al., 1968; Peacock et al., 1989, 1990; Julian and Mirsalimi, 1992; Wideman and Bottje, 1993). In addition to selecting a variable with considerable biological meaning, statistically, the models fit their data quite well. Logistic models do not use R2 as a measure TABLE 7. Use of each parameter identified via logistic or linear regression as a single independent variable to develop a linear regression equation to predict necropsy results 1 Predicted correctly in each trial Data set model Variable developed from T1 T2 T3 T4 Regression equation R 2 O2L T1 59.5 75.9 94.5 95.1 NEC = 2.697 0.0315 O2L 0.227 T3 59.5 70.7 90.9 95.1 NEC = 3.020 0.0366 O2L 0.659 BWL T1 86.5 91.4 85.5 90.2 NEC = 1.422 0.00055 BWL 0.541 T3 73.0 91.4 89.1 92.7 NEC = 1.714 0.00051 BWL 0.633 HCTI T1 67.6 81.0 32.7 73.2 NEC = 0.773 + 0.0384 HCTI 0.186 T3 51.4 43.1 74.5 87.8 NEC = 2.064 + 0.0629 HCTI 0.167 HRL T1 67.6 91.4 27.3 9.8 NEC = 0.498 + 0.00047 HRL 0.002 T3 45.9 34.5 80.0 95.1 NEC = 2.743 0.0065 HRL 0.256 SL T1 67.6 84.5 69.1 80.5 NEC = 0.338 1.1243 SL 0.076 T3 48.6 43.1 81.8 90.2 NEC = 0.076 1.9283 SL 0.381 DS T1 59.5 81.0 29.1 14.6 NEC = 0.650 + 0.0190 DS 0.000 T3 32.4 12.1 81.8 90.2 NEC = 0.030 2.130 DS 0.395 RVTVBW T1 89.2 93.1 89.1 92.7 NEC = 0.174 + 1289.974 RVTVBW 0.395 T3 59.5 93.1 90.9 95.1 NEC = 0.269 + 4009.958 RVTVBW 0.713 RVTVAGE T1 91.9 98.3 92.7 92.7 NEC = 0.207 + 84.291 RVTVAGE 0.541 T3 94.6 96.6 94.5 92.7 NEC = 0.594 + 120.030 RVTVAGE 0.740 1O2L = last percentage saturation of hemoglobin with oxygen available prior to death (percentage); BWL = last available body weight prior to death (grams); HCTI = hematocrit at Day 15 or 21 (percentage); HRL = last heart rate available prior to death (beats per minute); SL = last electrocardiogram, lead II S wave amplitude (millivolts) available prior to death; DS = change in electrocardiogram, lead II S wave amplitude (millivolts) between SL and SI; RVTVAGE = ratio of right ventricular weight to total ventricular weight divided by the age of bird at time of necropsy (no units); RVTVBW = ratio of right ventricular weight to total ventricular weight divided by the last available body weight prior to death (no units).

PREDICTIVE MODEL FOR ASCITES 397 FIGURE 1. Comparison of the abilities of logistic and linear regression models to correctly predict development of ascites. The models derived using trial data set T1 (linear regression model LIN1, logistic regression models LOGAGE1 and LOGBW1) were applied to each of four data sets, T1, T2, T3 and T4, and then to the four data sets combined, POOLED. Ascites was induced in data sets T1 and T2 using a clamp on the left pulmonary artery, and in data sets T3 and T4 using cold exposure. The results are presented as the ability of the model to correctly predict the development of ascites or no ascites for each bird within a data set. Within a trial, models with no common letters indicate significant differences (P < 0.005). An asterisk indicates the difference between models approached significance (P < 0.062). of explained variation; instead they use the odds ratio. The odds ratio is the ratio of the odds of having ascites for one value of X to the odds of having ascites at X 1 {odds = [P(ascites)/P(no ascites)]}, as explained elsewhere in greater detail (Hosmer and Lemeshow, 1989). In all of the logistic models selected, the odds ratio for the parameter of interest was more than 999.0 (the maximum odds ratio presented for PC SAS Version 6.08, is 999.0). This ratio suggests that the selected variable was a good predictor of ascites. In comparison to the logistic models, the linear regression models were much more complex. Each model involved collecting data for four or five variables and at several time points. Not all of the variables for the two linear models were the same. Based on these data sets, the investigator would have to collect data for at least seven variables (HCTI, O2L, DS, SL, BWL, HRL, and RVTVAGE). Not all of the variables in the linear models seem to have as much biological meaning as other variables available. This is partially supported by the inconsistency between R2 and the predictive abilities of the models. For instance, the adjusted R2 for LIN1 and LIN3 were 0.776 and 0.855, respectively; hence, one would assume that LIN3 would be the more powerful model. Nevertheless, this was not the case. One possible reason for this peculiarity may be that LIN3 did not include RV:TV, or any derivations of RV:TV, a variable that has been shown to be strongly related to ascites. However, LIN1 did include RVTVAGE in its model and LIN1 predicted ascites with almost 5% greater accuracy than did LIN3. Of the seven different variables that would need to be collected for LIN1 and LIN3, only two, HCTI and O2L, were used in both models. Inclusion of O2L, BWL, and derivations of lead II S wave ECG are in agreement with other published reports identifying growth rate, inability of the bird to oxygenate its blood, increased S wave amplitude, and higher hematocrits (Julian et al., 1989; Odom et al., 1991, 1992; Lubritz and McPherson, 1994; Wideman and Kirby, 1995a,b; Wideman and Kirby, 1996). An association between heart rate and ascites is plausible, to the extent that an elevated heart rate is associated with the elevated cardiac output required to support the metabolic demands of fast-growing broilers (Wideman and Kirby, 1995b). It was surprising that HCTI was incorporated in both linear models, rather than HCTL or DHCT. Physiologically, it is the increase in hematocrit associated with pulmonary hypertension syndrome and systemic hypoxemia that has been used as an indicator of ascites susceptibility in several previous studies (Lubritz and McPherson, 1994; Wideman and Kirby, 1995a; Shlosberg et al., 1996). The

398 KIRBY ET AL. FIGURE 2. Comparison of the abilities of logistic and linear regression models to correctly predict development of ascites. The models derived using data set T3 (linear regression model LIN3, logistic regression models LOGAGE3 and LOGBW3) were applied to each of the four data sets, T1, T2, T3 and T4, and then to the four data sets combined, POOLED. Ascites was induced in data sets T1 and T2 using a clamp on the left pulmonary artery, and in data sets T3 and T4 using cold exposure. The results are presented as the ability of the model to correctly predict the development of ascites or no ascites for each bird within a data set. Within a trial, models with no common letters indicate significant differences (P value indicated on graph). An asterisk indicates the difference between models approached significance (P < 0.057). differences between ascitic and normal birds for the first hematocrit measurement were significant for T1 and T3 (P < 0.009 and P < 0.002, respectively). It would be worthwhile to examine whether hematocrits, prior to stress, would enter into the predictive equation as well as to find out how soon after stress is introduced, that the variable becomes important. Interestingly, when these variables were used to develop single-variable linear regression equations, either using T1 or T3 data, only RVTVAGE predicted over 91.9% correctly in all four data sets. This variable was not selected for use in either LIN1 or LIN3. Other than the variables using derivations of RV:TV, BWL was the only other singlevariable linear model that correctly predicted the occurrence of ascites or nonascites at a high rate, over 87% on average. Overall, in comparison to the logistic models, the only time that the linear models did a better (but not significantly better) or equivalent job of predicting ascites was when the ascites stressor was COLD, and then the margin was less than 5.5% (T3, using LOGBW1). In contrast, both logistic models averaged 11.6% better than LIN1 or LIN3 in each of the PAC models, with an extreme value of 30% better in T1. The models using RVTVAGE did the best overall job of correctly predicting ascites or nonascites, LOGAGE3 was significantly better than LIN3 (P < 0.005), and the difference between LOGAGE1 and LIN1 approached significance (P < 0.062). In addition to analyzing the outcome of the direct comparisons between linear and logistic regression, it is important to note that both methods of developing predictive equations have several benefits. Linear regression is easy to use in that it is familiar and accessible in a wide array of statistical analysis software programs. Furthermore, R2 provides a good measure of explained variation that is easily recognizable. Unfortunately, the assumptions of ANOVA, normally distributed errors and continuous variables, must be genuine in order for R2 to be meaningful. Two substantial benefits for using logistic regression on binary data sets are that the binomial distribution is accounted for (variances need not be homogeneous) and an inherent restriction exists that the probability estimates will be between 0 and 1. Collectively, the linear and logistic models predicted ascites correctly at least 85% of the time, with the exception of T1 models LIN3 and LOGBW3. The linear models predicted the incidence of ascites more accurately in COLD data sets than in PAC data sets. In comparison, the logistic models, which provide a more

PREDICTIVE MODEL FOR ASCITES 399 appropriate test statistic, predicted the incidence of ascites equally well in both ascites models, COLD and PAC. This suggests that the pathophysiological events leading up to ascites are similar in both PAC and COLD models. The predictive abilities of the logistic models, especially when using the variable RVTVAGE, are an improvement over the linear models: only one variable and one regression equation are needed. Two objectives were addressed in the present study. First, linear and logistic regression were evaluated as statistical approaches for assessing binary data. In this context, logistic regression offered several advantages, as indicated above. The second objective was to develop a model for predicting susceptibility to ascites in subclinical individuals, prior to the onset of terminal symptoms. To our knowledge, this is the first published account of using logistic regression analysis to create a predictive model for ascites. A model of this type would be useful as a research tool for segregating and then comparing the physiological and genetic characteristics of clinically healthy susceptible and resistant broilers. The same predictive model might prove useful within the selection programs of commercial poultry breeders. In the present study, many of the criteria identified by both linear and logistic models unfortunately were terminal criteria, including indices such as AGE and RV: TV. However, further refinements in the timing and circumstances under which noninvasive criteria, such as percentage saturation of hemoglobin with oxygen and ECG values, are obtained may improve our ability to develop entirely noninvasive strategies for categorizing the relative ascites susceptibility of apparently healthy broilers. REFERENCES Burton, R. R., E. L. Besch, and A. H. Smith, 1968. Effect of chronic hypoxia on the pulmonary arterial blood pressure of the chicken. Am. J. Physiol. 214:1438 1442. Hosmer, D. 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