Comparison of four regression models for the study of herd risk factors for binomial correlated data

Abstract

THE OBJECTIVES OF THIS STUDY WERE TO COMPARE FOUR LINEAR OR LOGISTIC REGRESSION MODELS AND TO DETERMINE THEIR EFFECTS ON THE LEVEL OF SIGNIFICANCE AND PARAMETER ESTIMATES, USING THE DATA FROM A STUDY ON SEROPREVALENCE OF BRUCELLOSIS IN GOATS. INFORMATION ON 5 114 DOES TESTED DURING 2002-2003 FROM 79 HERDS IN THE BAJIO REGION IN MICHOACAN, MEXICO WAS USED. THE MODELS WERE: THE PREVALENCE OF SEROPOSITIVE ANIMALS PER HERD (V1), ANALYZED BY A GENERAL LINEAR MODEL (GLM), HERDS WITH AT LEAST ONE SEROPOSITIVE ANIMAL, ANALYZED BY STANDARD LOGISTIC REGRESSION (SLRH); V1 ANALYZED BY STANDARD LOGISTIC REGRESSION (SLR), ASSUMING INDEPENDENCE AMONG RESULTS WITHIN A SAME HERD (SLRA); AND V1 ANALYZED BY MIXED LR, CONSIDERING THE HERD AS RANDOM EFFECT (MLR). THE RISK FACTORS INCLUDED IN THE FOUR MODELS WERE: THE PRESENCE OF ABORTIONS THE YEAR PREVIOUS TO THE STUDY, CLEANNESS OF THE CORRAL (HYGIENE) AND LENGTH OF LACTATION. THE V1 VARIABLE TRANSFORMED TO ARCSINE-SQUARE ROOT DID NOT SHOW A NORMAL DISTRIBUTION. SLRH MODEL (SLR ASSUMING THE HERD AS THE UNIT OF INTEREST) AND MLR WERE NOT COMPARED BECAUSE THEY WERE NOT NESTED MODELS. MLR MODEL ADJUSTED THE DATA BETTER THAN THE SLRA MODEL. THE DEVIANCE (-2LL) FROM MODEL SLRH (70.6) WAS SIMILAR TO THEIR DEGREES OF FREEDOM (75), SUGGESTING THAT THE MODEL ADJUSTED THE DATA VERY WELL. LEVELS OF SIGNIFICANCE FOR THE RISK FACTORS WERE DIFFERENT, DEPENDING OF THE MODEL USED. GLM AND SLRH MODELS SHOWED SIGNIFICANT EFFECTS (P < 0.02) ONLY FOR THE PRESENCE OF ABORTIONS; SLRA MODEL SHOWED SIGNIFICANT EFFECT (P < 0.05) FOR THE THREE RISK FACTORS, AND MLR, EFFECTS OF THE PRESENCE OF ABORTIONS AND LACTATION LENGTH, BUT NOT FOR HYGIENE. THE VALUES FOR THE ODD RATIOS (OR) FOR THE SLRA AND MLR MODELS WERE DIFFERENT; THE NARROWEST CONFIDENCE INTERVALS CORRESPONDED TO THE SLRA MODEL, AND THE WIDEST TO THE SLRH MODEL.