Ian R. Dohoo

An overview of techniques for dealing with large numbers of independent variables in epidemiologic studies

Many studies of health and production problems in livestock involve the simultaneous evaluation of large numbers of risk factors. These analyses may be complicated by a number of problems including: multicollinearity (which arises because many of the risk factors may be related (correlated) to each other), confounding, interaction, problems related to sample size (and hence the power of the study), and the fact that many associations are evaluated from a single dataset. This paper focuses primarily on the problem of multicollinearity and discusses a number of techniques for dealing with this problem. However, some of the techniques discussed may also help to deal with the other problems identified above. The first general approach to dealing with multicollinearity involves reducing the number of independent variables prior to investigating associations with the disease. Techniques to accomplish this include: (1) excluding variables after screening for associations among independent variables; (2) creating indices or scores which combine data from multiple factors into a single variable; (3) creating a smaller set of independent variables through the use of multivariable techniques such as principal components analysis or factor analysis. The second general approach is to use appropriate steps and statistical techniques to investigate associations between the independent variables and the dependent variable. A preliminary screening of these associations may be performed using simple statistical tests. Subsequently, multivariable techniques such as linear or logistic regression or correspondence analysis can be used to identify important associations. The strengths and limitations of these techniques are discussed and the techniques are demonstrated using a dataset from a recent study of risk factors for pneumonia in swine. Emphasis is placed on comparing correspondence analysis with other techniques as it has been used less in the epidemiology literature.

Associations between passive immunity and morbidity and mortality in dairy heifers in Florida, USA

n Abstractn n A prospective cohort study was undertaken to determine calf-level factors that affected calf health status between birth and 6 months of age. A convenience sample of approximately 3300 female Holstein calves born in 1991 on two large Florida dairy farms was used for the study. Data collected on each calf at birth included farm of origin, weight, height at the pelvis, birth date, and serum total protein (a measure of colostral immunoglobulin absorption). Birth season was dichotomized into summer and winter using meteorological data collected by University of Florida Agricultural Research Stations. Health data including date of initial treatment and number of treatments were collected for the diseases diarrhea, omphalitis, septicemia and pneumonia. All calves were followed for 6 months. Cumulative incidences of mortality and occurrence of diarrhea, omphalitis, septicemia and pneumonia were 0.12, 0.35, 0.11, 0.24 and 0.21, respectively. Serum total protein (TP) was a significant risk factor for mortality. The association of TP and mortality was quadratic and showed a dramatic decrease in mortality as TP increased from 4.0 to 5.0 g/dl, a small improvement from 5.0 to 6.0 g/dl and virtually no improvement in mortality rates as TP increased over 6.0 g/dl. The hazard mortality ratio was constant from birth to six months, indicating that the increased risk of mortality associated with low levels of TP was evident through six months of age. No interactions between TP, farm, season, or birth weight were found in these analyses. Serum total protein concentration was a significant risk factor for the occurrences, age of onset and severity of septicemia and pneumonia. The association between TP and septicemia was linear and an interaction with birth season was found. The association between TP and pneumonia was quadratic, and in contrast to the TP-and-septicemia relationship, the morbidity hazard ratio for pneumonia was not constant over the time measured; that is, colostral immunity protected the calf from developing pneumonia early in life, but this effect disappeared as the calf got older. Total protein was not a significant risk factor for diarrhea or omphalitis.n n

Calf and disease factors affecting growth in female holstein calves in Florida, USA

A prospective cohort study was undertaken to determine calf-level factors that affect performance (growth) between birth and 14 months of age in a convenience sample of approximately 3300 female Holstein calves born in 1991 on two large Florida dairy farms. Data collected on each calf at birth included farm of origin, birth date, weight, height at the pelvis, and serum total protein (a measure of colostral immunoglobulin absorption). Birth season was dichotomized into summer and winter using meteorological data collected by University of Florida Agricultural Research Stations. Data collected at approximately 6 and 14 months of age included age, weight, height at the pelvis, and height at the withers. Growth in weight and stature (height) was calculated for each growth period; growth period 1 (GP1) = birth to 6 months, and growth period 2 (GP2) = 6 to 14 months. Health data collected included data of initial treatment and number of treatments for the diseases diarrhea, omphalitis, septicemia, pneumonia and keratoconjunctivitis. After adjusting for disease occurrence, passive transfer of colostral immunoglobulins had no significant effect on body weight gain or pelvic height growth. Season of birth and occurrence of diarrhea, septicemia and respiratory disease were significant variables decreasing heifer growth (height and weight) in GP1. These variables plus farm, birth weight and exact age when 6 month data were collected explained 20% and 31% of the variation in body weight gain and pelvic height growth, respectively, in GP1. The number of days treated for pneumonia before 6 months of age significantly decreased average daily weight gain in GP2 (P < 0.025), but did not affect stature growth. Treatment for pneumonia after 6 months of age did not significantly affect weight or height gain after age 6 months. Neither omphalitis nor keratoconjunctivitis explained variability in growth in either of the growth periods.

Age pattern of mortality in eight breeds of insured dogs in Sweden

The objective of this study was to use several methods to describe the age patterns for risk of death in selected breeds of dogs insured for life in a Swedish animal-insurance company in 1996. Data on eight breeds were analyzed for age at death (including euthanasia). If dogs left the insurance for reasons other than death, they were regarded as censored. Dogs were only insured up to 10 years of age. Four analytical approaches were used. First, descriptive statistics of age distributions (e.g. breed-specific median ages at death, breed- and age-specific mortality risks) were computed. Second, age-specific estimates of survival were calculated using the formula: survival=(1-risk(age<1 year))(1-risk(age 1<2 year))... (1-risk(age 9<1 0 year)). Third, Cox regression (proportional-hazards model) was used to estimate survival and hazard functions. Finally, hierarchically coded Poisson regression was used to determine age-specific cut-points in the risk of death. The hazards from Cox and the incidence-density rates from the hierarchically coded models were transformed to estimates of risk: risk=1-exp¿-(hazard)¿ or 1-exp¿-(incidence-density rate)¿. The breeds studied were Beagle, Bernese mountain dog, Boxer, Cavalier King Charles spaniel, Drever, German shepherd dog, Mongrel and Poodle, together representing over 50000 dogs each year. The yearly breed-specific mortality risk varied between 1.7% (Poodle) and 6.5% (Bernese mountain dog). In all breeds, the risk of death increased with age but the pattern varied by breed. The probability of survival at 5 years of age varied between 94% (Cavalier King Charles spaniel and Poodle) and 83% (Bernese mountain dog, Drever, German shepherd dog) and the survival at 10 years between 83% (Poodle) and 30% (Bernese mountain dog). The survival estimates from Cox and those derived using the combined-risk formula were similar. The cut-point risk estimates provided a simplified picture of when the risk of death changed significantly compared to previous age categories. As anticipated, breeds differed widely in survival up to 10 years of age and there were marked differences in age patterns of mortality. The implications of these findings should be considered in multivariable analyses, where the confounding effect of age is often controlled for using a single age variable common to several breeds.

Evaluation of anti-Ostertagia ostertagi antibodies in individual milk samples as decision parameter for selective anthelmintic treatment in dairy cows

The aim of this study was to explore whether anti-Ostertagia ostertagi antibody levels measured by ELISA in individual milk samples hold promise as a decision parameter for either herd-level decisions or selective anthelmintic treatments by investigating (1) the relationship between individual and bulk-tank milk ELISA results; (2) the relationships of individual milk ELISA results with non-parasitic cow factors and (3) the relationship between individual milk ELISA results and the milk production response after anthelmintic treatment. Twelve farms were randomly allocated to a whole-herd treatment with eprinomectin or a placebo in October 2004 and individual milk samples and a bulk-tank milk sample were collected 1 month before and 1 month after treatment. Linear mixed models were used to investigate the associations of ELISA results with (a) breed, actual milk production, lactation stage, somatic cell count, age and sampling month and (b) the milk production response after anthelmintic treatment. There was a reasonable correlation between the mean individual and bulk-tank milk ELISA results (r=0.72). Individual cow ELISA results increased with higher lactation number and were lower in November than September. The associations with the other non-parasitic factors were weak and not significant. Milk yield responses to anthelmintic treatment were greater when treatment was given in early lactation and increased with the pre-treatment ELISA result and cow age. However, these latter two interaction terms were not significant when they were put in the model together. We conclude that (1) O. ostertagi ELISA results from individual milk samples may provide more information on the herds parasitic status than a single bulk-tank milk result; (2) lactation number should be taken into account when interpreting ELISA results from individual milk samples and (3) the value of the O. ostertagi antibody level in individual cow milk samples to predict individual production responses after anthelmintic treatment remains equivocal.

Risk factors for the between-herd spread of Mycobacterium bovis in Canadian cattle and cervids between 1985 and 1994

Microorganisms of the genus Mycobacterium cause tuberculosis in many animal species including humans. Generally, Mycobacterium bovis (M. bovis) infects cattle and cervids, but it has the potential to infect virtually all species of mammals. This study examined and analysed the data from the nine outbreaks of tuberculosis in Canadian cattle and cervids from 1985 to 1994. For the purposes of this study, a positive herd was one with at least one culture-positive animal. A reactor herd had at least one animal which was positive or suspicious on a mid-cervical, comparative cervical, or gross or histopathologic test for tuberculosis. Herd classification was either reactor/positive or negative. Data for the study were collected from the outbreak records in the Regional or District offices of Agriculture and Agri-Food Canada. Logistic regression was used to study spread of tuberculosis between herds. Two risk factors were identified: increasing herd size; and, the reason why a herd was investigated as part of the outbreak. This latter factor was interpreted as a surrogate measure for the nature of contact between the study herd and other potentially infected herds in the outbreak. Increasing herd size was associated with an increased risk of being positive for tuberculosis with herds of 16-35, 36-80, and >80 animals having odds ratios of 2.9, 5.8, and 9.3, respectively, when compared to a herd size of <16 animals (p < 0.001). When compared to perimeter testing (i.e. testing herds within a specified radius of an infected herd), all other reasons for investigation had higher odds ratios (p < 0.001). These odds ratios were 57.8 for traceout herds (i.e. herds which had purchased animal(s) from a reactor/positive herd), 31.8 for herds with pasture or fence-line contact with a reactor/positive herd, and 14.9 for traceback herds (i.e. herds which had been a source of animals for reactor/positive herd(s)).

Using pseudogold standards and latent-class analysis in combination to evaluate the accuracy of three diagnostic tests

We previously reported our use of latent-class models to estimate the sensitivity (Se) and specificity (Sp) for each of three tests used to monitor farmed salmon for infectious salmon anaemia virus (ISAv). Those tests were reverse-transcriptase polymerase chain reaction (RT-PCR), virus isolation (VI), and an indirect immunofluorescent-antibody test (IFAT). We used tissues from 403 salmon from four populations presumed to have different prevalence of ISAv. However, no formal evaluation of the assumptions of conditional independence and constant accuracy had been carried out. In our present study, we adjusted that and used two pseudogold standards (a composite reference standard and a study pseudogold), as indicative of the true health status of each fish. The assumption of constant accuracy across populations was evaluated using separate random-effects logistic-regression models for fish classified as D+ or D- (disease positive or negative, according to the pseudogold standards) with study population included in the model to determine if it affected the probability of a positive test result. Where there was evidence of variation in test accuracy across populations, the issue was further investigated using separate latent-class models with informative priors for each study population. Our results suggested that only one PCR test had an accuracy that varied across populations. The assumption of conditional independence among tests was first evaluated using log-linear models of D+ and D- fish with significant interaction between test results indicative of conditional dependence. Latent-class models which incorporated up to two pairs of between-test dependencies were also fit using Bayesian methods. The two approaches showed considerable evidence of dependence between IFAT and VI and some evidence of dependence between one PCR and IFAT. Results obtained from both maximum-likelihood models and from Bayesian analyses of models allowing for conditional dependence between two pairs of tests were consistent with those obtained with the pseudogold standards. The results suggest that pseudogold standards can help in choosing a correct dependence structure and should be used in combination with latent-class models.

A case-control study of lameness in dairy cows

A case-control study was conducted to compare the physical hoof properties of digits responsible for clinical lameness with those of other digits on the same cows and with those of equivalent digits on non-lame control cows. The control cows were herd-mates matched by age, breed and stage of lactation. Hoof moisture, hoof hardness and sole concavity were measured on-farm. The resilience, compressive strength and elastic modulus of both sole and wall hoof were measured on biophys samples collected from both case and control digits. n nWhite line disease, sole bruising and septic pododermatitis accounted for 92% of the clinical lameness lesions in the case digits examined. Less severe forms of white line disease and hoof haemorrhage were also observed frequently in the non-lame digits of both the case and control cows. n nIndependent variables were screened for unconditional associations with case-control status using Students paired t-test and Wilcoxons matched pairs test. Conditional logistic regression analysis was finally used to identify which risk factors were associated with lameness. n nWhen equivalent digits on the matched cows were used as controls, sole and heel moisture, sole haedness, sole concavity and wall colour were selected for inclusion in the model derived to explain differences between the physical properties of lame and control digits. Values for each of these properties were lower in the lame digits than in the controls. The control digits had a higher percentage of black coloration than the lame digits. n nSole hardness and sole concavity (both lower in the lame digits) were also selected for inclusion in the conditional logistic regression model derived when the adjoining digits on the same legs of the lame cows were used as controls. n nNone of the physical hoof properties measured were associated with lameness when attempts were made to fit a model using the equivalent digits on the opposite legs of the lame cows as controls. n nProduction of the lame cows was also compared with that of matched herd-mates. Total lactation yields of milk, milk fat and milk protein were lower for the lame cows than for the control cows (P < 0.05).

Estimates of within-herd incidence rates of Mycobacterium bovis in Canadian cattle and cervids between 1985 and 1994.

We analysed the individual-animal data from six of the nine outbreaks of tuberculosis in Canadian cattle and cervids from 1985 to 1994. A positive/reactor animal was one which had either a positive culture or a positive or suspicious reaction on a mid-cervical, comparative cervical, or gross or histopathological test for tuberculosis. Individual-animal data were collected only for herds which had one or more positive/reactor animals. Data were collected from the outbreak records in the Regional or District offices of Agriculture and Agri-food Canadas Animal and Plant Health Directorate. The within-herd spread of Mycobacterium bovis was studied by determining the most-likely date at which the herd was first exposed to M. bovis and the number of reactions which had developed by the time the herd was investigated. The animal-time units at risk in the herd were probably overestimated, resulting in conservative estimates of the within-herd incidence rates. Negative-binomial regression was used to investigate factors which might have influenced the within-herd spread of tuberculosis. Increasing age appeared to be a risk factor for being a positive/reactor animal. When compared to animals 0-12 months old, animals 13-24 months old had an incidence rate ratio (IRR) of 7.6, while animals >24 months old had an IRR of 10.4 (p=0.009). Actual and predicted incidence rates for tuberculosis in mature (>24 months old) animals were calculated. Actual and predicted incidence rates were similar for cervids, within an outbreak. There was more variability between actual and predicted rates in the dairy and beef animals. In the one outbreak (Ontario) where there were positive/reactor cervid, dairy and beef herds, the actual incidence rate for cervids (IR=9.3 cases per 100 animal-years) was almost twice that of dairy cattle (IR=5.0) and three times that of beef cattle (IR=3.1).

Culling decisions of dairy farmers during a 3-year Salmonella control study.

Salmonella enterica subsp. enterica-serotypes lead to periodically increased morbidity and mortality in cattle herds. The bacteria can also lead to serious infections in humans. Consequently, Denmark has started a surveillance and control programme in 2002. The programme focuses on Salmonella Dublin which is the most prevalent and most persistent serotype in the Danish cattle population. A field study in 10 dairy herds with persistent Salmonella infections was carried out over three years to gain experience with control procedures including risk assessment, targeted control actions and test-and-cull procedures. From autumn 2003 until end of 2006 quarterly milk quality control samples from all lactating cows and biannual blood samples from all young stock above the age of three months were tested using an indirect antibody ELISA. The most recent and previous test results were used to categorise all animals into risk groups. These risk groups and all individual ELISA-results were communicated to the farmers as colour-coded lists four to six times per year. Farmers were advised to manage the risk of Salmonella transmission from cattle with repeatedly high ELISA results (flagged as red) or cows with at least one recent moderately high ELISA result (flagged as yellow) on the lists. Risk management included, e.g. culling or separation of the cows at calving. We analysed culling decisions using two models. For heifers a hierarchical multivariable logistic model with herd as random effect evaluated if animals with red and yellow flags had higher probability of being slaughtered or sold before first calving than animals without any risk flags. For adult cows a semi-parametric proportional hazard survival model was used to test the effect of number of red and yellow flags on hazards of culling at different time points and interactions with prevalence in the herd while accounting for parity, stage of lactation, milk yield, somatic cell count and the hierarchical structure of the data with animals clustered at herd level. This study illustrates how investigation of culling decisions made by herd managers when they have access to test-status of individual animals and overall apparent prevalence during control of an infection can lead to useful new knowledge. Overall herd managers were more likely to cull cattle with increasing number of yellow and red flags than animals with no flags. However, cattle were more likely to be culled with yellow and red flags during times with low or medium high within-herd seroprevalence than at times with high seroprevalence. These results are valuable knowledge for modelling and planning of control strategies and for making recommendations to farmers about control options.