Study population

Results of questionnaires completed for a different study were reviewed in detail and data regarding diabetic phenotype, age, and sex of Australian Terriers were retrieved [11]. Data were also collected from an online questionnaire (http://www.vet.upenn.edu/diabetes) that was launched to investigate the prevalence of spontaneous diabetes in dogs across the United States [S1 Appendix: 1, 11]. The survey was promoted by the American Kennel Club (AKC), numerous breed clubs including the Australian Terrier Club of America, 29 academic institutions, 14 private referral practices, and various social media outlets [S1 Appendix: 1, 11]. Data collected for all dogs included age at the time of survey or questionnaire completion, breed, sex, neuter status, presence or absence of diabetes, AKC number if available, names and contact information of owners of immediate dog relatives if known, and owner contact information. Additional data collected for dogs with diabetes included neuter status just prior to diagnosis of diabetes and age at the time of diabetes diagnosis. Australian Terriers recruited from the online survey were included if they were entered into the database by August 31, 2019, but questionnaires were launched as early as 2007. Owners and breeders of Australian Terriers were also contacted directly to collect identical data about other related dogs. AKC pedigrees were used to ascertain pure breed status and ancestry in all study dogs. Australian Terriers with diabetes were included only if an AKC registered pedigree was available for review and if the owner or breeder could be contacted to confirm the diabetic phenotype. Australian Terriers without diabetes or with an unknown phenotype were included only if they were directly related (e.g. sibling, offspring, parent, or grandparent) to a dog with diabetes, as previously described [12]. Australian Terriers bred outside of the United States were excluded. University of Pennsylvania Institutional Animal Care and Use Committee approval for the questionnaire and survey were sought but were waived because dogs were not physically examined. University of Pennsylvania Institutional Review Board approval was also sought and waived because questions other than contact information pertained to the dog and not to the owner.

Definition of phenotype

Dogs were defined as cases if their owner or breeder asserted that a veterinarian had diagnosed the dog with insulin treated diabetes. Dogs were defined as controls that do not have diabetes if their owner or breeder reported that the dog had no clinical signs consistent with diabetes (polyuria, polydipsia, polyphagia, or weight loss) and was not being treated with insulin. Dogs were defined as having an unknown phenotype if their owner or breeder could not be contacted. Sex was ultimately classified as female or male because neuter status was unknown in many dogs.

Estimation of heritability

Heritability was estimated as previously described [12]. The binary disease phenotype (i.e., diabetes and control) dictated the use of logistic regression (logit) to model the risk of disease as a function of explanatory variables (e.g., sex) along with a presumed quantitative genetic contribution. Disease probability was defined as p_ij for the i-th sex and the j-th dog and the logit of this probability was defined as:

The logit was modeled linearly as a function of sex and a quantitative genotype, as follows: where μ is an unknown constant common to all dogs, sex_i is the additive contribution of the i-th (i = female or male) sex to the risk of disease, a_j is the additive genetic contribution to the risk of disease for the j-th (j = 1,2,3,…) dog, and e_j is an unknown random residual contribution to the risk of disease particular to the j-th dog. The unknown disease risk (e_j) is a function of undetermined environmental factors such as diet, exercise, climate, and veterinary care. Estimation of these unknown effects and predictions of the risk of disease were implemented with the Bayesian statistical package Stan executed with the public domain language R [13, 14]. A hierarchical Bayesian model with weakly informative prior distributions for the unknown effects can help stabilize the estimation process, especially in data sets with a complex pedigree [15].

Defining the prior distributions of these unknown parameters, it was assumed that the intercept (μ) and sex contribution (sex_i) were each drawn from a prior distribution of N(0, 16), that the additive genetic effects (a_j) were drawn from the multivariate normal distribution N(0, ), with A as the known numerator relationship matrix among all Australian Terriers in the study pedigree and defined as the unknown additive genetic variance of disease risk. It was also assumed that σ_a was drawn from the positive values of a Cauchy (0, 2.5), as recommended for weakly informative prior distributions [16]. Finally, the residual term (e_j), was assumed to be drawn from a standard normal density [i.e., N(0, 1)] as required for this parameterization of a binary trait analysis [17]. Heritability was estimated with h², which is the proportion of trait variance that is due to additive genetic factors. Accordingly, the heritability of disease risk was estimated as:

The simulation process was conducted across four chains, where each chain was built on a draw of 40,000 total samples, and a “burn-in” process of 15,000 samples followed by thinning to every 25-th sample. In this way, each chain generated 1,000 sample parameter estimates, and 4,000 samples were generated across the four chains. Convergence of the process was visualized through trace plots of all the unknown values and computation of the Gelman-Rubin statistic for convergence being below 1.05 [18].

Mode of inheritance

Complex segregation analysis was performed, as previously described, to evaluate whether a single gene of large effect impacts the risk of diabetes in Australian Terriers [12]. Complex segregation analysis was performed using the publicly available package SEGREG, one of several programs available in the S.A.G.E. (v6.4) library [19, 20].

Implementation of this analysis, however, required the elimination of “loops in the pedigree,” a well-known challenge in the application of the Elston-Stewart algorithm [21]. Accordingly, prior to the complex segregation analysis, a loop-breaking algorithm was implemented, and dogs were duplicated to remove loops generated by inbreeding [22]. For example, if one dog was related to two different families, this dog was duplicated, and one duplicate remained in one family whereas the other duplicate was assigned to the other family. After implementation of the loop-breaking algorithm, 60 dogs were duplicated and added to a reconfigured pedigree which now included 543 dogs in 45 families. Although likely to decrease the power to detect the linkage of a major locus, the strategy was intended to minimize the impact of this pedigree simplification.

The ensuing analysis applied a model aiming to mimic the logistic regression model outlined above, including a term for the sex of each dog, and a parameter to accommodate shared polygenic terms of family members, as well as the putative major locus effects [23]. Various models with and without Mendelian inheritance were assessed to confirm or exclude the presence of a single gene of large effect [19]. Six models were considered. The simplest was a sporadic model, which assumes no major locus effect, but does consider a term for sex and an accommodation of a polygenic contribution to disease [23]. This was followed by an evaluation of three simple mixed major locus models, considering a dominant, recessive, or codominant major locus all of which follow the expected transmission of alleles outlined by Mendel. That is, for putative major genotypes AA, AB, and BB, the transmission probability for the A allele of these genotypes is set at 1.0, 0.5 and 0.0, respectively. Next, a model that considers environmental transmission of disease, where the polygenic term is removed and the transmission probabilities are set to being identically equal to the estimated allele frequency for all three putative major genotypes, was examined. Finally, a general model was considered where the transmission probabilities of the A allele were estimated from the data set. The Akaike Information Criterion (AIC), in which the goodness-of-fit is evaluated with a penalty for the number of parameters estimated, was used to compare models. Of the biologically feasible models, the one with the smallest AIC was considered the most appropriate for the data.

Age at the time of death or phenotype determination in control dogs, and age at the time of diabetes diagnosis, were normally distributed as determined visually and by the Skewness and Kurtosis tests for normality. Therefore, results for age are reported as mean (and standard deviation) and the two independent samples t-test was used for comparison of these ages. A p value of <0.05 was considered significant. These statistical evaluations were performed using a statistical software package (Stata 14.0 for Mac, Stata Corporation, College Station, TX).

Study population

The study population was comprised of 483 Australian Terriers, including 383 dogs unaffected by diabetes (controls), 86 dogs with diabetes (cases), and 14 dogs with an unknown phenotype. Most dogs (328) were enrolled by directly contacting owners and breeders of Australian Terriers. An additional 128 dogs were enrolled from the survey that was obtained as part of the study investigating the insulin gene region in Australian Terriers, and the remaining 27 dogs were recruited from the online questionnaire (http://www.vet.upenn.edu/diabetes) launched to investigate the prevalence of spontaneous diabetes in dogs across the United States [11, 12]. Contact information for owners and breeders who were contacted directly was made available by these two surveys. According to AKC records, the number of Australian Terrier puppies born from AKC litters between 2007 and 2019 was 5,418 (personnel communication, AKC Canine Health Foundation Raleigh, NC 27675).

The sex and neuter status of the 383 control dogs included 194 females with an unknown neuter status, 171 males with an unknown neuter status, eight neutered females, seven neutered males, two intact females, and one intact male. The sex and neuter status of the 86 diabetic dogs included 33 neutered males, 30 neutered females, 11 males with an unknown neuter status, 8 females with an unknown neuter status, two intact females, and two intact males.

Age of dogs at the time of diabetes diagnosis was known for 74 dogs. Mean (+/- SD) age of these 74 diabetic Australian Terriers at the time of diabetes diagnosis was 9.1 +/- 2.6 years. The mean age at the time of phenotype determination or at the time of death for 49 control dogs in which this age was known, was 11.4 +/- 3.1 years. The age of control dogs at the time of phenotype determination or death was significantly older than the age at which dogs with diabetes were diagnosed with the disease (p< 0.0001).

Pedigree analysis

A graphic depiction of the pedigree is portrayed in Fig 1. Heritability of diabetes risk in Australian Terrier dogs in a mixed logistic regression model was estimated as 0.18 (95% posterior interval 0.00–0.67). The model included only two sexes (female and male) because the neuter status of many dogs was not known. There was no significant difference in the sex effect on the risk of diabetes detected in the mixed logistic regression model (0.37, 95% posterior interval -0.23–0.94). Age was also not associated with risk of disease.

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Fig 1. A graphic depiction of the United States Australian Terrier pedigree under investigation.

Females are represented as circles and males are represented as squares. The illustration includes 86 case dogs with diabetes (designated in red), 383 control dogs without diabetes (designated in black), and 14 dogs with unknown phenotype (designated in blue).

https://doi.org/10.1371/journal.pone.0239542.g001

Complex segregation analysis was performed twice, with and without the sex variable. Results of the complex segregation analysis in the model including sex are reported on a logistic scale in Table 1. Results in Table 1 are reported for females, although males provided similar values. Results of the complex segregation analysis in the model excluding sex are reported on a logistic scale in Table 2. The results of both analyses suggest that the best model to describe the mode of diabetes inheritance in Australian Terriers is the polygenic sporadic model (Tables 1 and 2). In both analyses, the AIC of the sporadic model was smaller than the AIC values of the major locus models (dominant, recessive, and codominant), indicating that the goodness-of-fit of the major locus models was not better than the goodness-of-fit of the sporadic model. In both analyses, the smallest AIC was associated with the general model. However, in both general models the transmission probabilities for the putative A allele estimated from the data were not biologically plausible because they were non- Mendelian and therefore the general models were not considered further.

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Table 1. Genetic models tested and their results from the complex segregation analysis of diabetes in Australian Terriers dogs, in a model including sex (results presented for females).

https://doi.org/10.1371/journal.pone.0239542.t001

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Table 2. Genetic models tested and their results from the complex segregation analysis of diabetes in Australian Terriers dogs, in a model excluding sex.

https://doi.org/10.1371/journal.pone.0239542.t002