Portuguese Water Dogs have been noted to have a disproportionate number of Addisonian cases [1, 2]. To clarify the heritability and predict the mode of inheritance of Addison's disease in the Portuguese Water Dog, a study was initiated in conjunction with the Portuguese Water Dog Club of America. Interested owners of Portuguese Water Dogs submitted survey questionnaires which asked for registered name, sire and dam, date of birth, sex, whether intact or altered, whether Addisonian or not, how diagnosis was made, age of diagnosis, and whether the dog received steroid treatment prior to diagnosis. Pedigree information was obtained from the American Kennel Club records.
A dog was designated as Addisonian if the diagnosis was made following an adrenocorticotropin hormone (ACTH) stimulation test administered by a veterinarian. The ACTH test measures the competence of the adrenal cortex by evaluating blood cortisol concentrations before and after the exogenous ACTH stimulation. In a clinically normal animal, the baseline blood cortisol prior to the ACTH stimulation would be 0.5 to 4.0 μg of cortisol/dl that would rise to 8.0 to 20 μg/dl following ACTH stimulation. Dogs failing to respond to the ACTH stimulation with elevated circulating cortisol are classified as Addisonian . Most owners were prompted to test their Portuguese Water Dogs for Addison's disease because of signs of lethargy, vomiting, or collapse. The ACTH stimulation criteria for diagnosis allows for an accurate and repeatable assessment of the disease. Dogs included in the present study were classified as either Addison-affected (based on the above criteria) or unaffected Portuguese Water Dogs.
Addisonian disease incidence data were collected on 804 Portuguese Water Dogs from the United States, though with pedigree information an additional 1,273 animals were included in the study; these additional animals did not have a recorded observation for Addison's disease. The total of 2,077 dogs included in the analysis is derived from one large family (with 2,051 dogs), three families of seven dogs, and 5 dogs of unassigned pedigree. The only additional variable included in our analysis was sex. No additional phenotypic information was recorded along with the diagnosis of Addison's disease (e.g., coat color). Specifically, there were 458 females (396 unaffected and 62 affected) and 346 males (305 unaffected and 41 affected) with known health status. Figure 1, representing a small subset of the dogs in the study, is provided to demonstrate transmission of the disorder. However, the parents of all affected Portuguese Water Dogs in this study trace back to common ancestors. The Portuguese Water Dog population in the United States was established from two separate Portuguese kennel lines (Algarbiorum and Alvalade) beginning in the late 1960s .
For the affected dogs included in the analyses, the mean age of Addisonian diagnosis was 46 months (median 36 months). The mean age of the dogs in the study designated unaffected was 48.5 months (median 37 months). Caution must be exercised to avoid designating a dog as being Addisonian when in fact the responsiveness of the adrenal has been blunted by exogenous administration of glucocorticoids. For 6.4% of the Addisonian dogs in the present study, owners reported that the dogs had received some sort of short term steroid treatment at some point prior to the Addisonian diagnosis. However, in the United States, the standard veterinary protocol for an ACTH stimulation test is to gradually withdraw exogenous corticosteroids prior to administration of the ACTH challenge (R. Nelson, personal communication). In addition, those survey questionnaires that included the ACTH stimulation test values, Addisonian dogs had pre and post-ACTH cortisol levels of less than 0.2 μg/dl which differ from the expected values of a clinically normal dog as stated earlier. Taken together, this suggests that the diagnosis of Addison's disease for the dogs in this study were Addisonian and not phenocopies. For the dogs with alteration status recorded, the vast majority of dogs (88%) were diagnosed after being reproductively altered.
Estimation of heritability
For the objective of estimating the heritability of Addison's disease in the Portuguese Water Dog, a threshold model for the liability to disease was used. This method assumes that a dog can be assigned to a specific disease class (unaffected/affected) when an underlying, unobservable risk (or liability) for disease exceeds a threshold of τ = 0. The distribution of the unobservable liability was assumed to be multivariate normal. The correlation in liability of two dogs i and j was modeled to be ρij = aij h2 + δij σe2 where ρij is the correlation in liability to disease between dogs i and j; aij is the additive relationship between dogs i and j; h2 is the narrow sense heritability of liability to disease; δij is the coefficient for the random environmental component for dogs i and j such that δij equals 1 if i equals j and zero otherwise; and σe2 = 1 - h2, with no loss of generality. The null hypothesis of no genetic contribution (i.e., h2 = 0) was tested with a likelihood ratio test, comparing the full model likelihood with that of the restricted model where h2 = 0. Heritability is expressed as the mean ± standard error of the mean. It should be noted that because the data represent owner submissions, the data were collected in a non-random fashion. Further, being a study of inheritance, the data set was constructed around probands. Such data require an adjustment for ascertainment bias. However, the mixed linear models utilized in this study accommodate nonrandomly sampled data  as long as the dogs added into the study to complete the pedigree associations can be considered a random sample of Portuguese Water Dogs. In addition, a test of the effect of sex on the liability of Addison's disease was also tested through the likelihood ratio test. Calculations were implemented through the computer program SOLAR [25, 26], making use of the binary trait analysis first described in Duggirala et al. .
Complex segregation analysis
The possibility that Addison's disease in Portuguese Water dogs is influenced by the action of a single segregating locus of large effect can also be examined. Complex segregation analysis, developed by Bonney , is intended to integrate Mendelian transmission genetics at a single locus with the patterns of covariance expected in polygenic inheritance. Lynch and Walsh  provide a more complete description of complex segregation analysis. Elston et al.  outlined the criteria that must be satisfied before acceptance of the single major locus model so as to reduce the risk of false positive declarations of a major locus model. Evaluation of the models necessary for complex segregation analysis was conducted with the Bayesian software package iBay http://www.lucjanss.com. The iBay software is an extension of MaGGic , rewritten to accommodate complex segregation analysis in binary traits for pedigrees that include inbreeding.
The software selected to conduct the complex segregation analysis is built upon a Bayesian foundation, making use of Monte Carlo Markov chains (MCMC) through a Gibbs sampler. Accordingly, point estimates of unknown parameters are not derived, but rather estimates of the posterior density for unknown parameters. The iBay  package was recently used to evaluate the contribution of a major locus to osteochodral diseases in pigs , where a more complete outline of the MCMC approach is detailed. The goal of this strategy was to simultaneously estimate the posterior density for a polygenic contribution to Addison's disease along with the contributions of a putative Mendelian locus. Specifically, for this mixed-inheritance model, the strategy allowed the evaluation of a polygenic variance component, the additive and dominance contributions of a single locus (the parameters -a, d, and a for the putative major locus genotypes AA, AB, and BB, respectively) and the frequency of allele A of the putative major locus (defined as "q"). Given our scoring of phenotypes, where affected is 1 and unaffected scored as zero, the "B" allele represent the putative disease-enhancing allele. Note also that the iBay software models the unobservable scale of this threshold trait such that the residual variance is fixed at 1.0 (i.e., σe2 = 1).
Creation of the Gibbs sample requires several key assumptions about the behavior of these unknown parameters. Though a variety of models can be considered, all are some variant of the following: sex as a fixed effect with a flat (i.e., uniform) prior density, the polygenic variance component with a flat prior density, as well as flat prior densities for the additive, dominance, and allele frequency parameters. A Gibbs sample of 9,000 was generated, beginning with the creation of 350,000 total samples, a "burn-in" of 50,000 and a sampling rate of every 100-th Gibbs value. This process was repeated two additional times, to create three replicate chains. From the 9,000 Gibbs samples, the mean, standard deviation, mode and the upper and lower limits of a 95% highest density region (HDR) was computed for each of the unknown parameters. HDR were computed according to Hyndman  with the public domain software hdrcde , a package within the R-program .