Measurement of statistical evidence on an absolute scale following thermodynamic principles.

Statistical analysis is used throughout biomedical research and elsewhere to assess strength of evidence. We have previously argued that typical outcome statistics (including p values and maximum likelihood ratios) have poor measure-theoretic properties: they can erroneously indicate decreasing evidence as data supporting an hypothesis accumulate; and they are not amenable to calibration, necessary for meaningful comparison of evidence across different study designs, data types, and levels of analysis. We have also previously proposed that thermodynamic theory, which allowed for the first time derivation of an absolute measurement scale for temperature (T), could be used to derive an absolute scale for evidence (E). Here we present a novel thermodynamically based framework in which measurement of E on an absolute scale, for which "one degree" always means the same thing, becomes possible for the first time. The new framework invites us to think about statistical analyses in terms of the flow of (evidential) information, placing this work in the context of a growing literature on connections among physics, information theory, and statistics.

Panic disorder is associated with the serotonin transporter gene (SLC6A4) but not the promoter region (5-HTTLPR).

Panic disorder (PD) and social anxiety disorder (SAD) are moderately heritable anxiety disorders. We analyzed five genes, derived from pharmacological or translational mouse models, in a new case-control study of PD and SAD in European Americans: (1) the serotonin transporter (SLC6A4), (2) the serotonin receptor 1A, (3) catechol-O-methyltransferase, (4) a regulator of g-protein signaling and (5) the gastrin-releasing peptide receptor. Cases were interviewed using the schedule for affective disorders and schizophrenia and were required to have a probable or definite lifetime diagnosis of PD (N=179), SAD (161) or both (140), with first onset by age 31 and a family history of anxiety. Final diagnoses were determined using the best estimate procedure, blind to genotyping data. Controls were obtained from the National Institute of Mental Health Human Genetics Initiative; only subjects above 25 years of age who screened negative for all psychiatric symptoms were included (N=470). A total of 45 single nucleotide polymorphisms were successfully genotyped over the five selected genes using Applied Biosystems SNPlex protocol. SLC6A4 provided strong and consistent evidence of association with the PD and PD+SAD groups, with the most significant association in both groups being at rs140701 (chi(2)=10.72, P=0.001 with PD and chi(2)=8.59, P=0.003 in the PD+SAD group). This association remained significant after multiple test correction. Those carrying at least one copy of the haplotype A-A-G constructed from rs3794808, rs140701 and rs4583306 have 1.7 times the odds of PD than those without the haplotype (95% confidence interval: 1.2-2.3). The SAD only group did not provide evidence of association, suggesting a PD-driven association. The findings remained after adjustment for age and sex, and there was no evidence that the association was due to population stratification. The promoter region of the gene, 5-HTTLPR, did not provide any evidence of association, regardless of whether analyzed as a triallelic or biallelic locus, nor did any of the other four candidate genes tested. Our findings suggest that the serotonin transporter gene may play a role in PD; however, the findings require replication. Future studies should attend to the entire genetic region rather than the promoter.

The quantitative genetic basis of polyandry in the parasitoid wasp, Nasonia vitripennis.

Understanding the evolution of female multiple mating (polyandry) is crucial for understanding sexual selection and sexual conflict. Despite this interest, little is known about its genetic basis or whether genetics influences the evolutionary origin or maintenance of polyandry. Here, we explore the quantitative genetic basis of polyandry in the parasitoid wasp Nasonia vitripennis, a species in which female re-mating has been observed to evolve in the laboratory. We performed a quantitative genetic experiment on a recently collected population of wasps. We found low heritabilities of female polyandry (re-mating frequency after 18 h), low heritability of courtship duration and a slightly higher heritability of copulation duration. However, the coefficients of additive genetic variance for these traits were all reasonably large (CV(A)>7.0). We also found considerable dam effects for all traits after controlling for common environment, suggesting either dominance or maternal effects. Our work adds to the evidence that nonadditive genetic effects may influence the evolution of mating behaviour in Nasonia vitripennis, and the evolution of polyandry more generally.

Using lod scores to detect sex differences in male-female recombination fractions.

Human recombination fraction (RF) can differ between males and females, but investigators do not always know which disease genes are located in genomic areas of large RF sex differences. Knowledge of RF sex differences contributes to our understanding of basic biology and can increase the power of a linkage study, improve gene localization, and provide clues to possible imprinting. One way to detect these differences is to use lod scores. In this study we focused on detecting RF sex differences and answered the following questions, in both phase-known and phase-unknown matings: (1) How large a sample size is needed to detect a RF sex difference? (2) What are "optimal" proportions of paternally vs. maternally informative matings? (3) Does ascertaining nonoptimal proportions of paternally or maternally informative matings lead to ascertainment bias? Our results were as follows: (1) We calculated expected lod scores (ELODs) under two different conditions: "unconstrained," allowing sex-specific RF parameters (theta(female), theta(male)); and "constrained," requiring theta(female) = theta(male). We then examined the DeltaELOD (identical with difference between maximized constrained and unconstrained ELODs) and calculated minimum sample sizes required to achieve statistically significant DeltaELODs. For large RF sex differences, samples as small as 10 to 20 fully informative matings can achieve statistical significance. We give general sample size guidelines for detecting RF differences in informative phase-known and phase-unknown matings. (2) We defined p as the proportion of paternally informative matings in the dataset; and the optimal proportion p(circ) as that value of p that maximizes DeltaELOD. We determined that, surprisingly, p(circ) does not necessarily equal (1/2), although it does fall between approximately 0.4 and 0.6 in most situations. (3) We showed that if p in a sample deviates from its optimal value, no bias is introduced (asymptotically) to the maximum likelihood estimates of theta(female) and theta(male), even though ELOD is reduced (see point 2). This fact is important because often investigators cannot control the proportions of paternally and maternally informative families. In conclusion, it is possible to reliably detect sex differences in recombination fraction.

BMPR2 germline mutations in pulmonary hypertension associated with fenfluramine derivatives.

This study investigated whether patients developing pulmonary arterial hypertension (PAH) after exposure to the appetite suppressants fenfluramine and dexfenfluramine have mutations in the bone morphogenetic protein receptor 2 (BMPR2) gene, as reported in primary pulmonary hypertension. BMPR2 was examined for mutations in 33 unrelated patients with sporadic PAH, and in two sisters with PAH, all of whom had taken fenfluramine derivatives, as well as in 130 normal controls. The PAH patients also underwent cardiac catheterisation and body mass determinations. Three BMPR2 mutations predicting changes in the primary structure of the BMPR-II protein were found in three of the 33 unrelated patients (9%), and a fourth mutation was found in the two sisters. No BMPR2 mutations were identified in the 130 normal controls. This difference in frequency was statistically significant. Moreover, the mutation-positive patients had a somewhat shorter duration of fenfluramine exposure before illness than the mutation-negative patients, a difference that was statistically significant when the two sisters were included in the analysis. In conclusion, the present authors have detected bone morphogenetic protein receptor 2 mutations that appear to be rare in the general population but may combine with exposure to fenfluramine derivatives to greatly increase the risk of developing severe pulmonary arterial hypertension.

The IDDM13 region containing the insulin-like growth factor binding protein-5 (IGFBP5) gene on chromosome 2q33-q36 and the genetic susceptibility to rheumatoid arthritis.

We considered that the constitutive over-expression by cultured rheumatoid arthritis (RA) fibroblast-lineage synoviocytes of genes like IGFBP5 could indicate new candidate susceptibility genes. IGFBP5 is located in a region where an insulin-dependent diabetes mellitus (IDDM) susceptibility locus, IDDM13 (2q33-q36), has been mapped. Previous evidence that non-MHC IDDM loci overlap RA susceptibility loci made IGFBP5 and its region an interesting candidate locus which was tested for linkage. Forty-nine sibships (2-4 affected siblings per sibship) with RA were genotyped with microsatellite markers covering an 11.2 cM interval in the IGFBP5/IDDM13 region. Both the two-point LOD scores and a 'nonparametric' allele-sharing analysis revealed no evidence for linkage (max LOD = 0.54, P = 0.5, respectively). Adjustments for the presence of 'shared-epitope' alleles did not significantly change the LOD scores. These results suggest that, despite the involvement of the 2q33-q36 chromosomal region in another organ-specific autoimmune disease, it is unlikely that this region harbors a RA susceptibility locus.

Excess of twins among affected sibling pairs with autism: implications for the etiology of autism.

It is widely accepted that genes play a role in the etiology of autism. Evidence for this derives, in part, from twin data. However, despite converging evidence from gene-mapping studies, aspects of the genetic contribution remain obscure. In a sample of families selected because each had exactly two affected sibs, we observed a remarkably high proportion of affected twin pairs, both MZ and DZ. Of 166 affected sib pairs, 30 (12 MZ, 17 DZ, and 1 of unknown zygosity) were twin pairs. Deviation from expected values was statistically significant (P<10(-6) for all twins); in a similarly ascertained sample of individuals with type I diabetes, there was no deviation from expected values. We demonstrate that to ascribe the excess of twins with autism solely to ascertainment bias would require very large ascertainment factors; for example, affected twin pairs would need to be, on average, approximately 10 times more likely to be ascertained than affected non-twin sib pairs (or 7 times more likely if "stoppage" plays a role). Either risk factors (related to twinning or to fetal development) or other factors (genetic or nongenetic) in the parents may contribute to autism.

Model-free vs. model-based linkage analysis: a false dichotomy?

The aim of this article is to dispel some misunderstandings concerning the concepts of model-free or nonparametric linkage analysis (usually meaning affecteds-only analysis) and model-based or parametric analysis (usually meaning classical lod scores) and the implications of these concepts for the linkage analysis of complex genetic diseases. I review basic principles and then briefly indicate actual research findings. Readers may be surprised to learn that, technically, lod score analysis is also nonparametric. All this taken together indicates that classical lod score analysis, performed under a couple of different sets of genetic assumptions and corrected for multiple tests, is often actually superior to model-free analyses, even when the true genetic model is complex and unknown.

Stoppage: an issue for segregation analysis.

Segregation analysis assumes that the observed family-size distribution (FSD), i.e., distribution of number of offspring among nuclear families, is independent of the segregation ratio p. However, for certain serious diseases with early onset and diagnosis (e.g., autism), parents may change their original desired family size, based on having one or more affected children, thus violating that assumption. Here we investigate "stoppage," the situation in which such parents have fewer children than originally planned. Following Brookfield et al. [J Med Genet 25:181-185, 1988], we define a stoppage probability d that after the birth of an affected child, parents will stop having children and thus not reach their original desired family size. We first derive the full correct likelihood for a simple segregation analysis as a function of p, d, and the ascertainment probability pi. We show that p can be estimated from this likelihood if the FSD is known. Then, we show that under "random" ascertainment, the presence of stoppage does not bias estimates of p. However, for other ascertainment schemes, we show that is not the case. We use a simulation study to assess the magnitude of bias, and we demonstrate that ignoring the effect of stoppage can seriously bias the estimates of p when the FSD is ignored. In conclusion, stoppage, a realistic scenario for some complex diseases, can represent a serious and potentially intractable problem for segregation analysis.

No association or linkage between polymorphisms in the genes encoding cholecystokinin and the cholecystokinin B receptor and panic disorder.

Growing animal data implicate cholecystokinin in the regulation of anxiety, while human clinical research confirms the role of cholecystokinin in the provocation of panic attacks. Antipanic medications suppress the ability of cholecystokinin to induce panic attacks, and may alter the expression of the cholecystokinin gene. Thus, there is increased interest in understanding the molecular genetic component of these observations. Recent association studies using persons with panic disorder described some association between polymorphisms in the genes encoding cholecystokinin and the cholecystokinin B-receptor and panic disorder. In this study, we used a family-based design, employing 596 individuals in 70 panic disorder pedigrees, as well as 77 haplotype relative risk 'triads'. Subjects were genotyped for two polymorphisms: the polymorphic microsatellite marker in the CCK-BR locus using PCR-based genotyping and at a single nucleotide polymorphism in the CCK promoter using a fluorescence polarization detection assay, and the data were analyzed for genetic association and linkage. Employing a variety of diagnostic and genetic models, linkage analysis produced no significant lod scores at either locus. Family-based tests of association, the haplotype-based haplotype relative risk statistic and the transmission disequilibrium test, were likewise non-significant. The results reported here provide little support for the role of these polymorphisms in panic disorder.

Markov chain Monte Carlo linkage analysis: effect of bin width on the probability of linkage.

We analyzed part of the Genetic Analysis Workshop (GAW) 12 simulated data using Monte Carlo Markov chain (MCMC) methods that are implemented in the computer program Loki. The MCMC method reports the "probability of linkage" (PL) across the chromosomal regions of interest. The point of maximum PL can then be taken as a "location estimate" for the location of the quantitative trait locus (QTL). However, Loki does not provide a formal statistical test of linkage. In this paper, we explore how the bin width used in the calculations affects the max PL and the location estimate. We analyzed age at onset (AO) and quantitative trait number 5, Q5, from 26 replicates of the general simulated data in one region where we knew a major gene, MG5, is located. For each trait, we found the max PL and the corresponding location estimate, using four different bin widths. We found that bin width, as expected, does affect the max PL and the location estimate, and we recommend that users of Loki explore how their results vary with different bin widths.

Drawbacks of GENEHUNTER for larger pedigrees: application to panic disorder.

Large pedigrees can pose a problem for GENEHUNTER linkage analysis software. Differences in two-point and multipoint lodscores were observed when comparing GENEHUNTER to other linkage software. Careful consideration must be given when selecting linkage analysis programs. Am. J. Med. Genet. (Neuropsychiatr. Genet.) 96:781-783, 2000.

A measure of phase ambiguity in pairs of SNPs in the presence of linkage disequilibrium.

The extent of haplotype ambiguity in a string of single-nucleotide polymorphisms (SNPs) was quantified by Hodge et al. [Nat Genet 1999;21:360]. In their measure, the level of ambiguity increases with increasing numbers of loci and as loci become more polymorphic. That work assumed linkage equilibrium (LE). However, linkage disequilibrium (LD) provides additional information about the haplotypes at a site, thereby diluting the level of ambiguity. The ambiguity vanishes altogether when LD reaches its maximum value. Here, we introduce the ambiguity measure, Phi, to allow for LD (between pairs of SNPs). We derive the formula Phi = 4x(2)x(3) for ambiguity in individuals, where x(1), x(2), x(3) and x(4) are the probabilities of the A(1)A(2), A(1)B(2), B(1)A(2) and B(1)B(2) haplotypes, respectively, and w.l.o.g. x(1)x(4) > or = x(2)x(3). Alternatively, Phi can be expressed in terms of the allele frequencies and the LD parameter delta. We also extend the formula to triads of two parents plus one child. We estimate our measure Phi for relevant SNPs in the published lipoprotein lipase (LPL) gene dataset [Clark et al., Am J Hum Genet 1998;63:595; Nickerson et al., Nat Genet 1998;19:233], obtaining values ranging from a low of 0 to a high of 0.11 among adjacent pairs of sites. In genome-wide LD studies to map common disease genes, a dense map of SNPs may be utilized to detect association between a marker and disease. Therefore, the measurement of ambiguity can potentially help investigators to determine a more efficient map, designed to minimize ambiguity and subsequent information loss.

Investigation of dopamine receptor (DRD4) and dopamine transporter (DAT) polymorphisms for genetic linkage or association to panic disorder.

Clinical and animal studies suggest a role for the neurotransmitter dopamine in anxiety states. In humans, one such condition is panic disorder, which is typified by recurrent panic attacks accompanied by anticipatory anxiety. Family, segregation, and twin studies imply a genetic component to the pathophysiology of panic disorder. In this study, we examined the genes for the D4 dopamine receptor (DRD4) and the dopamine transporter (DAT) using three common sequence polymorphisms. Two of these polymorphisms were in DRD4, a 12 base-pair insertion/deletion in exon 1 and a 48 base-pair repeat in exon 3, and the third was a 40 base-pair repeat in the 3' untranslated region of DAT. We employed a family-based design, using 622 individuals in 70 families, as well as 82 haplotype relative risk "trios". Subjects were genotyped at the polymorphic loci, and the data were analyzed for genetic association and linkage. There were no significant differences in allele frequencies or occurrence of genotypes within the triads for any of the three polymorphisms. No significant linkage between the DRD4 or DAT polymorphisms and panic disorder was observed in the multiplex families, using a variety of simulations for dominant and recessive models of inheritance. However, LOD scores of approximately 1.1 and 1.05 were observed for the DAT and DRD4 exon 1 loci, respectively. The results reported here provide little support for the role of these polymorphisms in panic disorder.

Familial primary pulmonary hypertension (gene PPH1) is caused by mutations in the bone morphogenetic protein receptor-II gene.

Familial primary pulmonary hypertension is a rare autosomal dominant disorder that has reduced penetrance and that has been mapped to a 3-cM region on chromosome 2q33 (locus PPH1). The phenotype is characterized by monoclonal plexiform lesions of proliferating endothelial cells in pulmonary arterioles. These lesions lead to elevated pulmonary-artery pressures, right-ventricular failure, and death. Although primary pulmonary hypertension is rare, cases secondary to known etiologies are more common and include those associated with the appetite-suppressant drugs, including phentermine-fenfluramine. We genotyped 35 multiplex families with the disorder, using 27 microsatellite markers; we constructed disease haplotypes; and we looked for evidence of haplotype sharing across families, using the program TRANSMIT. Suggestive evidence of sharing was observed with markers GGAA19e07 and D2S307, and three nearby candidate genes were examined by denaturing high-performance liquid chromatography on individuals from 19 families. One of these genes (BMPR2), which encodes bone morphogenetic protein receptor type II, was found to contain five mutations that predict premature termination of the protein product and two missense mutations. These mutations were not observed in 196 control chromosomes. These findings indicate that the bone morphogenetic protein-signaling pathway is defective in patients with primary pulmonary hypertension and may implicate the pathway in the nonfamilial forms of the disease.

Fine mapping of PPH1, a gene for familial primary pulmonary hypertension, to a 3-cM region on chromosome 2q33.

Familial primary pulmonary hypertension (PPH) is a rare autosomal dominant disease characterized by distinctive changes in pulmonary arterioles that lead to increased pulmonary artery pressures, right ventricular failure, and death. Our previous studies had mapped the disease locus, PPH1, to a 27-cM region on chromosome 2q31-q33, with a maximum multipoint logarithm of the odds favoring genetic linkage score of 3.87 with markers D2S350 and D2S364. To narrow the minimal genetic region for PPH, we physically mapped 33 highly polymorphic microsatellite markers and used them to genotype 44 affected individuals and 133 unaffected individuals from 17 families with PPH. We observed recombination events that substantially reduced the interval for PPH1 to the approximately 3-cM region that separates D2S311 and D2S1384. This entire region lies within chromosome 2q33. A maximum two-point lod score of 7.23 at a recombination fraction of zero was obtained for marker D2S307. A maximum multipoint lod score of 7.41 was observed close to marker D2S1367. The current minimal genetic region contains multiple candidate genes for PPH, including a locus thought to play a role in lung cancer.

Potential panic disorder syndrome: clinical and genetic linkage evidence.

This paper reports evidence for a possible "chromosome 13 syndrome," which includes panic disorder, kidney or bladder problems, serious headaches, thyroid problems (usually hypothyroid), and/or mitral valve prolapse (MVP). In the course of a genetic linkage study of panic disorder, we noted these medical conditions in individual family members. (We were blind to family relationships and marker data.) We hypothesized that there may exist a subgroup of panic families with these medical conditions, which for simplicity we called it the "syndrome." Subsequently we reclassified the families as with or without the "syndrome" and extended the phenotype for analysis to include the above medical conditions. All these classifications were also done before the analysis and blind to marker data. We then examined our linkage results, looking for significant differences between families with and without the "syndrome" (using several definitions of the "syndrome")-i.e., testing for genetic heterogeneity. When the families with and without bladder/kidney problems were separated from each other, one marker-D13S779 (ATA26D07)-yielded a lod score of over 3 in the families with bladder/kidney problems. This lod score went up to 4.2 in these families when we diagnosed any individual with any one of the "syndrome" conditions as affected. These results were statistically significant even after applying an extremely overconservative Bonferroni correction for multiple tests. We present these results in order to alert other investigators working on panic disorder, for replication. If replicated, one may hypothesize that a candidate gene for the syndrome should be expressed in CNS, kidney, gut, thyroid, etc. We also noted that two independent studies report recent linkage findings between schizophrenia and the same region on chromosome 13. No connection between schizophrenia and panic disorder has ever been reported. Finally, we suggest that genetic studies of psychiatric disorders might prove more fruitful if phenotypes were expanded to include possible manifestations of the disorder in medical (non-mental) symptoms. Am. J. Med. Genet.(Neuropsychiatr. Genet.) 96:24-35, 2000.

The "Circular" Problems of Calculating Risk: Dealing with Consanguinity.

An ongoing problem in the genetics clinic is the calculation of inbreeding coefficients and recurrence risks for complex pedigrees, particularly when multiple "loops" are present. Although the Human Genome Project promises information about more of our genes in the foreseeable future, the actual assignment of disease status to specific loci will continue at a slower pace, so that accurate risk calculations are needed. In the past few months several families with consanguinity were referred to us to confirm the calculations performed by the genetic counselor, and we became aware of some confusion in the field. We present here both (a) a clarification of definitions and concepts and (b) a review of how to perform the calculations, for several quantities (coefficient of relationship, coefficient of inbreeding, coefficient of kinship, and recurrence risk), in complex pedigrees. We discuss the availability of computer algorithms to assist in these calculations, and we encourage counselors to call on a reliable computer program for any but the simplest cases. At the same time, we reiterate our belief that computer algorithms do not relieve the counselor of the responsibility of knowing what to calculate and when.