Bernard Prum

A new method to test genetic models in HLA associated diseases: the MASC method

We propose a new method to analyse data on HLA associated diseases. The method uses the simultaneous information on the marker associations and segregation with the disease. It may also take into account the differential risk of being affected for specific relatives of a patient as well as the differential HLA haplotype sharing according to the marker genotype of the patient. It is based on the principle of minimization of a sum of independent chi‐squares. It allows us to test the goodness‐of‐fit of various models in an easy and economical way.

Rheumatoid arthritis seropositive for the rheumatoid factor is linked to the protein tyrosine phosphatase nonreceptor 22-620W allele

The protein tyrosine phosphatase nonreceptor type 22 (PTPN22) gene encodes for lymphoid tyrosine phosphatase LYP, involved in the negative regulation of early T-cell activation. An association has recently been reported between the PTPN22-620W functional allele and rheumatoid factor-positive (RF+) rheumatoid arthritis (RA), among other autoimmune diseases. Expected linkage proof for consistency cannot be definitely produced by an affected sib-pair (ASP) analysis. Our aim was therefore to search for linkage evidence with the transmission disequilibrium test.DNA from the French Caucasian population was available for two samples of 100 families with one RA patient and both parents, and for 88 RA index cases from RA ASP families. Genotyping was carried out by PCR-restriction fragment length polymorphism. The analysis was performed using the transmission disequilibrium test, genotype relative risk and ASP-based analysis.The transmission disequilibrium test of the PTPN22-620W allele revealed linkage and association for RF+ RA (61% of transmission, P = 0.037). The genotype relative risk showed the risk allele in 34% of RF+ RA patients and in 24% of controls derived from nontransmitted parental chromosomes (P = 0.047, odds ratio = 1.69, 95% confidence interval = 1.03–2.78). The ASP investigation showed no enriched risk allele in RA multiplex families, resulting in a lack of power of ASP analysis, explaining the published negative results.This study is the first to show linkage of PTPN22 to RF+ RA, consistent with PTPN22 as a new RA gene.

Validation of the reshaped shared epitope HLA-DRB1 classification in rheumatoid arthritis

Recently, we proposed a classification of HLA-DRB1 alleles that reshapes the shared epitope hypothesis in rheumatoid arthritis (RA); according to this model, RA is associated with the RAA shared epitope sequence (72–74 positions) and the association is modulated by the amino acids at positions 70 and 71, resulting in six genotypes with different RA risks. This was the first model to take into account the association between the HLA-DRB1 gene and RA, and linkage data for that gene. In the present study we tested this classification for validity in an independent sample. A new sample of the same size and population (100 RA French Caucasian families) was genotyped for the HLA-DRB1 gene. The alleles were grouped as proposed in the new classification: S1 alleles for the sequences A-RAA or E-RAA; S2 for Q or D-K-RAA; S3D for D-R-RAA; S3P for Q or R-R-RAA; and X alleles for no RAA sequence. Transmission of the alleles was investigated. Genotype odds ratio (OR) calculations were performed through conditional logistic regression, and we tested the homogeneity of these ORs with those of the 100 first trio families (one case and both parents) previously reported. As previously observed, the S2 and S3P alleles were significantly over-transmitted and the S1, S3D and X alleles were under-transmitted. The latter were grouped as L alleles, resulting in the same three-allele classification. The risk hierarchy of the six derived genotypes was the same: (by decreasing OR and with L/L being the reference genotype) S2/S3P, S2/S2, S3P/S3P, S2/L and S3P/L. The homogeneity test between the ORs of the initial and the replication samples revealed no significant differences. The new classification was therefore considered validated, and both samples were pooled to provide improved estimates of RA risk genotypes from the highest (S2/S3P [OR 22.2, 95% confidence interval 9.9–49.7]) to the lowest (S3P/L [OR 4.4, 95% confidence interval 2.3–8.4]).

Associations between genetic factors, tobacco smoking and autoantibodies in familial and sporadic rheumatoid arthritis

Objectives: The objective of this study was to investigate the association between genes (HLA-DRB1 and PTPN22) and tobacco smoking, separately as well as combined, and serological markers of rheumatoid arthritis (RA) in a French population with RA. Methods: 274 patients with RA with half of them belonging to RA multicase families, were genotyped for HLA-DRB1 allele and for PTPN22-1858 polymorphism. IgM rheumatoid factor and anti-cyclic citrullinated peptide (anti-CCP) antibodies were determined by ELISA method. The search for association relied on χ2 test and odds ratio with 95% confidence interval calculation. The interaction study relied on the departure-from-additivity-based method. Results: The presence of at least one shared epitope (SE) allele was associated with anti-CCP antibodies presence (82.5% vs. 68.4%, p = 0.02), particularly with HLA-DRB1*0401 allele (28.0% vs. 16.4%, p = 0.01). Tobacco exposure was associated with anti-CCP antibodies, but only in presence of SE. A tendency toward an interaction was found between tobacco, the presence of at least one HLA-DRB1*0401 allele and anti-CCP antibodies (attributable proportion due to interaction = +0.24 (−0.21+0.76)). The cumulative dose of cigarette smoking was correlated with anti-CCP antibody titres (r = 0.19, p = 0.04). The presence of both SE and 1858T alleles was associated with a higher, but not significantly different, risk for anti-CCP antibodies presence than for each separately. No association was found between PTPN22-1858T allele and tobacco smoking for autoantibody positivity. Conclusions: Our findings suggest an association between SE alleles and tobacco smoking for anti-CCP positivity and a tendency toward an interaction between the HLA-DRB1*0401 allele and smoking for anti-CCP positivity in this sample of RA.

IRF5 rs2004640‐T allele, the new genetic factor for systemic lupus erythematosus, is not associated with rheumatoid arthritis

Background: Recently, a new genetic factor within the interferon regulatory factor 5 (IRF5) gene was demonstrated for systemic lupus erythematosus (SLE) through linkage and association: the rs2004640-T allele. IRF5 is involved in the production of rheumatoid arthritis (RA) cytokines, and SLE already shares with RA one genetic factor within the tyrosine phosphatase PTPN22 gene. Aim: To test the hypothesis that the SLE IRF5 genetic factor could also be shared with RA. Patients and methods: 100 French Caucasian trio families with RA were genotyped and analysed with the transmission disequilibrium test, the frequency comparison of the transmitted and untransmitted alleles, and the genotype relative risk. 97% power was available to detect at least a trend in favour of a factor similar to that reported for SLE. Results: The analysis showed the absence of linkage and association globally and in “autoimmune” RA subsets, with a weak non-significant trend against the IRF5rs20046470-T allele. Given the robustness of familial-based analysis, this slight negative trend provided strong evidence against even a weaker factor than that reported for SLE. Conclusion: Our results exclude the IRF5rs2004640-T allele as a major genetic factor for RA in this French Caucasian population.

Stochastic processes on a lattice and Gibbs measures

1 - Aspects of the Ising Model.- 1. Introduction.- 2. Peieriss Argument.- 3. Imposed Field, Thermodynamic Quantities.- 4. The Unidimensional Case and Tree.- 5. Antiferromagnetism.- 2 - Gibbs Measures.- 1. The DLR Problem.- 2. The Structure of G.- 3. Gibbs Specifications, Gibbs Measures.- 4. Relations with Thermodynamics.- 3 - The Existence of Gibbs Measures.- 1. Markovian Properties.- 2. Existence of Gibbs Measures when ? is Finite.- 3. Existence of Gibbs Measures - the General Case.- 4. Models of the P(?)-Type, Gaussian Gibbs Measures S.- 4 - Phase Transitions - 1: Methods of Convex Analysis.- 1. Holleys Inequality.- 2. The FKG Inequality.- 3. Attracting Specifications.- 4. The Ising Model on ?2.- 5. Symmetry Breaking on ?d for d ? 3.- 5 - Other Inequalities.- 1. Urse11 Functions.- 2. GK S Inequalities.- 3. The GHS Inequality.- 4. The Simon-Lieb Inequality.- S. Additional Inequalities.- 6 - Phase Transitions - 2: Phase Diagrams and Perturbed Hamiltonians.- 1. Fundamental Configurations.- 2. Perturbed Hamiltonians.- 3. The Pirogov-Sinai Theorem.- 4. Boundary Models.- S. Principle of the Proof.- 7 - Phase Transitions - 3: Positive Reflexivity.- 1. Reflexive Positivity.- 2. The Unidimensional Case.- 3. Checkerboard Estimate.- 4. Gaussian Domination.- 5. The Infrared Domination.- 8 - Continuous Symmetry and Other Methods.- 1. The Case of Continuous Symmetry.- 2. The Lack of Symmetry Breaking when d = 2.- 3. Spontaneous Magnetization when d ? 3.- 4. Onsager s Method.- 5. Combinatorial Approach.- 6. The Lee-Yang Theorem.- 9 - The Dynamics of Ising Systems.- 1. Introduction.- 2. A Finite Number of Sites.- 3. An Infinite Number of Sites.- 10 - Statistics and Applications.- 1. Ergodicity.- 2. Statistics.- 3. Image Processing.- 4. Other Applications.

On the use of x2 tests for nested categorized data

The use of the ordinary %2 test in the MASC method of comparing various genetic models is rigorously justified.

Searching gene transfers on Bacillus subtilis using hidden Markov models

We present an analysis of the Bacillus subtilis chromosome, to search horizontal gene transfers. DNA statistical composition differs according to species, and therefore, hidden Markov models, which can cut up a sequence into segments, on the basis of their local oligonucleotide composition, provide good statistical tools to identify horizontal transfers in the sequence. Crossing statistical results with a featured DNA physical map, and on the basis of gene sequence homologies, we detected four new resistance bearing potential horizontal gene transfers. A fifth segment shows all characteristics of an integron, issued from the transposon family.

Caution in the interpretation of MLS

We study the statistical properties of the maximum likelihood score (MLS) test. We show that the criteria for reaching conclusions about linkage are not the same for single point analysis as for multipoint, where the maximization is performed over an additional parameter, the position in the marker interval where the MLS is computed. In addition, this test is shown to be very sensitive to errors in allele frequencies and recombination fraction.

Parameter Estimation when Various Models are Available

The aim of this paper is to give an answer to the problem posed by data for which various models are possible, by means of a pre-test estimator using a likelihood criteria on exponential families. In the framework of contiguity, we will investigate the asymptotic behaviour of this estimator, comparing it with the classical ones. We illustrate those results on a practical example issued from segregation analysis in genetics.