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Summary In this article we develop a method based on model-X knockoffs to find conditional associations that are consistent across environments, while controlling the false discovery rate. The motivation for this problem is that large datasets may contain numerous associations that are statistically significant and yet misleading, as they are induced by confounders or sampling imperfections. However, associations replicated under different conditions may be more interesting. In fact, sometimes consistency provably leads to valid causal inferences even if conditional associations do not. Although the proposed method is widely applicable, in this paper we highlight its relevance to genome-wide association studies, in which robustness across populations with diverse ancestries mitigates confounding due to unmeasured variants. The effectiveness of this approach is demonstrated by simulations and applications to UK Biobank data.

Summary We introduce a multiple testing procedure that controls global error rates at multiple levels of resolution. Conceptually, we frame this problem as the selection of hypotheses that are organized hierarchically in a tree structure. We describe a fast algorithm and prove that it controls relevant error rates given certain assumptions on the dependence between the $p$-values. Through simulations, we demonstrate that the proposed procedure provides the desired guarantees under a range of dependency structures and that it has the potential to gain power over alternative methods. Finally, we apply the method to studies on the genetic regulation of gene expression across multiple tissues and on the relation between the gut microbiome and colorectal cancer.

Summary The goal of expression quantitative trait loci (eQTL) studies is to identify the genetic variants that influence the expression levels of the genes in an organism. High throughput technology has made such studies possible: in a given tissue sample, it enables us to quantify the expression levels of approximately 20 000 genes and to record the alleles present at millions of genetic polymorphisms. While obtaining this data is relatively cheap once a specimen is at hand, obtaining human tissue remains a costly endeavor: eQTL studies continue to be based on relatively small sample sizes, with this limitation particularly serious for tissues as brain, liver, etc.—often the organs of most immediate medical relevance. Given the high-dimensional nature of these datasets and the large number of hypotheses tested, the scientific community has adopted early on multiplicity adjustment procedures. These testing procedures primarily control the false discoveries rate for the identification of genetic variants with influence on the expression levels. In contrast, a problem that has not received much attention to date is that of providing estimates of the effect sizes associated with these variants, in a way that accounts for the considerable amount of selection. Yet, given the difficulty of procuring additional samples, this challenge is of practical importance. We illustrate in this work how the recently developed conditional inference approach can be deployed to obtain confidence intervals for the eQTL effect sizes with reliable coverage. The procedure we propose is based on a randomized hierarchical strategy with a 2-fold contribution: (1) it reflects the selection steps typically adopted in state of the art investigations and (2) it introduces the use of randomness instead of data-splitting to maximize the use of available data. Analysis of the GTEx Liver dataset (v6) suggests that naively obtained confidence intervals would likely not cover the true values of effect sizes and that the number of local genetic polymorphisms influencing the expression level of genes might be underestimated.

We performed a whole genome microsatellite marker scan in six multiplex families with bipolar (BP) mood disorder ascertained in Antioquia, a historically isolated population from North West Colombia. These families were characterized clinically using the approach employed in independent ongoing studies of BP in the closely related population of the Central Valley of Costa Rica. The most consistent linkage results from parametric and non-parametric analyses of the Colombian scan involved markers on 5q31-33, a region implicated by the previous studies of BP in Costa Rica. Because of these concordant results, a follow-up study with additional markers was undertaken in an expanded set of Colombian and Costa Rican families; this provided a genome-wide significant evidence of linkage of BPI to a candidate region of approximately 10 cM in 5q31-33 (maximum non-parametric linkage score=4.395, P0.00004). Interestingly, this region has been implicated in several previous genetic studies of schizophrenia and psychosis, including disease association with variants of the enthoprotin and gamma-aminobutyric acid receptor genes.

Motivation: In systems like Escherichia Coli, the abundance of sequence information, gene expression array studies and small scale experiments allows one to reconstruct the regulatory network and to quantify the effects of transcription factors on gene expression. However, this goal can only be achieved if all information sources are used in concert. Results: Our method integrates literature information, DNA sequences and expression arrays. A set of relevant transcription factors is defined on the basis of literature. Sequence data are used to identify potential target genes and the results are used to define a prior distribution on the topology of the regulatory network. A Bayesian hidden component model for the expression array data allows us to identify which of the potential binding sites are actually used by the regulatory proteins in the studied cell conditions, the strength of their control, and their activation profile in a series of experiments. We apply our methodology to 35 expression studies in E.Coli with convincing results. Availability: Supplementary information: The supplementary material are available at Bioinformatics online. Contact: csabatti@mednet.ucla.edu

Benign recurrent vertigo (BRV) is a common disorder affecting up to 2% of the adult population and may be etiologically related to migraine because of similarities in the clinical spectrum of the phenotypes and a high co-morbidity within families. Many families have multiple-affected genetically related individuals suggesting familial transmission of the disorder with moderate to high penetrance. While clinically similar to episodic ataxias, there are currently no genes identified that contribute to BRV and no systematic linkage studies performed. In an initial effort to genetically define BRV, we have selected from our Neurology Clinic population a subset of 20 multigenerational families with apparent autosomal dominant transmission, and performed genetic linkage mapping using both parametric and non-parametric linkage (NPL) approaches. The Affymetrix 10K SNP Mapping Assay was used for the genotyping. Heterogeneity LOD (HLOD) analysis reveals the evidence of genetic heterogeneity for BRV and evidence of linkage in a subset of the families to 22q12 (HLOD = 4.02). An additional region was identified by NPL analysis at 5p15 (LOD = 2.63). As migraine is observed substantially more commonly both within the BRV-affected individuals and the related family members, it is possible that a form of migraine is allelic to the BRV locus at 22q12. However, testing linkage or the chromosome 22q12 region to a broader migraine/vertigo phenotype by defining affectation status as either migrainous headaches or BRV greatly weakened the linkage signal, and no significant other peaks were detected. Thus, BRV and migraine does not appear to be allelic disorders within these families. We conclude that BRV is a heterogeneous genetic disorder, appears genetically distinct from migraine with aura and is linked to 22q12. Additional family and population-based linkage and association studies will be needed to determine the causative alleles.

Motivation: Gene expression arrays enable measurements of transcription values for a large number or all genes in the genome. In order to better interpret these resluts and to use them to reconstruct transcription networks, information on location of binding sites for regulatory proteins in the entire genome is needed. In particular, this represents an open problem in Escherichia coli.Results: We describe the first implementation of dictionary-style models to the study of transcription factors binding sites in an entire genome. Vocabulon's unique feature is that it can both reconstruct binding sites characterized by unknown motifs and impute locations of known binding sites in long sequences by simultaneous search. On one hand, the dictionary model specifies a probability for the entire sequence taking simultaneously into account all the possible binding sites. This greatly reduces the number of false positives. On the other hand, the possibility of refining motif description, as an increasig number of binding sites are identified, augments the sensitivity of the method. We illustrate these properties with examples in E.coli. The results of gene expression arrays are used both to guide the search and corroborate it.Availability: For copy of the Vocabulon program and other details please contact csabatti@mednet.ucla.eduContact: csabatti@mednet.ucla.edu

We explore the implications of the false discovery rate (FDR) controlling procedure in disease gene mapping. With the aid of simulations, we show how, under models commonly used, the simple step-down procedure introduced by Benjamini and Hochberg controls the FDR for the dependent tests on which linkage and association genome screens are based. This adaptive multiple comparison procedure may offer an important tool for mapping susceptibility genes for complex diseases.

We illustrate how homozygosity of haplotypes can be used to measure the level of disequilibrium between two or more markers. An excess of either homozygosity or heterozygosity signals a departure from the gametic phase equilibrium: We describe the specific form of dependence that is associated with high (low) homozygosity and derive various linkage disequilibrium measures. They feature a clear biological interpretation, can be used to construct tests, and are standardized to allow comparison across loci and populations. They are particularly advantageous to measure linkage disequilibrium between highly polymorphic markers.

Compared to mixed populations, population isolates such as Finland show distinct differences in the prevalence of disease mutations. However, little information exists of the differences on the prevalence of different disease alleles in regional populations with different history of multiple bottlenecks. We constructed a DNA-array and monitored the prevalence of 31 rare and common disease mutations underlying 27 clinical phenotypes in a large population-based study sample. Over 64 000 genotypes were assigned in 2151 samples from four geographical areas representing early and late settlement regions of Finland. Each sample was analyzed in duplicate and a total of 142 000 array-derived genotyping calls were made. On average one in three individuals was found to be a carrier of one of the 31 monitored mutations. This should remove fears of the stigmatizing effect of a carrier-screening program monitoring multiple diseases. Regional differences were found in the prevalence of mutations, providing molecular evidence for the deviating population histories of regional subisolates. The mutations introduced early into the population revealed relatively even distribution in different subregions. More recently introduced rare mutations showed local clustering of disease alleles, indicating the persistence of population subisolates and the effect of multiple bottlenecks in molding the population gene pool. Regional differences were observed also for common disease alleles. Such precise information of the carrier frequencies could form the basis for targeted genetic screens in this population. Our approach describes a general paradigm for large-scale carrier-screening programs also in other populations.

SUMMARY Although Monte Carlo methods have frequently been applied with success, indiscriminate use of Markov chain Monte Carlo leads to unsatisfactory performances in numerous applications. We present a generalised version of the Gibbs sampler that is based on conditional moves along the traces of groups of transformations in the sample space. We explore its connection with the multigrid Monte Carlo method and its use in designing more efficient samplers. The generalised Gibbs sampler provides a framework encompassing a class of recently proposed tricks such as parameter expansion and reparameterisation. To illustrate, we apply this new method to Bayesian inference problems for nonlinear state-space models, ordinal data and stochastic differential equations with discrete observations.

WE thank R.-C. Yang ([2003][1], this issue) for drawing attention to the connection between our work on homozygosity and linkage disequilibrium (LD; [Sabatti and Risch 2002][2]) and his work on zygotic associations ([Yang 2000][3]). As he clearly points out in his letter ([Yang 2003][1]), our

Archival formalin-fixed, paraffin-embedded and ethanol-fixed tissues represent a potentially invaluable resource for gene expression analysis, as they are the most widely available material for studies of human disease. Little data are available evaluating whether RNA obtained from fixed (archival) tissues could produce reliable and reproducible microarray expression data. Here we compare the use of RNA isolated from human archival tissues fixed in ethanol and formalin to frozen tissue in cDNA microarray experiments. Since an additional factor that can limit the utility of archival tissue is the often small quantities available, we also evaluate the use of the tyramide signal amplification method (TSA), which allows the use of small amounts of RNA. Detailed analysis indicates that TSA provides a consistent and reproducible signal amplification method for cDNA microarray analysis, across both arrays and the genes tested. Analysis of this method also highlights the importance of performing non-linear channel normalization and dye switching. Furthermore, archived, fixed specimens can perform well, but not surprisingly, produce more variable results than frozen tissues. Consistent results are more easily obtainable using ethanol-fixed tissues, whereas formalin-fixed tissue does not typically provide a useful substrate for cDNA synthesis and labeling.