Comparison of regmed and BayesNetty for exploring causal models with many variables.

Here we compare a recently proposed method and software package, regmed, with our own previously developed package, BayesNetty, designed to allow exploratory analysis of complex causal relationships between biological variables. We find that regmed generally has poorer recall but much better precision than BayesNetty. This is perhaps not too surprising as regmed is specifically designed for use with high-dimensional data. BayesNetty is found to be more sensitive to the resulting multiple testing problem encountered in these circumstances. However, as regmed is not designed to handle missing data, its performance is severely affected when missing data is present, whereas the performance of BayesNetty is only slightly affected. The performance of regmed can be rescued in this situation by first using BayesNetty to impute the missing data, and then applying regmed to the resulting "filled-in" data set.

A Bayesian network approach incorporating imputation of missing data enables exploratory analysis of complex causal biological relationships.

Bayesian networks can be used to identify possible causal relationships between variables based on their conditional dependencies and independencies, which can be particularly useful in complex biological scenarios with many measured variables. Here we propose two improvements to an existing method for Bayesian network analysis, designed to increase the power to detect potential causal relationships between variables (including potentially a mixture of both discrete and continuous variables). Our first improvement relates to the treatment of missing data. When there is missing data, the standard approach is to remove every individual with any missing data before performing analysis. This can be wasteful and undesirable when there are many individuals with missing data, perhaps with only one or a few variables missing. This motivates the use of imputation. We present a new imputation method that uses a version of nearest neighbour imputation, whereby missing data from one individual is replaced with data from another individual, their nearest neighbour. For each individual with missing data, the subsets of variables to be used to select the nearest neighbour are chosen by sampling without replacement the complete data and estimating a best fit Bayesian network. We show that this approach leads to marked improvements in the recall and precision of directed edges in the final network identified, and we illustrate the approach through application to data from a recent study investigating the causal relationship between methylation and gene expression in early inflammatory arthritis patients. We also describe a second improvement in the form of a pseudo-Bayesian approach for upweighting certain network edges, which can be useful when there is prior evidence concerning their directions.

Bayesian network analysis incorporating genetic anchors complements conventional Mendelian randomization approaches for exploratory analysis of causal relationships in complex data.

Mendelian randomization (MR) implemented through instrumental variables analysis is an increasingly popular causal inference tool used in genetic epidemiology. But it can have limitations for evaluating simultaneous causal relationships in complex data sets that include, for example, multiple genetic predictors and multiple potential risk factors associated with the same genetic variant. Here we use real and simulated data to investigate Bayesian network analysis (BN) with the incorporation of directed arcs, representing genetic anchors, as an alternative approach. A Bayesian network describes the conditional dependencies/independencies of variables using a graphical model (a directed acyclic graph) with an accompanying joint probability. In real data, we found BN could be used to infer simultaneous causal relationships that confirmed the individual causal relationships suggested by bi-directional MR, while allowing for the existence of potential horizontal pleiotropy (that would violate MR assumptions). In simulated data, BN with two directional anchors (mimicking genetic instruments) had greater power for a fixed type 1 error than bi-directional MR, while BN with a single directional anchor performed better than or as well as bi-directional MR. Both BN and MR could be adversely affected by violations of their underlying assumptions (such as genetic confounding due to unmeasured horizontal pleiotropy). BN with no directional anchor generated inference that was no better than by chance, emphasizing the importance of directional anchors in BN (as in MR). Under highly pleiotropic simulated scenarios, BN outperformed both MR (and its recent extensions) and two recently-proposed alternative approaches: a multi-SNP mediation intersection-union test (SMUT) and a latent causal variable (LCV) test. We conclude that BN incorporating genetic anchors is a useful complementary method to conventional MR for exploring causal relationships in complex data sets such as those generated from modern "omics" technologies.

Increased Power for Detection of Parent-of-Origin Effects via the Use of Haplotype Estimation.

Parent-of-origin (or imprinting) effects relate to the situation in which traits are influenced by the allele inherited from only one parent and the allele from the other parent has little or no effect. Given SNP genotype data from case-parent trios, the parent of origin of each allele in the offspring can often be deduced unambiguously; however, this is not true when all three individuals are heterozygous. Most existing methods for investigating parent-of-origin effects operate on a SNP-by-SNP basis and either perform some sort of averaging over the possible parental transmissions or else discard ambiguous trios. If the correct parent of origin at a SNP could be determined, this would provide extra information and increase the power for detecting the effects of imprinting. We propose making use of the surrounding SNP information, via haplotype estimation, to improve estimation of parent of origin at a test SNP for case-parent trios, case-mother duos, and case-father duos. This extra information is then used in a multinomial modeling approach for estimating parent-of-origin effects at the test SNP. We show through computer simulations that our approach has increased power over previous approaches, particularly when the data consist only of duos. We apply our method to two real datasets and find a decrease in significance of p values in genomic regions previously thought to possibly harbor imprinting effects, thus weakening the evidence that such effects actually exist in these regions, although some regions retain evidence of significant effects.

Causal modeling in a multi-omic setting: insights from GAW20.

BACKGROUND: Increasingly available multilayered omics data on large populations has opened exciting analytic opportunities and posed unique challenges to robust estimation of causal effects in the setting of complex disease phenotypes. The GAW20 Causal Modeling Working Group has applied complementary approaches (eg, Mendelian randomization, structural equations modeling, Bayesian networks) to discover novel causal effects of genomic and epigenomic variation on lipid phenotypes, as well as to validate prior findings from observational studies. RESULTS: Two Mendelian randomization studies have applied novel approaches to instrumental variable selection in methylation data, identifying bidirectional causal effects of CPT1A and triglycerides, as well as of RNMT and C6orf42, on high-density lipoprotein cholesterol response to fenofibrate. The CPT1A finding also emerged in a Bayesian network study. The Mendelian randomization studies have implemented both existing and novel steps to account for pleiotropic effects, which were independently detected in the GAW20 data via a structural equation modeling approach. Two studies estimated indirect effects of genomic variation (via DNA methylation and/or correlated phenotypes) on lipid outcomes of interest. Finally, a novel weighted R2 measure was proposed to complement other causal inference efforts by controlling for the influence of outlying observations. CONCLUSIONS: The GAW20 contributions illustrate the diversity of possible approaches to causal inference in the multi-omic context, highlighting the promises and assumptions of each method and the benefits of integrating both across methods and across omics layers for the most robust and comprehensive insights into disease processes.

Imputation without doing imputation: a new method for the detection of non-genotyped causal variants.

Genome-wide association studies allow detection of non-genotyped disease-causing variants through testing of nearby genotyped SNPs. This approach may fail when there are no genotyped SNPs in strong LD with the causal variant. Several genotyped SNPs in weak LD with the causal variant may, however, considered together, provide equivalent information. This observation motivates popular but computationally intensive approaches based on imputation or haplotyping. Here we present a new method and accompanying software designed for this scenario. Our approach proceeds by selecting, for each genotyped "anchor" SNP, a nearby genotyped "partner" SNP, chosen via a specific algorithm we have developed. These two SNPs are used as predictors in linear or logistic regression analysis to generate a final significance test. In simulations, our method captures much of the signal captured by imputation, while taking a fraction of the time and disc space, and generating a smaller number of false-positives. We apply our method to a case/control study of severe malaria genotyped using the Affymetrix 500K array. Previous analysis showed that fine-scale sequencing of a Gambian reference panel in the region of the known causal locus, followed by imputation, increased the signal of association to genome-wide significance levels. Our method also increases the signal of association from P ≈ 2 × 10⁻6 to P ≈ 6 × 10⁻¹¹. Our method thus, in some cases, eliminates the need for more complex methods such as sequencing and imputation, and provides a useful additional test that may be used to identify genetic regions of interest.

Understanding foot-and-mouth disease virus transmission biology: identification of the indicators of infectiousness.

The control of foot-and-mouth disease virus (FMDV) outbreaks in non-endemic countries relies on the rapid detection and removal of infected animals. In this paper we use the observed relationship between the onset of clinical signs and direct contact transmission of FMDV to identify predictors for the onset of clinical signs and identify possible approaches to preclinical screening in the field. Threshold levels for various virological and immunological variables were determined using Receiver Operating Characteristic (ROC) curve analysis and then tested using generalized linear mixed models to determine their ability to predict the onset of clinical signs. In addition, concordance statistics between qualitative real time PCR test results and virus isolation results were evaluated. For the majority of animals (71%), the onset of clinical signs occurred 3-4 days post infection. The onset of clinical signs was associated with high levels of virus in the blood, oropharyngeal fluid and nasal fluid. Virus is first detectable in the oropharyngeal fluid, but detection of virus in the blood and nasal fluid may also be good candidates for preclinical indicators. Detection of virus in the air was also significantly associated with transmission. This study is the first to identify statistically significant indicators of infectiousness for FMDV at defined time periods during disease progression in a natural host species. Identifying factors associated with infectiousness will advance our understanding of transmission mechanisms and refine intra-herd and inter-herd disease transmission models.

PREMIM and EMIM: tools for estimation of maternal, imprinting and interaction effects using multinomial modelling.

BACKGROUND: Here we present two new computer tools, PREMIM and EMIM, for the estimation of parental and child genetic effects, based on genotype data from a variety of different child-parent configurations. PREMIM allows the extraction of child-parent genotype data from standard-format pedigree data files, while EMIM uses the extracted genotype data to perform subsequent statistical analysis. The use of genotype data from the parents as well as from the child in question allows the estimation of complex genetic effects such as maternal genotype effects, maternal-foetal interactions and parent-of-origin (imprinting) effects. These effects are estimated by EMIM, incorporating chosen assumptions such as Hardy-Weinberg equilibrium or exchangeability of parental matings as required. RESULTS: In application to simulated data, we show that the inference provided by EMIM is essentially equivalent to that provided by alternative (competing) software packages such as MENDEL and LEM. However, PREMIM and EMIM (used in combination) considerably outperform MENDEL and LEM in terms of speed and ease of execution. CONCLUSIONS: Together, EMIM and PREMIM provide easy-to-use command-line tools for the analysis of pedigree data, giving unbiased estimates of parental and child genotype relative risks.

Confirmation of the superior performance of the causal Graphical Analysis Using Genetics (cGAUGE) pipeline in comparison to various competing alternatives.

Various methods exist that utilise information from genetic predictors to help identify potential causal relationships between measured biological or clinical traits. Here we conduct computer simulations to investigate the performance of a recently proposed causal Graphical Analysis Using Genetics (cGAUGE) pipeline, used as a precursor to Mendelian randomization analysis, in comparison to our previously proposed Bayesian Network approach for addressing this problem. We use the same simulation (and analysis) code as was used by the developers of cGAUGE, adding in a comparison with the Bayesian Network approach. Overall, we find the optimal method (in terms of giving high power and low false discovery rate) is the cGAUGE pipeline followed by subsequent analysis using the MR-PRESSO Mendelian randomization approach.

Temporal trends in the discovery of human viruses.

On average, more than two new species of human virus are reported every year. We constructed the cumulative species discovery curve for human viruses going back to 1901. We fitted a statistical model to these data; the shape of the curve strongly suggests that the process of virus discovery is far from complete. We generated a 95% credible interval for the pool of as yet undiscovered virus species of 38-562. We extrapolated the curve and generated an estimate of 10-40 new species to be discovered by 2020. Although we cannot predict the level of health threat that these new viruses will present, we conclude that novel virus species must be anticipated in public health planning. More systematic virus discovery programmes, covering both humans and potential animal reservoirs of human viruses, should be considered.

Application of Bayesian networks to GAW20 genetic and blood lipid data.

BACKGROUND: Bayesian networks have been proposed as a way to identify possible causal relationships between measured variables based on their conditional dependencies and independencies. We explored the use of Bayesian network analyses applied to the GAW20 data to identify possible causal relationships between differential methylation of cytosine-phosphate-guanine dinucleotides (CpGs), single-nucleotide polymorphisms (SNPs), and blood lipid trait (triglycerides [TGs]). METHODS: After initial exploratory linear regression analyses, 2 Bayesian networks analyses were performed. First, we used the real data and modeled the effects of 4 CpGs previously found to be associated with TGs in the Genetics of Lipid Lowering Drugs and Diet Network Study (GOLDN). Second, we used the simulated data and modeled the effect of a fictional lipid modifying drug with 5 known causal SNPs and 5 corresponding CpGs. RESULTS: In the real data we show that relationships are present between the CpGs, TGs, and other variables-age, sex, and center. In the simulated data, we show, using linear regression, that no CpGs and only 1 SNP were associated with a change in TG levels, and, using Bayesian network analysis, that relationships are present between the change in TG levels and most SNPs, but not with CpGs. CONCLUSIONS: Even when the causal relationships between variables are known, as with the simulated data, if the relationships are not strong then it is challenging to reproduce them in a Bayesian network.

Using penalized regression to predict phenotype from SNP data.

BACKGROUND: In a typical genome-enabled prediction problem there are many more predictor variables than response variables. This prohibits the application of multiple linear regression, because the unique ordinary least squares estimators of the regression coefficients are not defined. To overcome this problem, penalized regression methods have been proposed, aiming at shrinking the coefficients toward zero. METHODS: We explore prediction of phenotype from single nucleotide polymorphism (SNP) data in the GAW20 data set using a penalized regression approach (LASSO [least absolute shrinkage and selection operator] regression). We use 10-fold cross-validation to assess predictive performance and 10-fold nested cross-validation to specify a penalty parameter. RESULTS: By analyzing approximately 600,000 SNPs we find that, when the sample size comprises a few hundred individuals, SNP effects are heavily penalized, resulting in a poor predictive performance. Increasing the sample size to a few thousand individuals results in a much smaller penalization of the true effects, thus greatly improving the prediction. CONCLUSIONS: LASSO regression results in a heavy shrinkage of the regression coefficients, and also requires large sample sizes (several thousand individuals) to achieve good prediction.

Further investigations of the W-test for pairwise epistasis testing.

Background: In a recent paper, a novel W-test for pairwise epistasis testing was proposed that appeared, in computer simulations, to have higher power than competing alternatives. Application to genome-wide bipolar data detected significant epistasis between SNPs in genes of relevant biological function. Network analysis indicated that the implicated genes formed two separate interaction networks, each containing genes highly related to autism and neurodegenerative disorders. Methods: Here we investigate further the properties and performance of the W-test via theoretical evaluation, computer simulations and application to real data. Results: We demonstrate that, for common variants, the W-test is closely related to several existing tests of association allowing for interaction, including logistic regression on 8 degrees of freedom, although logistic regression can show inflated type I error for low minor allele frequencies,  whereas the W-test shows good/conservative type I error control. Although in some situations the W-test can show higher power, logistic regression is not limited to tests on 8 degrees of freedom but can instead be tailored to impose greater structure on the assumed alternative hypothesis, offering a power advantage when the imposed structure matches the true structure. Conclusions: The W-test is a potentially useful method for testing for association - without necessarily implying interaction - between genetic variants disease, particularly when one or more of the genetic variants are rare. For common variants, the advantages of the W-test are less clear, and, indeed, there are situations where existing methods perform better. In our investigations, we further uncover a number of problems with the practical implementation and application of the W-test (to bipolar disorder) previously described, apparently due to inadequate use of standard data quality-control procedures. This observation leads us to urge caution in interpretation of the previously-presented results, most of which we consider are highly likely to be artefacts.

Examination of previously identified associations within the Genetic Analysis Workshop 19 data.

We investigate the possible replication of "known" associated single-nucleotide polymorphisms (SNPs) with blood pressure and expression phenotypes. Previous studies have provided a list of 95 SNPs thought to be associated with blood pressure phenotypes, of which 44 were present in the Genetic Analysis Workshop 19 (GAW19) family-imputed genome-wide association studies (GWAS) data and 4 in the GAW19 unrelateds sequence data. Using only the real (not simulated) GAW19 data, we show through the use of statistical tests that account for family relatedness, using FaST-LMM (Factored Spectrally Transformed Linear Mixed Model), that none of our candidate SNPs yields a significant p value. Furthermore, a study of epistasis, aiming to detect statistical interactions between loci with respect to their association with transcription levels has provided a list of 30 associated interacting SNP pairs, of which 13 are present in the GAW19 family GWAS and expression data. We show for this set of results, using the program GEMMA (genome-wide efficient mixed-model analysis) to account for family relatedness, that there is evidence of replication within the real GAW19 data. Two individual SNP pairs reach significance, and the set of remaining results give a combined p value of 0.017 that at least 1 of these remaining SNP pairs interacts to influence an expression phenotype.

Accounting for relatedness in family-based association studies: application to Genetic Analysis Workshop 18 data.

In the last few years, a bewildering variety of methods/software packages that use linear mixed models to account for sample relatedness on the basis of genome-wide genomic information have been proposed. We compared these approaches as implemented in the programs EMMAX, FaST-LMM, Gemma, and GenABEL (FASTA/GRAMMAR-Gamma) on the Genetic Analysis Workshop 18 data. All methods performed quite similarly and were successful in reducing the genomic control inflation factor to reasonable levels, particularly when the mean values of the observations were used, although more variation was observed when data from each time point were used individually. From a practical point of view, we conclude that it makes little difference to the results which method/software package is used, and the user can make the choice of package on the basis of personal taste or computational speed/convenience.

Human viruses: discovery and emergence.

There are 219 virus species that are known to be able to infect humans. The first of these to be discovered was yellow fever virus in 1901, and three to four new species are still being found every year. Extrapolation of the discovery curve suggests that there is still a substantial pool of undiscovered human virus species, although an apparent slow-down in the rate of discovery of species from different families may indicate bounds to the potential range of diversity. More than two-thirds of human viruses can also infect non-human hosts, mainly mammals, and sometimes birds. Many specialist human viruses also have mammalian or avian origins. Indeed, a substantial proportion of mammalian viruses may be capable of crossing the species barrier into humans, although only around half of these are capable of being transmitted by humans and around half again of transmitting well enough to cause major outbreaks. A few possible predictors of species jumps can be identified, including the use of phylogenetically conserved cell receptors. It seems almost inevitable that new human viruses will continue to emerge, mainly from other mammals and birds, for the foreseeable future. For this reason, an effective global surveillance system for novel viruses is needed.

Modelling the within-host dynamics of the foot-and-mouth disease virus in cattle.

In this paper we investigate the within-host dynamics of the foot-and-mouth disease virus (FMDV) in cattle using previously published data for 8 experimentally infected cows. An 8-compartment, 14-parameter differential equation model was fitted to data collected from each cow every 24 h over the course of an infection on: (i) the concentration of FMDV genomes in the blood, (ii) the concentration of infectious virus in the blood, (iii) antibody levels, and (iv) interferon levels. Model parameters were estimated using maximum-likelihood methods. The likelihood surface was sampled using Markov chain Monte Carlo methods giving credible intervals for each of the model parameters. The model was able to capture the within-host dynamics well for 6 of the infections, with both the innate (type 1 interferon) and antibody responses playing key roles in determining the height and duration of peak levels of virus. There was considerable variation between virus dynamics in individual cattle which was only partly accounted for by inferred differences in the dose of virus received. A better understanding of the within-host dynamics also provides insights into the dynamics of infectiousness and the transmission of virus to new hosts.

Finding genes that influence quantitative traits with tree-based clustering.

We present a new statistical method to identify genes in which one or more variants influence quantitative traits. We use the Genetic Analysis Workshop 17 (GAW17) data set of unrelated individuals as a test of the method on the raw GAW17 phenotypes and on residuals after fitting linear models to individual-based covariates. By performing appropriate randomization tests, we found many significant results for a proportion of the genes that contain variants that directly contribute to disease but that have an increased type I error for analyses of raw phenotypes. Power calculations show that our methods have the ability to reliably identify a subset of the loci contributing to disease. When we applied our method to derived phenotypes, we removed many false positives, giving appropriate type I error rates at little cost to power. The correlation between genome-wide heterozygosity and the value of the trait Q1 appears to drive much of the type I error in this data set.

Relationship between clinical signs and transmission of an infectious disease and the implications for control.

Control of many infectious diseases relies on the detection of clinical cases and the isolation, removal, or treatment of cases and their contacts. The success of such "reactive" strategies is influenced by the fraction of transmission occurring before signs appear. We performed experimental studies of foot-and-mouth disease transmission in cattle and estimated this fraction at less than half the value expected from detecting virus in body fluids, the standard proxy measure of infectiousness. This is because the infectious period is shorter (mean 1.7 days) than currently realized, and animals are not infectious until, on average, 0.5 days after clinical signs appear. These results imply that controversial preemptive control measures may be unnecessary; instead, efforts should be directed at early detection of infection and rapid intervention.

Sheep movement networks and the transmission of infectious diseases.

BACKGROUND AND METHODOLOGY: Various approaches have been used to investigate how properties of farm contact networks impact on the transmission of infectious diseases. The potential for transmission of an infection through a contact network can be evaluated in terms of the basic reproduction number, R(0). The magnitude of R(0) is related to the mean contact rate of a host, in this case a farm, and is further influenced by heterogeneities in contact rates of individual hosts. The latter can be evaluated as the second order moments of the contact matrix (variances in contact rates, and co-variance between contacts to and from individual hosts). Here we calculate these quantities for the farms in a country-wide livestock network: >15,000 Scottish sheep farms in each of 4 years from July 2003 to June 2007. The analysis is relevant to endemic and chronic infections with prolonged periods of infectivity of affected animals, and uses different weightings of contacts to address disease scenarios of low, intermediate and high animal-level prevalence. PRINCIPAL FINDINGS AND CONCLUSIONS: Analysis of networks of Scottish farms via sheep movements from July 2003 to June 2007 suggests that heterogeneities in movement patterns (variances and covariances of rates of movement on and off the farms) make a substantial contribution to the potential for the transmission of infectious diseases, quantified as R(0), within the farm population. A small percentage of farms (<20%) contribute the bulk of the transmission potential (>80%) and these farms could be efficiently targeted by interventions aimed at reducing spread of diseases via animal movement.