A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.

A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

An Incremental EM-based Learning Approach for On-Line Prediction of Hospital Resource Utilization

Objective: Inpatient length of stay (LOS) is an important measure of hospital activity, health care resource consumption, and patient acuity. This research work aims at developing an incremental expectation maximization (EM) based learning approach on mixture of experts (ME) system for on-line prediction of LOS. The use of a batchmode learning process in most existing artificial neural networks to predict LOS is unrealistic, as the data become available over time and their pattern change dynamically. In contrast, an on-line process is capable of providing an output whenever a new datum becomes available. This on-the-spot information is therefore more useful and practical for making decisions, especially when one deals with a tremendous amount of data. Methods and material: The proposed approach is illustrated using a real example of gastroenteritis LOS data. The data set was extracted from a retrospective cohort study on all infants born in 1995-1997 and their subsequent admissions for gastroenteritis. The total number of admissions in this data set was n = 692. Linked hospitalization records of the cohort were retrieved retrospectively to derive the outcome measure, patient demographics, and associated co-morbidities information. A comparative study of the incremental learning and the batch-mode learning algorithms is considered. The performances of the learning algorithms are compared based on the mean absolute difference (MAD) between the predictions and the actual LOS, and the proportion of predictions with MAD < 1 day (Prop(MAD < 1)). The significance of the comparison is assessed through a regression analysis. Results: The incremental learning algorithm provides better on-line prediction of LOS when the system has gained sufficient training from more examples (MAD = 1.77 days and Prop(MAD < 1) = 54.3%), compared to that using the batch-mode learning. The regression analysis indicates a significant decrease of MAD (p-value = 0.063) and a significant (p-value = 0.044) increase of Prop(MAD

Challenges in the diagnosis of Marfan syndrome

Marfan syndrome (MFS) is a multisystem disorder of connective tissue that is inherited in an autosomal dominant fashion, and results from mutations in the FBN1 gene on chromosome 15. Diagnosis is challenging as it requires definition of diverse clinical features and input from a variety of specialists. Genetic testing of FBN1 is time consuming, expensive and complex, and may not solve the diagnostic dilemma. Failure to make a diagnosis or making an inappropriate diagnosis of MFS has social, lifestyle and medical consequences for the individual as well as the family.

Handedness in twins: Joint analysis of data from 35 samples

Simultaneous analysis of handedness data from 35 samples of twins (with a combined sample size of 21,127 twin pairs) found a small but significant additive genetic effect accounting for 25.47% of the variance (95% confidence interval [CI] 15.69-29.51%). No common environmental influences were detected (C = 0.00; 95% Cl 0.00-7.67%), with the majority of the variance, 74.53%, explained by factors unique to the individual (95% Cl 70.49-78.67%). No significant heterogeneity was observed within studies that used similar methods to assess handedness, or across studies that used different methods. At an individual level the majority of studies had insufficient power to reject a purely unique environmental model due to insufficient power to detect familial aggregation. This lack of power is seldom mentioned within studies, and has contributed to the misconception that twin studies of handedness are not informative.

Sex Differences in Symptoms of Depression in Unrelated Individuals and Opposite-Sex Twin and Sibling Pairs

Diagnosis of a major depressive episode by the Diagnostic and Statistical Manual of Mental Disorders of the American Psychiatric Association requires 5 out of 9 symptoms to be present. Therefore, individuals may differ in the specific symptoms they experience and reach a diagnosis of depression via different pathways. It has been suggested that depressed women more often report symptoms of sleep disturbance, appetite or weight disturbance, fatigue, feelings of guilt/worthlessness and psychomotor retardation than depressed men. In the current study, we investigate whether depressed men and women differ in the symptoms they report. Two samples were selected from a sample of Dutch and Australian twins and siblings. First, Dutch and Australian unrelated depressed individuals were selected. Second, a matched epidemiological sample was created consisting of opposite-sex twin and sibling pairs in which both members were depressed. No sex differences in prevalence rates for symptoms were found, with the exception of decreased weight in women in the sample of unrelated individuals. In general, the similarities in symptoms seem to far outweigh the differences in symptoms between men and women. This signifies that men and women are alike in their symptom profiles for major depression and genes for depression are probably expressed in the same way in the two sexes.

Empirical Evaluation of the Genetic Similarity of Samples From Twin Registries in Australia and the Netherlands Using 359 STRP Markers

One way to achieve the large sample sizes required for genetic studies of complex traits is to combine samples collected by different groups. It is not often clear, however, whether this practice is reasonable from a genetic perspective. To assess the comparability of samples from the Australian and the Netherlands twin studies, we estimated F,, (the proportion of total genetic variability attributable to genetic differences between cohorts) based on 359 short tandem repeat polymorphisms in 1068 individuals. IF,, was estimated to be 0.30% between the Australian and the Netherlands cohorts, a smaller value than between many European groups. We conclude that it is reasonable to combine the Australian and the Netherlands samples for joint genetic analyses.

Longitudinal Genetic Analysis of Plasma Lipids

The consensus from published studies is that plasma lipids are each influenced by genetic factors, and that this contributes to genetic variation in risk of cardiovascular disease. Heritability estimates for lipids and lipoproteins are in the range .48 to .87, when measured once per study participant. However, this ignores the confounding effects of biological variation measurement error and ageing, and a truer assessment of genetic effects on cardiovascular risk may be obtained from analysis of longitudinal twin or family data. We have analyzed information on plasma high-density lipoprotein (HDL) and low-density lipoprotein (LDL) cholesterol, and triglycerides, from 415 adult twins who provided blood on two to five occasions over 10 to 17 years. Multivariate modeling of genetic and environmental contributions to variation within and across occasions was used to assess the extent to which genetic and environmental factors have long-term effects on plasma lipids. Results indicated that more than one genetic factor influenced HDL and LDL components of cholesterol, and triglycerides over time in all studies. Nonshared environmental factors did not have significant long-term effects except for HDL. We conclude that when heritability of lipid risk factors is estimated on only one occasion, the existence of biological variation and measurement errors leads to underestimation of the importance of genetic factors as a cause of variation in long-term risk within the population. In addition our data suggest that different genes may affect the risk profile at different ages.

Subtypes of Illicit Drug Users: A Latent Class Analysis of Data From an Australian Twin Sample

This article applies methods of latent class analysis (LCA) to data on lifetime illicit drug use in order to determine whether qualitatively distinct classes of illicit drug users can be identified. Self-report data on lifetime illicit drug use (cannabis, stimulants, hallucinogens, sedatives, inhalants, cocaine, opioids and solvents) collected from a sample of 6265 Australian twins (average age 30 years) were analyzed using LCA. Rates of childhood sexual and physical abuse, lifetime alcohol and tobacco dependence, symptoms of illicit drug abuse/dependence and psychiatric comorbidity were compared across classes using multinomial logistic regression. LCA identified a 5-class model: Class 1 (68.5%) had low risks of the use of all drugs except cannabis; Class 2 (17.8%) had moderate risks of the use of all drugs; Class 3 (6.6%) had high rates of cocaine, other stimulant and hallucinogen use but lower risks for the use of sedatives or opioids. Conversely, Class 4 (3.0%) had relatively low risks of cocaine, other stimulant or hallucinogen use but high rates of sedative and opioid use. Finally, Class 5 (4.2%) had uniformly high probabilities for the use of all drugs. Rates of psychiatric comorbidity were highest in the polydrug class although the sedative/opioid class had elevated rates of depression/suicidal behaviors and exposure to childhood abuse. Aggregation of population-level data may obscure important subgroup differences in patterns of illicit drug use and psychiatric comorbidity. Further exploration of a 'self-medicating' subgroup is needed.

Heritability and Stability of Resting Blood Pressure in Australian Twins

In Australian twins participating in three different studies (1979-1996), the contribution of genetic and environmental influences to variation in resting systolic (SBP) and diastolic blood pressure (DBP) was studied. The sample consisted of 368 monozygotic and 335 dizygotic twin pairs with measurements for both individuals. Blood pressure measurements in two studies were available for 115 complete twin pairs, and 49 twin pairs had measurements in three studies. This allowed assessment of blood pressure tracking over an average period of 12 years in the age range of 23 to 45 years. Multivariate analyses showed significant heritability (h(2)) of blood pressure in all studies (SBP h(2) = 19%-56%, DBP h(2) = 37%-52%). In addition, the analyses showed that the blood pressure tracking was explained by the same set of genetic factors. These results replicate an earlier finding in Dutch twins that also showed stability of the contribution of genetic factors to blood pressure tracking.

Migraine With Aura and Migraine Without Aura Are Not Distinct Entities: Further Evidence From a Large Dutch Population Study

It is often debated whether migraine with aura (MA) and migraine without aura (MO) are etiologically distinct disorders. A previous study using latent class analysis (LCA) in Australian twins showed no evidence for separate subtypes of MO and MA. The aim of the present study was to replicate these results in a population of Dutch twins and their parents, siblings and partners (N = 10,144). Latent class analysis of International Headache Society (IHS)-based migraine symptoms resulted in the identification of 4 classes: a class of unaffected subjects (class 0), a mild form of nonmigrainous headache (class 1), a moderately severe type of migraine (class 2), typically without neurological symptoms or aura (8% reporting aura symptoms), and a severe type of migraine (class 3), typically with neurological symptoms, and aura symptoms in approximately half of the cases. Given the overlap of neurological symptoms and nonmutual exclusivity of aura symptoms, these results do not support the MO and MA subtypes as being etiologically distinct. The heritability in female twins of migraine based on LCA classification was estimated at .50 (95% confidence intervals [0CI} .27 -.59), similar to IHS-based migraine diagnosis (h(2) = .49, 95% Cl .19-.57). However, using a dichotomous classification (affected-unaffected) decreased heritability for the IHS-based classification (h(2) = .33, 95% Cl .00-.60), but not the LCA-based classification (h(2) = .51, 95% Cl. 23-.61). Importantly, use of the LCA-based classification increased the number of subjects classified as affected. The heritability of the screening question was similar to more detailed LCA and IHS classifications, suggesting that the screening procedure is an important determining factor in genetic studies of migraine.

Increased DNA Methylation at the AXIN1 Gene in a Monozygotic Twin from a Pair Discordant for a Caudal Duplication Anomaly

The AXIN1 gene has been implicated in caudal duplication anomalies. Its coding region was sequenced in both members of a monozygotic ( MZ) twin pair discordant for a caudal duplication anomaly, but no mutation was found. Using bisulfite sequencing, we examined methylation at the promoter region of the AXIN1 gene in these twins and in twin and age-matched singleton controls. Methylation of the promoter region in peripheral blood mononucleated cells was variable among individuals, including MZ pairs. In the MZ pair discordant for the caudal duplication, this region of the affected twin was significantly more methylated than that of the unaffected twin (), which was significantly more P < .0001 methylated than those of the controls (). We have confirmed that this CpG island does function as a promoter P = .02 in vitro and that its activity is inversely proportional to the extent of methylation. This finding raises the possibility that hypermethylation of the AXIN1 promoter, by mechanisms as yet undetermined, is associated with the malformation. This case may be paradigmatic for some cases of MZ discordance.

Population differences in finger-length ratios: Ethnicity or latitude?

The relative length of the second and fourth fingers (the 2D:4D ratio) has been taken to be an indicator of prenatal exposure to testosterone, and hence possibly relevant to sexual orientation and other sex-differentiated behaviors. Studies have reported a difference in this ratio between Caucasian males in Britain and in the U.S.: higher average 2D:4D ratios were obtained in Britain. This raises the question of whether differences among different Caucasian gene pools were responsible or whether some environmental variable associated with latitude might be involved (e.g., exposure to sunlight or different day-length patterns). This question was explored by examining 2D:4D ratios for an Australian adolescent sample. The Australians were predominantly of British ancestry, but lived at distances from the equator more like those of the U.S. studies. The Australian 2D:4D ratios resembled those in Britain rather than those in the U.S., tending to exclude hypotheses related to latitude and making differences in gene pools a plausible explanation.

Genome-wide linkage scan for loci influencing plasma triglycerides

Background: Plasma triglyceride concentration is known to be a significant risk factor for cardiovascular disease (CVD). Previous studies have found that the level of triglycerides is strongly influenced by genetic factors. Methods: To identify quantitative trait loci influencing triglycerides, we conducted a genome-wide linkage scan on data from 485 Australian adult dizygotic twin pairs. Prior to linkage analysis, triglyceride values were adjusted for the effects of covariates including age, sex, time since last meal, time of blood collection (CT) and time to plasma separation. Results: The heritability estimate for ln(triglyceride) adjusted for all above fixed effects was 0.49. The highest multipoint LOD score observed was 2.94 (genome-wide p=0.049) on chromosome 7 (at 65cM). This 7p region contains several candidate genes. Two other regions with suggestive multipoint LOD scores were also identified on chromosome 4 (LOD score=2.26 at 62cM) and chromosome X (LOD score=2.01 at 81cM). Conclusions: The linkage peaks found represent newly identified regions for more detailed study, in particular the significant linkage observed on chromosome 7p13. \ (c) 2006 Elsevier B.V. All rights reserved.

A simple method to localise pleiotropic susceptibility loci using univariate linkage analyses of correlated traits

Univariate linkage analysis is used routinely to localise genes for human complex traits. Often, many traits are analysed but the significance of linkage for each trait is not corrected for multiple trait testing, which increases the experiment-wise type-I error rate. In addition, univariate analyses do not realise the full power provided by multivariate data sets. Multivariate linkage is the ideal solution but it is computationally intensive, so genome-wide analysis and evaluation of empirical significance are often prohibitive. We describe two simple methods that efficiently alleviate these caveats by combining P-values from multiple univariate linkage analyses. The first method estimates empirical pointwise and genome-wide significance between one trait and one marker when multiple traits have been tested. It is as robust as an appropriate Bonferroni adjustment, with the advantage that no assumptions are required about the number of independent tests performed. The second method estimates the significance of linkage between multiple traits and one marker and, therefore, it can be used to localise regions that harbour pleiotropic quantitative trait loci (QTL). We show that this method has greater power than individual univariate analyses to detect a pleiotropic QTL across different situations. In addition, when traits are moderately correlated and the QTL influences all traits, it can outperform formal multivariate VC analysis. This approach is computationally feasible for any number of traits and was not affected by the residual correlation between traits. We illustrate the utility of our approach with a genome scan of three asthma traits measured in families with a twin proband.