Mapping epistatic quantitative trait loci.

BACKGROUND: How to map quantitative trait loci (QTL) with epistasis efficiently and reliably has been a persistent problem for QTL mapping analysis. There are a number of difficulties for studying epistatic QTL. Linkage can impose a significant challenge for finding epistatic QTL reliably. If multiple QTL are in linkage and have interactions, searching for QTL can become a very delicate issue. A commonly used strategy that performs a two-dimensional genome scan to search for a pair of QTL with epistasis can suffer from low statistical power and also may lead to false identification due to complex linkage disequilibrium and interaction patterns. RESULTS: To tackle the problem of complex interaction of multiple QTL with linkage, we developed a three-stage search strategy. In the first stage, main effect QTL are searched and mapped. In the second stage, epistatic QTL that interact significantly with other identified QTL are searched. In the third stage, new epistatic QTL are searched in pairs. This strategy is based on the consideration that most genetic variance is due to the main effects of QTL. Thus by first mapping those main-effect QTL, the statistical power for the second and third stages of analysis for mapping epistatic QTL can be maximized. The search for main effect QTL is robust and does not bias the search for epistatic QTL due to a genetic property associated with the orthogonal genetic model that the additive and additive by additive variances are independent despite of linkage. The model search criterion is empirically and dynamically evaluated by using a score-statistic based resampling procedure. We demonstrate through simulations that the method has good power and low false positive in the identification of QTL and epistasis. CONCLUSION: This method provides an effective and powerful solution to map multiple QTL with complex epistatic pattern. The method has been implemented in the user-friendly computer software Windows QTL Cartographer. This will greatly facilitate the application of the method for QTL mapping data analysis.

Subchondral bone trabecular integrity predicts and changes concurrently with radiographic and magnetic resonance imaging-determined knee osteoarthritis progression.

OBJECTIVE: To evaluate subchondral bone trabecular integrity (BTI) on radiographs as a predictor of knee osteoarthritis (OA) progression. METHODS: Longitudinal (baseline, 12-month, and 24-month) knee radiographs were available for 60 female subjects with knee OA. OA progression was defined by 12- and 24-month changes in radiographic medial compartment minimal joint space width (JSW) and medial joint space area (JSA), and by medial tibial and femoral cartilage volume on magnetic resonance imaging. BTI of the medial tibial plateau was analyzed by fractal signature analysis using commercially available software. Receiver operating characteristic (ROC) curves for BTI were used to predict a 5% change in OA progression parameters. RESULTS: Individual terms (linear and quadratic) of baseline BTI of vertical trabeculae predicted knee OA progression based on 12- and 24-month changes in JSA (P < 0.01 for 24 months), 24-month change in tibial (P < 0.05), but not femoral, cartilage volume, and 24-month change in JSW (P = 0.05). ROC curves using both terms of baseline BTI predicted a 5% change in the following OA progression parameters over 24 months with high accuracy, as reflected by the area under the curve measures: JSW 81%, JSA 85%, tibial cartilage volume 75%, and femoral cartilage volume 85%. Change in BTI was also significantly associated (P < 0.05) with concurrent change in JSA over 12 and 24 months and with change in tibial cartilage volume over 24 months. CONCLUSION: BTI predicts structural OA progression as determined by radiographic and MRI outcomes. BTI may therefore be worthy of study as an outcome measure for OA studies and clinical trials.

Multiple trait multiple interval mapping of quantitative trait loci from inbred line crosses.

BACKGROUND: Although many experiments have measurements on multiple traits, most studies performed the analysis of mapping of quantitative trait loci (QTL) for each trait separately using single trait analysis. Single trait analysis does not take advantage of possible genetic and environmental correlations between traits. In this paper, we propose a novel statistical method for multiple trait multiple interval mapping (MTMIM) of QTL for inbred line crosses. We also develop a novel score-based method for estimating genome-wide significance level of putative QTL effects suitable for the MTMIM model. The MTMIM method is implemented in the freely available and widely used Windows QTL Cartographer software. RESULTS: Throughout the paper, we provide compelling empirical evidences that: (1) the score-based threshold maintains proper type I error rate and tends to keep false discovery rate within an acceptable level; (2) the MTMIM method can deliver better parameter estimates and power than single trait multiple interval mapping method; (3) an analysis of Drosophila dataset illustrates how the MTMIM method can better extract information from datasets with measurements in multiple traits. CONCLUSIONS: The MTMIM method represents a convenient statistical framework to test hypotheses of pleiotropic QTL versus closely linked nonpleiotropic QTL, QTL by environment interaction, and to estimate the total genotypic variance-covariance matrix between traits and to decompose it in terms of QTL-specific variance-covariance matrices, therefore, providing more details on the genetic architecture of complex traits.

Composite interval mapping and multiple interval mapping: procedures and guidelines for using Windows QTL Cartographer.

Tremendous progress has been made in recent years on developing statistical methods for mapping quantitative trait loci (QTL) from crosses of inbred lines. In this chapter, we provide an introduction of composite interval mapping and multiple interval mapping methods for mapping QTL from inbred line crosses and also detailed instructions to perform the analyses in Windows QTL Cartographer. For each method, we discuss the meaning of each option in the analysis procedures and how to understand and interpret the mapping results through a work-out example.

GWAPower: a statistical power calculation software for genome-wide association studies with quantitative traits.

BACKGROUND: In designing genome-wide association (GWA) studies it is important to calculate statistical power. General statistical power calculation procedures for quantitative measures often require information concerning summary statistics of distributions such as mean and variance. However, with genetic studies, the effect size of quantitative traits is traditionally expressed as heritability, a quantity defined as the amount of phenotypic variation in the population that can be ascribed to the genetic variants among individuals. Heritability is hard to transform into summary statistics. Therefore, general power calculation procedures cannot be used directly in GWA studies. The development of appropriate statistical methods and a user-friendly software package to address this problem would be welcomed. RESULTS: This paper presents GWAPower, a statistical software package of power calculation designed for GWA studies with quantitative traits, where genetic effect is defined as heritability. Based on several popular one-degree-of-freedom genetic models, this method avoids the need to specify the non-centrality parameter of the F-distribution under the alternative hypothesis. Therefore, it can use heritability information directly without approximation. In GWAPower, the power calculation can be easily adjusted for adding covariates and linkage disequilibrium information. An example is provided to illustrate GWAPower, followed by discussions. CONCLUSIONS: GWAPower is a user-friendly free software package for calculating statistical power based on heritability in GWA studies with quantitative traits. The software is freely available at: http://dl.dropbox.com/u/10502931/GWAPower.zip.

Summarizing and quantifying multilocus linkage disequilibrium patterns with multi-order Markov chain models.

Studies on linkage disequilibrium (LD) are important in mapping disease genes. A novel statistical method, the multi-order Markov chain model has been recently developed to quantify the complexity level of multilocus LD patterns among single nucleotide polymorphism markers (Kim et al., 2008). In this study, mathematical relationships between two types of LD measures are derived to understand the Markov chain model parameters in terms of conventional LD measures. Statistical sample properties of the Markov chain order estimates are investigated by simulations. Two published data sets are reanalyzed to illustrate the proposed approach.

Trabecular morphometry by fractal signature analysis is a novel marker of osteoarthritis progression.

OBJECTIVE: To evaluate the effectiveness of using subchondral bone texture observed on a radiograph taken at baseline to predict progression of knee osteoarthritis (OA) over a 3-year period. METHODS: A total of 138 participants in the Prediction of Osteoarthritis Progression study were evaluated at baseline and after 3 years. Fractal signature analysis (FSA) of the medial subchondral tibial plateau was performed on fixed flexion radiographs of 248 nonreplaced knees, using a commercially available software tool. OA progression was defined as a change in joint space narrowing (JSN) or osteophyte formation of 1 grade according to a standardized knee atlas. Statistical analysis of fractal signatures was performed using a new model based on correlating the overall shape of a fractal dimension curve with radius. RESULTS: Fractal signature of the medial tibial plateau at baseline was predictive of medial knee JSN progression (area under the curve [AUC] 0.75, of a receiver operating characteristic curve) but was not predictive of osteophyte formation or progression of JSN in the lateral compartment. Traditional covariates (age, sex, body mass index, knee pain), general bone mineral content, and joint space width at baseline were no more effective than random variables for predicting OA progression (AUC 0.52-0.58). The predictive model with maximum effectiveness combined fractal signature at baseline, knee alignment, traditional covariates, and bone mineral content (AUC 0.79). CONCLUSION: We identified a prognostic marker of OA that is readily extracted from a plain radiograph using FSA. Although the method needs to be validated in a second cohort, our results indicate that the global shape approach to analyzing these data is a potentially efficient means of identifying individuals at risk of knee OA progression.

Quantitative trait loci mapping and the genetic basis of heterosis in maize and rice.

Despite its importance to agriculture, the genetic basis of heterosis is still not well understood. The main competing hypotheses include dominance, overdominance, and epistasis. NC design III is an experimental design that has been used for estimating the average degree of dominance of quantitative trait loci (QTL) and also for studying heterosis. In this study, we first develop a multiple-interval mapping (MIM) model for design III that provides a platform to estimate the number, genomic positions, augmented additive and dominance effects, and epistatic interactions of QTL. The model can be used for parents with any generation of selfing. We apply the method to two data sets, one for maize and one for rice. Our results show that heterosis in maize is mainly due to dominant gene action, although overdominance of individual QTL could not completely be ruled out due to the mapping resolution and limitations of NC design III. For rice, the estimated QTL dominant effects could not explain the observed heterosis. There is evidence that additive x additive epistatic effects of QTL could be the main cause for the heterosis in rice. The difference in the genetic basis of heterosis seems to be related to open or self pollination of the two species. The MIM model for NC design III is implemented in Windows QTL Cartographer, a freely distributed software.

Multiple-interval mapping for ordinal traits.

Many statistical methods have been developed to map multiple quantitative trait loci (QTL) in experimental cross populations. Among these methods, multiple-interval mapping (MIM) can map QTL with epistasis simultaneously. However, the previous implementation of MIM is for continuously distributed traits. In this study we extend MIM to ordinal traits on the basis of a threshold model. The method inherits the properties and advantages of MIM and can fit a model of multiple QTL effects and epistasis on the underlying liability score. We study a number of statistical issues associated with the method, such as the efficiency and stability of maximization and model selection. We also use computer simulation to study the performance of the method and compare it to other alternative approaches. The method has been implemented in QTL Cartographer to facilitate its general usage for QTL mapping data analysis on binary and ordinal traits.