Statistical methods in genetics

In recent years, a very large variety of statistical methodologies, at various levels of complexity, have been put forward to analyse genotype data and detect genetic variations that may be responsible for increasing the susceptibility to disease. This review provides a concise account of a number of selected statistical methods for population-based association mapping, from single-marker tests of association to multi-marker data mining techniques for gene-gene interaction detection.     

Statistical methods in spatial genetics

The joint analysis of spatial and genetic data is rapidly becoming the norm in population genetics. More and more studies explicitly describe and quantify the spatial organization of genetic variation and try to relate it to underlying ecological processes. As it has become increasingly difficult to keep abreast with the latest methodological developments, we review the statistical toolbox available to analyse population genetic data in a spatially explicit framework. We mostly focus on statistical concepts but also discuss practical aspects of the analytical methods, highlighting not only the potential of various approaches but also methodological pitfalls.     

Growth factors and cell cultures: a new approach for research in ophthalmology

Tissue culture technology applied to ophtalmology has produced an extensive knowledge of ocular cell physiology. In this work, we review the various factors known to control proliferation and differentiation in lens epithelial cells and corneal endothelial cells. We discuss the role of a new ocular growth factor that we discovered in the retina and whose ubiquitous distribution suggests that it could be involved in tissue-tissue interactions.     

Statistical approaches in landscape genetics: an evaluation of methods for linking landscape and genetic data

The goal of landscape genetics is to detect and explain landscape effects on genetic diversity and structure. Despite the increasing popularity of landscape genetic approaches, the statistical methods for linking genetic and landscape data remain largely untested. This lack of method evaluation makes it difficult to compare studies utilizing different statistics, and compromises the future development and application of the field. To investigate the suitability and comparability of various statistical approaches used in landscape genetics, we simulated data sets corresponding to five landscape-genetic scenarios. We then analyzed these data with eleven methods, and compared the methods based on their statistical power, type-1 error rates, and their overall ability to lead researchers to accurate conclusions about landscape-genetic relationships. Results suggest that some of the most commonly applied techniques (e.g. Mantel and partial Mantel tests) have high type-1 error rates, and that multivariate, non-linear methods are better suited for landscape genetic data analysis. Furthermore, different methods generally show only moderate levels of agreement. Thus, analyzing a data set with only one method could yield method-dependent results, potentially leading to erroneous conclusions. Based on these findings, we give recommendations for choosing optimal combinations of statistical methods, and identify future research needs for landscape genetic data analyses.     

Statistical methods in finite element analysis

Finite element analysis (FEA) is a commonly used tool within many areas of engineering and can provide useful information in structural analysis of mechanical systems. However, most analyses within the field of biomechanics usually take no account either of the wide variation in material properties and geometry that may occur in natural tissues or manufacturing imperfections in synthetic materials. This paper discusses two different methods of incorporating uncertainty in FE models. The first, Taguchi's robust parameter design, uses orthogonal matrices to determine how to vary the parameters in a series of FE models, and provides information on the sensitivity of a model to input parameters. The second, probabilistic analysis, enables the distribution of a response variable to be determined from the distributions of the input variables. The methods are demonstrated using a simple example of an FE model of a beam that is assigned material properties and geometry over a range similar to an orthopaedic fixation plate. In addition to showing how each method may be used on its own, we also show how computational effort may be minimised by first identifying the most important input variables before determining the effects of imprecision.     

Statistical methods for microarray assays

The paper shortly reviews statistical methods used in the area of DNA microarray studies. All stages of the experiment are taken into account: planning, data collection, data preprocessing, analysis and validation. Among the methods of data analysis, the algorithms for estimating differential expression, multivariate approaches, clustering methods, as well as classification and discrimination are reviewed. The need is stressed for routine statistical data processing protocols and for the search of links of microarray data analysis with quantitative genetic models.     

Statistical methods for QTL mapping in cereals

This paper gives an overview of the statistical theory suitable for mapping quantitative trait loci in experimental populations derived from inbred parents, with a particular emphasis on methodology for cereal crops. The basic theory is described, and some new areas of statistical research appropriate for mapping in cereal crops are discussed.     

Statistical and algorithmic methods for fluctuation analysis with SALVADOR as an implementation

This paper aims at removing certain long-standing impediments to more effective and widespread use of fluctuation analysis. The paper presents a method of constructing confidence intervals for mutation rates using data from fluctuation experiments. The method was inspired by a rediscovery of a little-known, not fully developed method of Lea and Coulson; substantial modifications have been made both to enhance computational efficiency and to widen the scope of the original method's applicability. A computer package named SALVADOR is presented that can be used for Monte Carlo simulation, for point and interval estimation of mutation rates, and for exploration of various hypotheses spawned by the directed mutation controversy. In addition to the maximum likelihood method, methods of considerable historical interest are also examined and included in SALVADOR to help the reader compare and assess some of the most popular methods for estimating mutation rates.     

Statistical analysis of microarray data: a Bayesian approach

The potential of microarray data is enormous. It allows us to monitor the expression of thousands of genes simultaneously. A common task with microarray is to determine which genes are differentially expressed between two samples obtained under two different conditions. Recently, several statistical methods have been proposed to perform such a task when there are replicate samples under each condition. Two major problems arise with microarray data. The first one is that the number of replicates is very small (usually 2-10), leading to noisy point estimates. As a consequence, traditional statistics that are based on the means and standard deviations, e.g. t-statistic, are not suitable. The second problem is that the number of genes is usually very large (approximately 10,000), and one is faced with an extreme multiple testing problem. Most multiple testing adjustments are relatively conservative, especially when the number of replicates is small. In this paper we present an empirical Bayes analysis that handles both problems very well. Using different parametrizations, we develop four statistics that can be used to test hypotheses about the means and/or variances of the gene expression levels in both one- and two-sample problems. The methods are illustrated using experimental data with prior knowledge. In addition, we present the result of a simulation comparing our methods to well-known statistics and multiple testing adjustments.     

Statistical assessment of population variability: a methodological approach

We have implemented a multivariate statistical methodology to assess the degree and pattern of cranial variability in skeletal samples. Specifically, the method is designed to test whether variability in a skeletal sample exceeds "normal within-group variability" defined in the present instance as variability present among crania from a cemetery associated with a village. It involves comparing a covariance matrix derived from a sample of unknown composition to one representing "normal within-group variability." The method has been applied to two Plains Indian craniometric samples. The Leavenworth site (39CO9) represents the remnants of previously autonomous Arikara Indian villages devastated by epidemic diseases in the late 1700s. The Bad River 2 Phase is an archaeological designation grouping together closely related sites in the Bad-Cheyenne region of South Dakota dating from 1740-1795 AD. We were able to show substantial heterogeneity among crania from Leavenworth. District burial areas at Leavenworth account for some of the heterogeneity, supporting the notion that they represent an attempt to maintain former social distinctions. We were unable to differentiate among sites within the Bad River 2 Phase, suggesting that it is a valid biological unit.     

Statistical methods for detecting molecular adaptation

The past few years have seen the development of powerful statistical methods for detecting adaptive molecular evolution. These methods compare synonymous and nonsynonymous substitution rates in protein-coding genes, and regard a nonsynonymous rate elevated above the synonymous rate as evidence for darwinian selection. Numerous cases of molecular adaptation are being identified in various systems from viruses to humans. Although previous analyses averaging rates over sites and time have little power, recent methods designed to detect positive selection at individual sites and lineages have been successful. Here, we summarize recent statistical methods for detecting molecular adaptation, and discuss their limitations and possible improvements.     

Statistical methods for geographical surveillance in veterinary epidemiology

Spatial clustering and cluster detection are statistical analysis developed to address relevant scientific hypothesis. The difficulty stays in the large number of alternative hypothesis due to the different mechanisms that could generate the anomalous cases aggregation. We review methods for marked point data (case/control) aimed to describe spatial intensity of disease risk, to test for randomness and to locate significant excesses. Bayesian Gaussian Spatial Exponential models are used to illustrate probabilistic aspects and the link with simpler non parametric tools are shown. We develop an informal guideline to the analysis and used data on faecal contamination and dog parasitic diseases in the city of Naples, Italy. Kernel density estimation resulted very sensitive to bandwidth choice and overemphasized localized excess, Ripley'K function and Cuzick-Edwards test were very consistent each other while the SatScan failed to detect excesses. The spatial range was around 600 meters and justifies several small clusters. Bayesian models were very powerful in reconstructing the phenomenon and allow inference on model parameters in good agreement with the non parametric analysis.     

Statistical methods in recent HIV noninferiority trials: reanalysis of 11 trials

Background

In recent years the “noninferiority” trial has emerged as the new standard design for HIV drug development among antiretroviral patients often with a primary endpoint based on the difference in success rates between the two treatment groups. Different statistical methods have been introduced to provide confidence intervals for that difference. The main objective is to investigate whether the choice of the statistical method changes the conclusion of the trials.

Methods

We presented 11 trials published in 2010 using a difference in proportions as the primary endpoint. In these trials, 5 different statistical methods have been used to estimate such confidence intervals. The five methods are described and applied to data from the 11 trials. The noninferiority of the new treatment is not demonstrated if the prespecified noninferiority margin it includes in the confidence interval of the treatment difference.

Results

Results indicated that confidence intervals can be quite different according to the method used. In many situations, however, conclusions of the trials are not altered because point estimates of the treatment difference were too far from the prespecified noninferiority margins. Nevertheless, in few trials the use of different statistical methods led to different conclusions. In particular the use of “exact” methods can be very confusing.

Conclusion

Statistical methods used to estimate confidence intervals in noninferiority trials have a strong impact on the conclusion of such trials.