A Manhattan plot is a type of plot, usually used to display data with a large number of data-points, many of non-zero amplitude, and with a distribution of higher-magnitude values. The plot is commonly used in genome-wide association studies (GWAS) to display significant SNPs. [1]
It gains its name from the similarity of such a plot to the Manhattan skyline: a profile of skyscrapers towering above the lower level "buildings" which vary around a lower height.
In GWAS Manhattan plots, genomic coordinates are displayed along the x-axis, with the negative logarithm of the association p-value for each single nucleotide polymorphism (SNP) displayed on the y-axis, meaning that each dot on the Manhattan plot signifies an SNP. Because the strongest associations have the smallest p-values (e.g., 10−15), their negative logarithms will be the greatest (e.g., 15). The different colors of each block usually show the extent of each chromosome.
Biostatistics are the development and application of statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results.
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation.
A logarithmic scale is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale. Rather, the numbers 10 and 100, and 60 and 600 are equally spaced. Thus moving a unit of distance along the scale means the number has been multiplied by 10. Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph. Another way to think about it is that the number of digits of the data grows at a constant rate. For example, the numbers 10, 100, 1000, and 10000 are equally spaced on a log scale, because their numbers of digits is going up by 1 each time: 2, 3, 4, and 5 digits. In this way, adding two digits multiplies the quantity measured on the log scale by a factor of 100.
A chart is a graphical representation for data visualization, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart". A chart can represent tabular numeric data, functions or some kinds of quality structure and provides different info.
A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded (color/shape/size), one additional variable can be displayed. The data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.
In genetics, a single-nucleotide polymorphism is a germline substitution of a single nucleotide at a specific position in the genome. Although certain definitions require the substitution to be present in a sufficiently large fraction of the population, many publications do not apply such a frequency threshold.
A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley's work in the early 1900s, and are useful tools in exploratory data analysis. Stemplots became more commonly used in the 1980s after the publication of John Tukey's book on exploratory data analysis in 1977. The popularity during those years is attributable to their use of monospaced (typewriter) typestyles that allowed computer technology of the time to easily produce the graphics. Modern computers' superior graphic capabilities have meant these techniques are less often used.
A tag SNP is a representative single nucleotide polymorphism (SNP) in a region of the genome with high linkage disequilibrium that represents a group of SNPs called a haplotype. It is possible to identify genetic variation and association to phenotypes without genotyping every SNP in a chromosomal region. This reduces the expense and time of mapping genome areas associated with disease, since it eliminates the need to study every individual SNP. Tag SNPs are useful in whole-genome SNP association studies in which hundreds of thousands of SNPs across the entire genome are genotyped.
In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point zi is replaced with the transformed value yi = f(zi), where f is a function. Transforms are usually applied so that the data appear to more closely meet the assumptions of a statistical inference procedure that is to be applied, or to improve the interpretability or appearance of graphs.
In genomics, a genome-wide association study, also known as whole genome association study, is an observational study of a genome-wide set of genetic variants in different individuals to see if any variant is associated with a trait. GWA studies typically focus on associations between single-nucleotide polymorphisms (SNPs) and traits like major human diseases, but can equally be applied to any other genetic variants and any other organisms.
In mathematics, the super-logarithm is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverse functions, super-roots and super-logarithms. There are several ways of interpreting super-logarithms:
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used. Graphs are a visual representation of the relationship between variables, which are very useful for humans who can then quickly derive an understanding which may not have come from lists of values. Given a scale or ruler, graphs can also be used to read off the value of an unknown variable plotted as a function of a known one, but this can also be done with data presented in tabular form. Graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas.
Relative species abundance is a component of biodiversity and is a measure of how common or rare a species is relative to other species in a defined location or community. Relative abundance is the percent composition of an organism of a particular kind relative to the total number of organisms in the area. Relative species abundances tend to conform to specific patterns that are among the best-known and most-studied patterns in macroecology. Different populations in a community exist in relative proportions; this idea is known as relative abundance.
WGAViewer is a bioinformatics software tool which is designed to visualize, annotate, and help interpret the results generated from a genome wide association study (GWAS). Alongside the P values of association, WGAViewer allows a researcher to visualize and consider other supporting evidence, such as the genomic context of the SNP, linkage disequilibrium (LD) with ungenotyped SNPs, gene expression database, and the evidence from other GWAS projects, when determining the potential importance of an individual SNP.
Fold change is a measure describing how much a quantity changes between an original and a subsequent measurement. It is defined as the ratio between the two quantities; for quantities A and B the fold change of B with respect to A is B/A. In other words, a change from 30 to 60 is defined as a fold-change of 2. This is also referred to as a "one fold increase". Similarly, a change from 30 to 15 is referred to as a "0.5-fold decrease". Fold change is often used when analysing multiple measurements of a biological system taken at different times as the change described by the ratio between the time points is easier to interpret than the difference.
In statistics, a volcano plot is a type of scatter-plot that is used to quickly identify changes in large data sets composed of replicate data. It plots significance versus fold-change on the y and x axes, respectively. These plots are increasingly common in omic experiments such as genomics, proteomics, and metabolomics where one often has a list of many thousands of replicate data points between two conditions and one wishes to quickly identify the most meaningful changes. A volcano plot combines a measure of statistical significance from a statistical test with the magnitude of the change, enabling quick visual identification of those data-points that display large magnitude changes that are also statistically significant.
GWAS Central is a publicly available database of summary-level findings from genetic association studies in humans, including genome-wide association studies (GWAS).
The "missing heritability" problem is the fact that single genetic variations cannot account for much of the heritability of diseases, behaviors, and other phenotypes. This is a problem that has significant implications for medicine, since a person's susceptibility to disease may depend more on 'the combined effect of all the genes in the background than on the disease genes in the foreground', or the role of genes may have been severely overestimated.
Genome-wide complex trait analysis (GCTA) Genome-based restricted maximum likelihood (GREML) is a statistical method for variance component estimation in genetics which quantifies the total narrow-sense (additive) contribution to a trait's heritability of a particular subset of genetic variants. This is done by directly quantifying the chance genetic similarity of unrelated individuals and comparing it to their measured similarity on a trait; if two unrelated individuals are relatively similar genetically and also have similar trait measurements, then the measured genetics are likely to causally influence that trait, and the correlation can to some degree tell how much. This can be illustrated by plotting the squared pairwise trait differences between individuals against their estimated degree of relatedness. The GCTA framework can be applied in a variety of settings. For example, it can be used to examine changes in heritability over aging and development. It can also be extended to analyse bivariate genetic correlations between traits. There is an ongoing debate about whether GCTA generates reliable or stable estimates of heritability when used on current SNP data. The method is based on the outdated and false dichotomy of genes versus the environment. It also suffers from serious methodological weaknesses, such as susceptibility to population stratification.
The GWAS catalog is a free online database that compiles data of genome-wide association studies (GWAS), summarizing unstructured data from different literature sources into accessible high quality data. It was created by the National Human Genome Research Institute (NHGRI) in 2008 and have become a collaborative project between the NHGRI and the European Bioinformatics Institute (EBI) since 2010. As of September 2018, it has included 71,673 SNP–trait associations in 3,567 publications.
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