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Eur J Hum Genet. Fast set-based association analysis using summary data from GWAS identifies novel gene loci for human complex traits. Scientific Reports 6, The executable files are released under the MIT license. We recommend to use the Linux version because the Windows and Mac versions have not been fully tested.
We have fixed a few bugs in the previous versions. If you find any bug in tihs version, please report it to Jian Yang at jian. The source code are released under GPL v3. The source code of the latest version will be released when it is stable. Therefore, when the sample size is small, it is not surprising to observe an estimate of SNP-heritability being 0 or 1 with a large standard error.
If the estimate hits the boundary 0 or 1 , the phenotypic variance-covariance matrix V will often become invertible and you will see error message. For unrelated individuals and common SNPs, you will need at least unrelated samples to get a SE down to 0. If the sample size n is huge, you can use --make-grm-part to reduce the memory usage minimize and boost performance by parts divided. See --make-grm-part for more details.
The REML process is a bit complicated. It involves a number of n x n matrices, e. GRM, variance-covariance V matrix, the projection P matrix and temporary matrices for V inverse calculation. Note that these calculations haven't taken into account vectors and the other matrices of smaller size. If there is only one genetic variance component i.
If you have multiple genetic variance components involved in your analysis e. In this case, you may need use the option --reml-lrt to specify which component s you want to test.
You can also calculate the LRT for multiple genetic variance components. For example, for a joint analysis of 22 chromosomes 22 genetic components in the model , you could test whether, for example, chromosomes 3 and 7 simultaneously by adding the option --reml-lrt 3 7 to the analysis:. You just need to specify the number of autosomes using the option --autosome-num when creating the GRM. On the observed scale disease status , the genetic variance can be greater Vp per definition, i.
By default, GCTA does not allow any estimate of variance component to be negative. However, you need to be cautious that any artefacts between cases and control will be estimated as 'genetic' variance, especially when cases and controls were genotyped separately e.
For a quantitative trait which is relatively robust to the artefacts in SNP data as compared to a case-control study , it is likely that your sample size is small so that the estimate varies within a great range i. It may also suggest that the true parameter i.
The reason for excluding close-relatives in Yang et al. If you are interested in the variance explained by a subset of SNPs in family data, you could fit the genetic relationship matrix GRM estimated from these SNPs along with a matrix of pedigree structure using the option --mgrm when running the REML analysis --reml.
If there are multiple cohorts and for some reason you are unable to pool all the individual-level genotype data together for a combined analysis, then it is OK to run a inverse-variance meta-analysis, i. However, this is less powerful than a combined analysis because the meta-analysis does not utilise the contrasts between individuals across cohorts. If the SNPs are selected by p-values from association analysis in an independent sample, then it's OK.
For example, in Wood et al. Note that these are the expected values. The realised GRM values come with sampling errors which is proportional to the number of markers used to compute the GRM. For distant relatives e. See Supplementary Note 2 of Yang et al. From the analysis above, you will have a output file test.
There is no header line. Columns are family ID, individual ID, an intermediate variable, the total genetic value, another intermediate variable and the residual. The result will be saved in a file test.
You can alway ignore the last column. Assuming individuals in sample 1 and individuals in sample 2, here is an example of the phenotype file "NA" represents missing data.
Then the analysis is to estimate genetic correlation between two samples for the same trait. If the covariate is a categorical covariate, there will be t - 1 variables where t is the number of categories, e. Therefore, the model can be written as. Note that the order of the categories are determined by their order of appearance in the data. Of course, we could also fit multiple quantitative covariates and multiple categorical covariates.
These fixed effects can be estimated using the --reml-est-fix option in a REML analysis. The estimates are shown in the log output following the order in the model above, i. Heritability h 2 is per definition non-negative. However, the estimate of h 2 is supposed to be following a normal distribution with mean h 2 and variance SE 2 where SE is the standard error of the estimate of h 2.
In practice, there are a least two scenarios when we would see negative estimate of h 2. In the Yang et al. If V is not positive definite, the inverse of V does not exist. We therefore could not estimate the variance component. This usually happens when one or more of the variance components are negative or constrained at zero. It might also indicate there is something wrong with the GRM or the data which you might need to check carefully. Unfortunately, there has not been an ultimate solution.
Tricks such as adding a small number of to the diagonal elements of V also do not guarantee the modified V being invertible. In some cases, you might be able to get around the problem by using alternative REML algorithms e. The "bending" approach guarantees to get an approximate of V-1 but it does not guarantee the REML analysis being converged. Note that the --reml-bendV option only provides an approximate inverse of V and has not been tested extensively. The results from analyses using this option might not be reliable.
This is a precision issue. It means that the p-value is extremely small. You can calculate a more precise p-value in R.
For example, if you specify the number of autosomes to be 19, then chromosomes 1 to 19 will be recognized as autosomes and chromosome 20 will be recognized as the X chromosome. The default number is 22 if this option not specified.
This option is particularly useful for a analysis excluding the MHC region. Input file format test. This option is invalid for the imputed dosage data only. For the best guess data usually in PLINK format , if you want to use a R 2 cut-off to filter SNPs, you need to use this option to read the imputation R 2 values from the specified file.
You can call the original --freq by the --freq-v1 flag. Output file format in the previous version test. The format of the input file is the same as the output format for the option --freq. Missing genotypes are replaced by their expected values i.
Missing genotypes are replaced by zero. Output file format test. The second line contains two nonsense words "Reference Allele" and the reference alleles of the SNPs.
Missing genotype is represented by "NA". In this tutorial, all the options used are not detailed. Please refer to the documentation of GCTA for details of the options and formats of the input or output files. You can type this command to calculate the genetic relationships between pairwise individuals from all the autosomal SNPs.
The genetic relationship matrix will be saved in the files test. For datasets with an extremely large number of SNPs and large sample size e. Please be aware that the cutoff value 0.
You can also include the first 4 or 10 eigenvectos from principal component analysis PCA as covariates by the command. You can also estimate the variance explained by the SNPs on each chromosome by fitting one chromosome at a time.
You are also allowed to include the first 4 or 10 eigenvectors from PCA as covariates in any of these analyses. For a case-control study, the phenotypic values of cases and controls should be specified as 1 and 0, respectively. You can type the following command to estimate the variance explained by all the autosomal SNPs on the observed scale and transform the estimate to that on the underlying liability scale assuming the disease prevalence is 0.
You can not open test. Currently, It can only used in combination with a limited number of other flags, i. You can use --make-grm-part to reduce the memory usage further. This option is designed to compute the GRM in a very large sample e. The memory usage of each run is the total memory required divided by m. Thus partitioning a large number of parts can reduce the memory usage significantly. As some computer clusters limit the virtual memory, allocating 1 to 2GB more memory to each job will be safer.
Due to the speciality of the GRM for the X-chromosome, it is not recommended to manipulate the matrix by --grm-cutoff or --grm-adj , or merge it with the GRMs for autosomes see below for the options of manipulating the GRM. See Yang et al. Method for estimating the GRM: Method for estimating the inbreeding coefficients and GCTA software: This option actually tells GCTA to read three files, e.
GCTA automatically adds suffix ". Same as --grm but read the GRM files in compressed text format generated by --make-grm-gz option. This option actually tells GCTA to read two files, e.
The root filenames of multiple GRMs are given in a file, e. Same as --mgrm but read the GRM files in compressed text format generated by --make-grm-gz. GCTA selectively removes individuals to maximize the remaining sample size rather than doing it at random. Currently, it can only be used in combination with other three flags, i.
This option will lead to two output files: It can be used in combination with --keep and --remove to manupulate the subjects. You need to use the option --update-sex to read sex information of the individuals from a file see the --update-sex option above. It is also possible to use these five commands in the REML analysis see the section below.
A demonstration of estimating variance explained by the X chromosome for height and BMI: The number of starting values specified should NOT be smaller than the number of variance components in the model. By default, GCTA will use equal variances of all the components as the starting values if this option is not specified.
The default option is 0, i. The default number is if this option is not specified. If the phenotypic value is coded as 0 or 1, then it will be recognized as a case-control study 0 for controls and 1 for cases. Missing value should be represented by "-9" or "NA". For example, --mpheno 2 tells GCTA to take the second trait for analysis the fourth column of the file. Apart from estimating the genetic variance, this command tells GCTA to estimate the variance of genotype-environment GE interaction.
Some programming languages employ both block and line comments with different comment delimiters. Other languages support only one type of comment. For example, Ada comments are line comments: How best to make use of comments is subject to dispute; different commentators have offered varied and sometimes opposing viewpoints. Comments can be used as a form of pseudocode to outline intention prior to writing the actual code. In this case it should explain the logic behind the code rather than the code itself.
If this type of comment is left in, it simplifies the review process by allowing a direct comparison of the code with the intended results. A common logical fallacy is that code that is easy to understand does what it's supposed to do.
Comments can be used to summarize code or to explain the programmer's intent. According to this school of thought, restating the code in plain English is considered superfluous; the need to re-explain code may be a sign that it is too complex and should be rewritten, or that the naming is bad.
Comments may also be used to explain why a block of code does not seem to fit conventions or best practices. This is especially true of projects involving very little development time, or in bug fixing.
Sometimes source code contains a novel or noteworthy solution to a specific problem. In such cases, comments may contain an explanation of the methodology. Such explanations may include diagrams and formal mathematical proofs. This may constitute explanation of the code, rather than a clarification of its intent; but others tasked with maintaining the code base may find such explanation crucial.
This might especially be true in the case of highly specialized problem domains; or rarely used optimizations, constructs or function-calls. For example, a programmer may add a comment to explain why an insertion sort was chosen instead of a quicksort , as the former is, in theory, slower than the latter. This could be written as follows:. Logos , diagrams, and flowcharts consisting of ASCII art constructions can be inserted into source code formatted as a comment.
Binary data may also be encoded in comments through a process known as binary-to-text encoding , although such practice is uncommon and typically relegated to external resource files. Although a section marking the code appears as a comment, the diagram itself actually appears in an XML CDATA section, which is technically considered distinct from comments, but can serve similar purposes.
Although this identical diagram could easily have been included as a comment, the example illustrates one instance where a programmer may opt not to use comments as a way of including resources in source code. In particular, many software maintainers put submission guidelines in comments to help people who read the source code of that program to send any improvements they make back to the maintainer.
When an algorithm in some section of the program is based on a description in a book or other reference, comments can be used to give the page number and title of the book or Request for Comments or other reference. A common developer practice is to comment out a code snippet , meaning to add comment syntax causing that block of code to become a comment, so that it will not be executed in the final program.
This may be done to exclude certain pieces of code from the final program, or more commonly it can be used to find the source of an error. By systematically commenting out and running parts of the program, the source of an error can be determined, allowing it to be corrected.
The above code fragment suggests that the programmer opted to disable the debugging option for some reason. Many IDEs allow quick adding or removing such comments with single menu options or key combinations. The programmer has only to mark the part of text they want to un comment and choose the appropriate option. Programming tools sometimes store documentation and metadata in comments.
Keeping documentation within source code comments is considered as one way to simplify the documentation process, as well as increase the chances that the documentation will be kept up to date with changes in the code. Forms of docstring are supported by Python , Lisp , Elixir , and Clojure. Occasionally syntax elements that were originally intended to be comments are re-purposed to convey additional information to a program, such as " conditional comments ".
Such "hot comments" may be the only practical solution that maintains backward-compatibility, but are widely regarded as a kludge. Sometimes comments in source code are used as a way to relieve stress by commenting about development tools, competitors, employers, working conditions, or the quality of the code itself.
There are various normative views and long-standing opinions regarding the proper use of comments in source code. Experts have varying viewpoints on whether, and when, comments are appropriate in source code. In between these views is the assertion that comments are neither beneficial nor harmful by themselves, and what matters is that they are correct and kept in sync with the source code, and omitted if they are superfluous, excessive, difficult to maintain or otherwise unhelpful.
Comments are sometimes used to document contracts in the design by contract approach to programming. Depending on the intended audience of the code and other considerations, the level of detail and description may vary considerably. For example, the following Java comment would be suitable in an introductory text designed to teach beginning programming:. This level of detail, however, would not be appropriate in the context of production code, or other situations involving experienced developers.
Such rudimentary descriptions are inconsistent with the guideline: There are many stylistic alternatives available when considering how comments should appear in source code. For larger projects involving a team of developers, comment styles are either agreed upon before a project starts, or evolve as a matter of convention or need as a project grows.
Usually programmers prefer styles that are consistent, non-obstructive, easy to modify, and difficult to break. The following code fragments in C demonstrate just a tiny example of how comments can vary stylistically, while still conveying the same basic information:. Factors such as personal preference, flexibility of programming tools, and other considerations tend to influence the stylistic variants used in source code.
For example, Variation Two might be disfavored among programmers who do not have source code editors that can automate the alignment and visual appearance of text in comments. Software consultant and technology commentator Allen Holub  is one expert who advocates aligning the left edges of comments: Different styles can be chosen for different areas of code, from individual lines to paragraphs, routines, files, and programs.
If the syntax supports both line comments and block comments, one method is to use line comments only for minor comments declarations, blocks and edits and to use block comments to describe higher-level abstractions functions, classes, files and modules.
Sometimes projects try to enforce rules like "one comment every ten lines". These kinds of rules can be counterproductive when too rigorous, but may provide a useful standard of measurement and consistency if the project participants deem it necessary. This choice continued in the C language, Ritchie's successor to B. Programmers may use informal tags in comments to assist in indexing common issues. They may then be able to be searched for with common programming tools, such as the Unix grep utility or even syntax-highlighted within text editors.
These are sometimes referred to as "codetags"   or "tokens". Typographic conventions to specify comments vary widely. Further, individual programming languages sometimes provide unique variants. For a detailed review, please consult the programming language comparison article. The Ada programming language uses '--' to indicate a comment up to the end of the line. This section of AppleScript code shows the two styles of comments used in that language.
This C code fragment demonstrates the use of a prologue comment or "block comment" to describe the purpose of a conditional statement. The comment explains key terms and concepts, and includes a short signature by the programmer who authored the code. Such comments are not , however, saved to non-volatile memory which contains the startup-config , nor are they displayed by the "show run" command.
By contrast, the following commands insert human-readable content that is actually part of the configuration, and may be saved to the NVRAM startup-config: The "description" command is used to add a description to the configuration of an interface or of a BGP neighbor, and the "name" parameter may be used to add a remark to a static route.
Access lists may also contain "remarks. These comments are caught by the ColdFusion engine and not printed to the browser. This Fortran IV code fragment demonstrates how comments are used in that language, which is very column-oriented.
A letter "C" in column 1 causes the entire line to be treated as a comment. Note that the columns of a line are otherwise treated as four fields: This Fortran code fragment demonstrates how comments are used in that language, with the comments themselves describing the basic formatting rules. Haskell also provides a literate programming method of commenting known as " Bird Style ".
One additional requirement is that you always leave a blank line before and after the code block:.