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Today, the editor will take you to understand the meaning of QmurQ plot diagram. The knowledge points in the article are introduced in great detail. Friends who feel helpful can browse the content of the article together with the editor, hoping to help more friends who want to solve this problem to find the answer to the problem. Let's follow the editor to learn more about "what is the meaning of QMQ plot diagram".

QmurQ plot is a classic solution for visualization of association analysis results. Here Q stands for quantile, meaning quantile. QmurQ plot for association analysis is shown below.

The x axis represents the expected p value, and the y axis represents the actual p value. Before explaining the meaning of this picture, it is necessary to understand what quantiles are.

Quantiles, also known as quantiles, the most common are median, quartile and so on. Taking the median as an example, after arranging the dataset from small to large, the point corresponding to the 50% area is the median. Similarly, quartiles correspond to 25%, 50% and 75%, respectively, which are called the first quartile, the second quartile and the third quartile. The second quartile is the median, and the three quartiles divide the data into four intervals, which is the origin of the fourth in its name.

The quartile is only three points in the quartile, and the starting quantile can be any proportion, such as 10% of the quartile and 20% of the quantile. Given a dataset, the code to calculate quantiles in R is as follows

Quantiles can well show the span of data from the minimum to the maximum, and can be used to represent the overall data when there are enough quantiles.

Based on this principle, QMQ plot calculates the quantile of two data respectively, and then draws a scatter plot. As you can imagine, if the two totals are exactly the same, its QMurQ plot is a straight line of yripx, with the code as follows

The result is shown in the following figure

On this basis, it is further inferred that if the two data conform to the same distribution, then the quantile should be linear, which is verified as follows.

The output is as follows

In the above code, x and y are generated by two uniformly distributed samples with different ranges, and it can be seen that the Qmurq plot is similar to a straight line. Through this example, we can see that the core function of QmurQ plot is to compare whether the distribution of the two data is consistent. The above code is only used to show the principle of QmurQ plot. The essence of the quantile solving process is to calculate the percentage after sorting the data from small to large. In the actual drawing of the QmurQ plot diagram, you can directly sort the two data from small to large. The code is as follows.

The output is as follows

As you can see, the trend is the same as drawing with quantiles. QmurQ plot has a wide range of applications and can compare the distribution of any two data sets. There are two common uses, the first one directly compares two real data sets to see if the distribution is consistent, and the second kind of real data is compared with a data calculated based on theoretical distribution to see if it conforms to the theoretical distribution.

Q plot of association analysis is the second usage, the theoretical distribution is uniform, and the p value of the actual correlation analysis is compared with the theoretical distribution. Why is the theoretical distribution uniform?

To judge the theoretical distribution of a data, the most intuitive way is to draw the density distribution map of the actual data. The density histogram of the p-value distribution in GWAS is as follows

In the figure above, the density in each bin is basically the same, which is typical of uniform distribution. By comparing the density distribution map of the actual data with that of various theoretical distributions, the candidate theoretical distribution can be determined quickly. From the comparison of peak patterns, only the uniform distribution is close to the distribution of the data. Show the method of QmurQ plot drawing with the dataset in qqman, the code is as follows

The output is as follows

QmurQ pot drawing is very simple, three sentences of code can be done. When drawing, the p value is converted to-log10, so the point on the right side of the diagram represents the snp site with significant p value. You can see that the points on the left are basically uniformly distributed, while the significant snp sites are above the standard line, indicating that the points with significant p value cause the actual quantile to be less than the theoretical quantile, as shown in the diagram below.

It shows that in a smaller range of p values, the distribution of the actual data is closer, when the correlation signal is detected, the p value of the correlation site must be relatively tight and small, and it is normal for the data to produce the distribution of the above figure. If it completely obeys the uniform distribution, that is, it is basically coincident with the straight line, it shows that the generation of p value is a random process, and the credibility of gwas analysis is low.

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