It isn't easy to draw the graph of a function when you don't know what the graph looks like. To draw the graph by using a computer, you need to know the domain of the function for the graph: the minimum value (xMin) and the maximum value (xMax) for plotting
A SAS programmer wanted to create a panel that contained two of the graphs side-by-side. The graphs were created by using calls to two different SAS procedures. This article shows how to select the graphs and arrange them side-by-side by using the ODS LAYOUT GRIDDED statement. The end of the
SAS SGPLOT already provides the necessary graphical elements for complex visualization. 3D or high-dimensional data can be easily visualized after being projected appropriately. With SAS' strong support for animation features, SAS users can create complicated 3D or high dimension visualizations quickly.
I previously wrote about partial leverage plots for regression diagnostics and why they are useful. You can generate a partial leverage plot in SAS by using the PLOTS=PARTIALPLOT option in PROC REG. One useful property of partial leverage plots is the ability to graphically represent the null hypothesis that a
A previous article shows how to compute the probability density function (PDF) for the multivariate normal distribution. In a similar way, you can compute the density function for the multivariate t distribution. This article discusses the density function for the multivariate t distribution, shows how to compute it, and visualizes
For a linear regression model, a useful but underutilized diagnostic tool is the partial regression leverage plot. Also called the partial regression plot, this plot visualizes the parameter estimates table for the regression. For each effect in the model, you can visualize the following statistics: The estimate for each regression
The ODS GRAPHICS statement in SAS supports more than 30 options that enable you to configure the attributes of graphs that you create in SAS. Did you know that you can display the current set of graphical options? Furthermore, did you know that you can temporarily set certain options and
M estimation is a robust regression technique that assigns a weight to each observation based on the magnitude of the residual for that observation. Large residuals are downweighted (assigned weights less than 1) whereas observations with small residuals are given weights close to 1. By iterating the reweighting and fitting
A common question on SAS discussion forums is how to randomly assign observations to groups. An application of this problem is assigning patients to cohorts in a clinical trial. For example, you might have 137 patients that you want to randomly assign to three groups: a control group, a group
Many modern statistical techniques incorporate randomness: simulation, bootstrapping, random forests, and so forth. To use the technique, you need to specify a seed value, which determines pseudorandom numbers that are used in the algorithm. Consequently, the seed value also determines the results of the algorithm. In theory, if you know
Amazing things can be created when you start with small pieces and stack them together. Just ask Bryan Berg. He is the current world record holder for the tallest house of cards. This same principle can be applied to the SGPLOT and SGPANEL procedures. You can take the individual plot
When creating bar charts, it is very common to display labels with the bars to make it easier to determine the bar values or to provide additional information in the chart. However, these labels can take away valuable data space, particularly if you generate a smaller-sized graph. As you see
Recently, I showed how to use a heat map to visualize measurements over time for a set of patients in a longitudinal study. The visualization is sometimes called a lasagna plot because it presents an alternative to the usual spaghetti plot. A reader asked whether a similar visualization can be
Many discussions and articles about SAS Viya emphasize its ability to handle Big Data, perform parallel processing, and integrate open-source languages. These are important issues for some SAS customers. But for customers who program in SAS and do not have Big Data, SAS Viya is attractive because it is the
Oh, no! Your boss just told you to change the way that SAS displays certain features in graphs, such as missing values. But you have a library of hundreds of SAS programs! Do you need to modify all of your previous programs? Fortunately, the answer is no. SAS provides ODS
In an article about how to visualize missing data in a heat map, I noted that the SAS SG procedures (such as PROC SGPLOT) use the GraphMissing style element to color a bar or tile that represents a missing value. In the HTMLBlue ODS style, the color for missing values
Longitudinal data are measurements for a set of subjects at multiple points in time. Also called "panel data" or "repeated measures data," this kind of data is common in clinical trials in which patients are tracked over time. Recently, a SAS programmer asked how to visualize missing values in a
Über die Umstellung der Zeit auf den Sommer
A previous article showed how to use SAS to compute finite-difference derivatives of smooth vector-valued multivariate functions. The article uses the NLPFDD subroutine in SAS/IML to compute the finite-difference derivatives. The article states that the third output argument of the NLPFDD subroutine "contains the matrix product J`*J, where J is
On this Pi Day, let's explore the "πth roots of unity." (Pi Day is celebrated in the US on 3/14 to celebrate π ≈ 3.14159....) It's okay if you've never heard of the πth roots of unity. This article starts by reviewing the better-known nth roots of unity. It then
Did you know that you can use π to partition the positive integers into two disjoint groups? It's not hard. One group is generated by the integer portions of multiples of π. The FLOOR function gives the integer portion of a positive number, so you can write integer that are
A SAS programmer asked an interesting question: If data in a time series has missing values, can you plot a dashed line to indicate that the response is missing at some times? A simple way to achieve this is by overlaying two lines. The first line (the "bottom" line in
This article implements Passing-Bablok regression in SAS. Passing-Bablok regression is a one-variable regression technique that is used to compare measurements from different instruments or medical devices. The measurements of the two variables (X and Y) are both measured with errors. Consequently, you cannot use ordinary linear regression, which assumes that
Recently, a SAS programmer commented about one of my blog posts. He said that he had found an alternative answer on another website. Whereas my answer was formulated in terms of the normal cumulative distribution function (CDF), the other answer used the ERF function. This article shows the relationship between
2021年11月、国が一時停止している子宮頸がんを防ぐHPV（ヒトパピローマウイルス）ワクチンの積極的な接種の勧奨の再開が厚生労働省の専門家による検討部会によって正式に承認されました。このHPVワクチンは世界保健機関（WHO）がその接種を推進しており、日本をはじめとして多くの先進国では公的接種とされています。この記事はData for Good活動の一環として、パブリックデータを用いて問題を可視化することで、子宮頸がんに対する認知や関心をより持っていただき、今後のHPVワクチンの普及につなげることを目的としています。 子宮頸がん 子宮頸がんのほとんどはヒトパピローマウイルス（HPV）というウイルスの感染が原因となり子宮の頸部に発生するがんの一種です。感染の経路は主に性的接触によるものであり、成人女性の大部分はHPVに感染するとされています。HPVに感染してもその多くは自然に消失しますが、一部は頸部の細胞が異常な変化を起こした子宮頸部異形成というがんの前段階（前がん病変）になります。そしてさらにその一部が数年から10年ほどで悪性腫瘍へと進展し、子宮頸がんを発症します。この子宮頸部異形成（前がん病変）の早期段階では自覚症状はほぼなく、病変を発見するためには子宮頸がん検診を受けることが必要ですが、自覚症状があまりないために検診を受けた段階で既に進行がかなり進んでしまっているケースもあります。 国立がん研究センターがん情報サービスは国立がん研究センターが運営している公式サイトであり、日本国内のがんに関する統計情報ががん種別に公開されています。今回はその統計情報の中から、子宮頸がんに該当するデータ（がん種：子宮頸部）を抜き出し、無料で利用可能なSAS OnDemand for Academicsを利用して可視化を行いました。日本での死亡者数は2019年度時点で年間約3,000名、罹患者数は2018年時点で約11,000名ほどとなっており、下図のように増加の一途をたどっています。 出典：国立がん研究センターがん情報サービス「がん統計」（人口動態統計） より作成 ま子宮頸がんの罹患者数は2009年～2018年（最新）まで10年連続で1万人を超えており、罹患者数は30歳頃から増え始め現在は45-49歳が最も罹患が多い年代層となっています。また罹患する年齢層が若年化していることも危険視されています。子宮頸がんに対して我々ができることは以下の二つです。 子宮頸がん検診を受けること（発見） HPVワクチンを接種すること（予防） 私たちにとって重要なことは、2年に1度の受診が推奨されている子宮頸がん検診によって異形成（前がん病変）を早期に発見すること。そして検診と同様に重要ことが、HPVワクチンを接種し対応するHPVの感染を防ぎ、子宮頸がんとなるリスクを下げることです。 HPVワクチン 子宮頸がんの原因となるHPV（ヒトパピローマウイルス）は現在100種類以上の存在が知られており、そのうちのいくつかは子宮頸がんを引き起こしやすいハイリスク型に分類されます。HPVワクチンにも様々なタイプがありますが、日本では定期接種の対象となっているのは2価（サーバリックス）と4価（ガーダシル）のワクチンで、接種することでおおよそ50~70%程の感染を防ぎ子宮頸がんになるリスクを減らすことが可能です。また2021年2月24日からは9価ワクチンも日本での取り扱いが開始されましたが定期接種の対象ではないため自費での接種となっています。 「接種の積極的な勧奨」について HPVワクチンは下図のようにいくつかの事業、法案の後押しもあり、その対象となる年齢の女性へ接種の積極的な勧奨が行われていました。しかし公費での定期接種開始後に副反応の報告が相次ぎ、副反応と接種との因果関係や、その頻度、海外での詳しい実態調査が必要とされ、厚生労働省は約半年間をめどに「接種の積極的な勧奨」の一時中止という決定を2013年6月に下しました。当初は半年間がめどとされていたものの、一時停止はその後も続き、ワクチンの有効性が様々な研究により示され2021年11月に接種の積極的な勧奨の再開が正式に決定されるまで約8年の月日がかかりました。 専門家らの研究結果によると、接種の積極的な勧奨が一時停止されるまではおおよそ70％であった定期接種の対象年齢での接種率もこの一時停止により現在は1％未満にまで落ち込んでしまっています。論文のデータをもとに出生年ごとのワクチン接種率を可視化したものが下図です。 Nakagawa S, Ueda Y, Yagi A, Ikeda S, Hiramatsu K, Kimura T. Corrected human papillomavirus vaccination rates for each birth fiscal year in Japan. Cancer Sci. 2020;111(6):2156-2162. doi:10.1111/cas.14406 より作成
In a previous article, I visualized seven Christmas-themed palettes of colors, as shown to the right. You can see that the palettes include many red, green, and golden colors. Clearly, the colors in the Christmas palettes are not a random sample from the space of RGB colors. Rather, they represent
In data visualization, colors can represent the values of a variable in a choropleth map, a heatmap, or a scatter plot. But how do you visualize a palette of colors from the RGB or hexadecimal values of the colors? One way is to use the HEATMAPDISC subroutine in SAS/IML, which
While discussing how to compute convex hulls in SAS with a colleague, we wondered how the size of the convex hull compares to the size of the sample. For most distributions of points, I claimed that the size of the convex hull is much less than the size of the
Did you know that the loess regression algorithm is not well-defined when you have repeated values among the explanatory variables, and you request a very small smoothing parameter? This is because loess regression at the point x0 is based on using the k nearest neighbors to x0. If x0 has
A scatter plot is my go-to graph! It's what I often start with to get a feel for the data ... and I often end up using just a scatter plot. But some scatter plots are better than others ... In this blog post, I create a scatter plot of
