Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.
— Richard Feynman
Art is Science in Love
— E.F. Weisslitz
The legend can be printed at 4" × 6". The bitmap resolution is 600 dpi.
For every case, we sequence the DNA to study the genome structure and the RNA to discover which genes are expressed and to what extent. The analysis is quite complex and brings together many steps: sequence alignment, structural variation detection, expression profiling, pathway analysis and so on. Every case is "summarized" by a lengthy report, such as the one below, which can run to over 40 pages.
One of the goals of the 5-year anniversary art was to represent the cases in a way to clearly show their number, classification as well as diversity. There are many metrics that can be used and I decided to choose the case's correlation to other cancer types.
For every POG case, the gene expression of 1,744 key genes is compared to that of 1,000's of cases in the TCGA database of cancer samples. For a given cancer type in the TCGA database (e.g. BRCA), we visualize the correlations using box plots. The box plot is ideal for showing the distribution of values in a sample.
The 10 largest Spearman correlation coefficients for the case shown above are
case corr type tissue ----------------------------------------------- POG661 0.436 BRCA Breast POG661 0.371 PRAD Urologic POG661 0.295 OV Gynecologic POG661 0.257 UCEC Gynecologic POG661 0.244 LUAD Thoracic POG661 0.235 CESC_CAD Gynecologic POG661 0.225 MB_Adult Central Nervous System POG661 0.222 KICH Urologic POG661 0.219 THCA Endocrine POG661 0.208 UCS Gynecologic
In the figure below I show how the final encoding of the correlations is done. First, the top three correlations are taken—using more generates a busy look and diminishes visual impact. The correlations are encoded as concentric rings.
Because in most cases the differences in the top 3 correlations are relatively small, differences are emphasized by non-linearly scaling the encoding (the correlations are first scaled `r^3`).
The type face is Proxima Nova. The colors for each tissue source are
Gastrointestinal ● 234,62,144 Breast ● 237,75,51 Thoracic ● 242,130,56 Gynecologic ● 253,188,61 Soft tissue ● 244,217,59 Skin ● 193,216,51 Urologic ● 114,197,49 Hematologic ● 29,166,68 Head and neck ● 43,168,224 Endocrine ● 71,82,178 Central nervous system ● 127,65,146 Other ● 150,150,150
Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"
Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.
Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.
Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nature Methods 16:451–452.
Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nature Methods 12:999–1000.
Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.
We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.
Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.
Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.
Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.
They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.
Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).
Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.
Celebrate `\pi` Day (March 14th) and set out on an exploration explore accents unknown (to you)!
This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.
A special kids' edition merges math with color and fat fonts.
One moment you're
:) and the next you're
Make sense of it all with my Tree of Emotional life—a hierarchical account of how we feel.