Nature Cancer Cover — April 2020 issue
Pan-cancer genomic landscapes of advanced tumors after therapy
Pleasance, E., Titmuss, E., Williamson, L. et al. (2020) Pan-cancer analysis of advanced patient tumors reveals interactions between therapy and genomic landscapes. Nat Cancer 1:452–468.
Art is science in love.
— E.F. Weisslitz
The design of the cover was inspired by Christian Stolte's DNA portraits from personal genomic data and PrintMyDNA. I've always loved Christian's style–respect the data but add playful flair. I am grateful for his allowing me to apply his approach to this design.
behind the design
respect the data, keep the eye interested
Every sample from the POG570 cohort corresponds to an individual patient and this is reflected in the design. The design is more compelling when samples are spatially distinct.
A core principle behind the design is intentionally managing and encouraging variation. If we have too much visual variation (in the extreme case, the data generation mechanism is a uniform random distribution), the eye sees nothing interesting. Although things are changing, there's nothing to lock onto. On the other hand, if we don't have enough variation, then the eye reacts with the same indifference.
To keep the eye happy (at least, our eyes), one approach is to have the shapes in a design split two or three categories. For example, the design has small ellipse systems and large ellipse systems. These are easy to spot and the eye can immediately begin to make some sense of what it sees, even though it may not yet know the reasons behind the patterns. Ideally, there should be a few cases that border on two categories, just to keep the category boundaries slightly ambiguous.
Within each category, there should be enough visual surprises that the eye wants to categorize further. Here is your opportunity to challenge it and vary things just enough so that this task isn't easy. The eye wants to group by shape and color similarity (Gestalt principles) and, to keep it challenged (but not frustrated or overwhelmed), make the first 40% of this grouping easy, the next 40% challenging and the last 20% impossible.
Below are three scenarios in increasing order of subjective interestingness. Too little or too much isn't as effective—find the Goldilocks zone. The "too interesting" case has ellipse properties sampled from a uniform distribution—it's always useful to see what your design looks like with random data so that you can figure out whether your data set has any kind of personality.
Practically, these considerations are retrofitted into a design once you narrow down the approach. They may not help you decide what to do but they're excellent at helping you evaluate what you've done.
And always: experiment and try not to go with your first idea.
spectrum of mutations
To explain the design, I'll use one of the 570 samples—a B-cell lymphoma—as an example. The method is the same for the other 569.
Using the genomic sequence of each sample, we first tabulate the number of mutations. These are classified into 7 classes: 6 kinds of single nucleotide variants (SNV: T>C, T>G, T>A, C>G, C>A, C>T) and indels (insertions or deletions). The use of the term SNV should be distinguished from SNP—typically SNP (single nucleotide polymorphism) is used to describe changes due to natural variation in the population (blue eyes, can roll your tongue, etc) but SNVs are somatic variants found in tumours.
Each sample has many other properties and a metric ton of data that describe it. We wanted to pick something that was easy to explain. For example, more categories of mutations are possible but our returns would diminish with each category.
The counts of these mutations are used to create a mutation spectrum composed of 7 ellipses. This is shown on the left of the legend.
ellipse: a mutation class
Individual ellipses represent a class of mutations. The color of the ellipse is based on its mutation class: SNVs are colored and indels are grey. This color scheme is used for the outline of the ellipse.
The median and maximum counts across the samples for each mutation class are shown below.
data %>% group_by(mutation_class)
%>% summarise(median=median(count),max=max(count))
class median max
T.G 361 15912
T.A 586 25997
C.G 578 31900
T.C 850 34438
C.A 974 65867
indel 422 146329
C.T 1995 397807
The ellipse fill also uses this color but at an opacity that is a function of the number of days between the time of advanced disease diagnosis and biopsy (`\sqrt{t}` mapped onto [0,1]). Sequencing of the sample was performed shortly after the biopsy.
mutation class context
Each of the 6 SNV classes (excluding indels) and are divided into 96 contexts based on what is either side of the mutated base. For example, TTC > TAC is a T>A change with a T on one side and a C on the other.
Below is the full profile of the SNV mutations (excluding indels) for the case used in the legend above. This signature is typical of lymphoid cell hypermutation—a phenomena by which B cells produce many distinct antibodies—and of alteration in polymerase activity.
In contrast, the profile below is of a "standard" rectal carcinoma defined as "broadly colorectal" in terms of genes that are driving it. The signature itself, however, is interesting because it was induced by the treatment the patient received before being sequenced.
ellipse layers
The ellipses for a sample are stacked based on the counts of mutations in their class.
The class with the most counts goes on the bottom—in our sample this is the C>A SNVs of which we have 10,422—and the class with the fewest counts goes on top—the indels of which the sample has 17.
Below are each of the 7 layers that make up the final design.
The first layer, made up of mutations with the fewest counts, is mostly T>G and C>G SNVs with a few indels. A few blue ellipses are from samples for which the class with fewest counts were the T>A SNVs.
As we go down the layers, we encounter classes with progressively more counts. In layer 2, blue ellipses(T>G SNVs) begin to appear. In layer 3, we start to see green (T>C SNVs) and orange (C>A SNVs) ellipses.
By the time we reach layer 7, where the most common mutations are, these are almost all C>T SNVs, with a few samples having indels (grey) as the most common class.
The outline on the ellipse gets thicker towards the bottom of the stack—this is a fixed progression that does not depend on the data.
The order of the layers could have been the other way: the most frequent mutations on top. And I'm sure that we could have made a go of it. As is, the least frequent mutations get an ellipse with a thin outline and these sit on ellipses with thicker outlines. This way, we're limit the ammount of a stroke that is occluded by strokes drawn above it.
ellipse size and angle
Whereas the layering tells us how the mutation classes are ranked within a sample, the size of the ellipse is related to the rank within a layer.
For a given ellipse we first find its layer. For our example sample, let's say we're looking at the layer 2 ellipse (486 C>G SNVs). We take all the mutation counts in that layer (remember, these are going to be of whatever class is the 2nd most rare in a sample) and map the 486 count onto a sigmoid curve made.
data %>% group_by(layer) %>% mutate(a = sigmoid(count,SoftMax=TRUE))
In this layer, the sample with the smallest ellipse is the one with the fewest counts in that layer and the sample with the largest ellipse is the one with the most counts (7,585). The median and maximum count values for each layer are shown below.
data %>% group_by(layer) %>% summarise(median=median(count),max=max(count))
layer median max
1 284 4201
2 398 7585
3 562 10714
4 704 18077
5 870 34438
6 1196 57499
7 2016 397807
The sigmoid mapping defines the major axis of the ellipse (`a`) with `b=a/2` thus a fixed eccentricity of `e = \sqrt{1-b^2/a^2} = \sqrt{3}/2`. The eccentricities of all the ellipses is the same. For a given ellipse size, the count may be different. This depends on its layer's sigmoid mapping as shown below.
The angle of the ellipse is `\theta = kN/n` where `n` is the ellipse's mutation class count, `N` is the total number of mutations in a sample and `k` is a magic sauce factor.
Note that the angle is inversely proportional to the count. This was done to avoid having the ellipses in the first layer (fewest counts) all at similar angles. By making the angle proportional to `1/n` the angle variation is increased and the design looks substantially better. We played around with how things looked for various values of `k` and picked one that looked best to our eyes.
If we made the angle proportional to the relative count, `\theta = \pi n /N`, the design would look very ridig and unintersting. The images below show this—notice that all ellipses in the first layer are essentially horizontal (small angle) because their relative counts are small (median 0.05). Similarly, all the ellipses in the last layer (most counts) are closer to vertical because the median of this layer's proportional count is about 0.33.
data %>% group_by(layer) %>% summarise(median=median(count/total))
layer median
1 0.0502
2 0.0676
3 0.0919
4 0.115
5 0.142
6 0.188
7 0.331
Notice that the ellipses have no absolute scale: every variable is scaled, either linearly, inversely or sigmoidally. I like relative scalings—once you split the data into sensible groups, relative scalings allow you to ask questions within a group.
When creating artistic data designs, explore different encodings, even if they break some rules. Always know what rules you're bending, breaking or ignoring.
This is true especially for cover designs, for which a more playful and interpretive approach is needed. There are more than enough accurate visualizations in the paper itself and a cover is usually no place for this.
Ultimately, the success of the design hinges on a combination of variation and uniformity and of symmetry and assymetry. Finding this balance is a kind of data exploration of its own.
Below are some of the experiments along the way. Notice that while each of these does show variation, there's a strong sense of uniformity across the panels. There are no surprises—after the first 10 ellipse sets (or so), each additional is more of the same.
let's see some exploration
Propensity score weighting
The needs of the many outweigh the needs of the few. —Mr. Spock (Star Trek II)
This month, we explore a related and powerful technique to address bias: propensity score weighting (PSW), which applies weights to each subject instead of matching (or discarding) them.
Kurz, C.F., Krzywinski, M. & Altman, N. (2025) Points of significance: Propensity score weighting. Nat. Methods 22:1–3.
Happy 2025 π Day—
TTCAGT: a sequence of digits
Celebrate π Day (March 14th) and sequence digits like its 1999. Let's call some peaks.
Crafting 10 Years of Statistics Explanations: Points of Significance
I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player
Points of Significance is an ongoing series of short articles about statistics in Nature Methods that started in 2013. Its aim is to provide clear explanations of essential concepts in statistics for a nonspecialist audience. The articles favor heuristic explanations and make extensive use of simulated examples and graphical explanations, while maintaining mathematical rigor.
Topics range from basic, but often misunderstood, such as uncertainty and P-values, to relatively advanced, but often neglected, such as the error-in-variables problem and the curse of dimensionality. More recent articles have focused on timely topics such as modeling of epidemics, machine learning, and neural networks.
In this article, we discuss the evolution of topics and details behind some of the story arcs, our approach to crafting statistical explanations and narratives, and our use of figures and numerical simulations as props for building understanding.
Altman, N. & Krzywinski, M. (2025) Crafting 10 Years of Statistics Explanations: Points of Significance. Annual Review of Statistics and Its Application 12:69–87.
Propensity score matching
I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player
In many experimental designs, we need to keep in mind the possibility of confounding variables, which may give rise to bias in the estimate of the treatment effect.
If the control and experimental groups aren't matched (or, roughly, similar enough), this bias can arise.
Sometimes this can be dealt with by randomizing, which on average can balance this effect out. When randomization is not possible, propensity score matching is an excellent strategy to match control and experimental groups.
Kurz, C.F., Krzywinski, M. & Altman, N. (2024) Points of significance: Propensity score matching. Nat. Methods 21:1770–1772.
Understanding p-values and significance
P-values combined with estimates of effect size are used to assess the importance of experimental results. However, their interpretation can be invalidated by selection bias when testing multiple hypotheses, fitting multiple models or even informally selecting results that seem interesting after observing the data.
We offer an introduction to principled uses of p-values (targeted at the non-specialist) and identify questionable practices to be avoided.
Altman, N. & Krzywinski, M. (2024) Understanding p-values and significance. Laboratory Animals 58:443–446.