Symmetric alternatives to the ordinary least squares regression

What immortal hand or eye, could frame thy fearful symmetry? — William Blake, "The Tyger"

This month, we look at symmetric regression, which, unlike simple linear regression, it is reversible — remaining unaltered when the variables are swapped.

Simple linear regression can summarize the linear relationship between two variables `X` and `Y` — for example, when `Y` is considered the response (dependent) and `X` the predictor (independent) variable.

However, there are times when we are not interested (or able) to distinguish between dependent and independent variables — either because they have the same importance or the same role. This is where symmetric regression can help.

▲ Nature Methods Points of Significance column: Symmetric alternatives to the ordinary least squares regression. Geometry of quantities minimized in OLS and symmetric regression. OLS minimizes `\Sigma e_y^2` in `Y` ~ `X` and `\Sigma e_x^2` `X` ~ `Y`. Pythagorean regression minimizes AB (magenta). Geometric means regression (GMR) minimizes area of ABP (orange). Orthogonal regression (OR) minimizes HP (blue). (read)

Luca Greco, George Luta, Martin Krzywinski & Naomi Altman (2025) Points of significance: Symmetric alternatives to the ordinary least squares regression. Nat. Methods 22:1610–1612.

Beyond Belief Campaign BRCA Art

Fuelled by philanthropy, findings into the workings of BRCA1 and BRCA2 genes have led to groundbreaking research and lifesaving innovations to care for families facing cancer.

This set of 100 one-of-a-kind prints explore the structure of these genes. Each artwork is unique — if you put them all together, you get the full sequence of the BRCA1 and BRCA2 proteins.

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.

▲ Nature Methods Points of Significance column: Propensity score weighting. (read)

Kurz, C.F., Krzywinski, M. & Altman, N. (2025) Points of significance: Propensity score weighting. Nat. Methods 22:638–640.

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.

▲ 2025 π DAY | TTCAGT: a sequence of digits. The digits of π are encoded into DNA sequence and visualized with Sanger sequencing. (details)

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.

▲ Crafting 10 Years of Statistics Explanations: Points of Significance. (read)

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.

▲ Nature Methods Points of Significance column: Propensity score matching. (read)

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.