Filippo Saatkamp | Searcharxiv

arXiv2026

The Symmetric Pair Matching Design: A Self-Controlled Method with Automatic Adjustment for Time Effects

Self-controlled study designs eliminate confounding by individual-level characteristics that remain constant during the observation time and are thus widely used in pharmacoepidemiology and vaccine safety research. However, existing methods remain vulnerable to time effects, including temporal trends and seasonality in the exposure or outcome, unless these are explicitly modeled or controlled through the study design. We introduce the symmetric pair matching design (SPM), a novel self-controlled method that combines design-based adjustment for time effects with automatic control of time-invariant confounding. Unlike previous design-based approaches that account for time effects, SPM uses observation time both before and after event occurrence, thereby retaining a larger proportion of the available information. We derive the theoretical properties of the method and evaluate its finite-sample performance through simulations. In the simulations, SPM produced unbiased estimates in the presence of temporal trends in both the outcome and exposure, while maintaining greater or comparable statistical efficiency than existing approaches. SPM extends the family of self-controlled methods by providing design-based control of time effects without requiring explicit modeling thereof. By combining robustness to temporal confounding with efficient use of observation time, SPM offers a practical alternative for observational studies with transient exposures. An accompanying R package is provided to facilitate its usage in applied research.

stat.ME↗

arXiv2023

Reformulation of Special Relativity and Electromagnetism in terms of Reference Frames defined as maps from spacetime onto affine spaces

A reference frame on a set $M$ is given by a 3-dimensional euclidean space $E$, a function from $M$ to $E$, a 1-dimensional affine space $A$ and a function from $M$ to $A$. The definition allows an intuitive and coordinate-free formulation of Newtonian mechanics, special relativity and electromagnetism in terms of frames instead of coordinates. In particular, the postulate of a set of charts on $M$ (an atlas) is replaced by the postulate of a set of frames. Then the charts can be re-obtained through the choice of affine coordinates. In addition, units enter the theory as elements of positive spaces and we obtain a geometric and manifestly unit-independent reformulation. Each frame allows us to identify spacetime with a 4-dimensional product-space and we can generalize the definition of differentiable manifolds such that the frames turn out to form an atlas. Then the only difference between Newtonian mechanics and special relativity is the assumed type of transition functions - Galilean transformations or Poincaré transformations between affine spaces. This allows us to highlight the common features and differences in the second chapter of the paper. For example, we define velocity reciprocity in mathematical terms and prove the phenomenon for both kind of transformations. The chapter concludes with a discussion of inertial and accelerated frames. In the third chapter we restrict our attention to the reformulation of special relativity and electromagnetism with a strong emphasis on covariance. World lines are introduced as particular subsets of spacetime, the proper time of world line is defined as an affine structure on the world line and the reformulation of electromagnetism is based on the representation of differential forms w.r.t. a frame.

physics.class-ph↗