arXiv subjects

David Richardson

Publications and source records attributed to David Richardson.

12 recordsLinked to original sources

arXiv2026

The Multiplicative Quasi-Instrumental Variable Model

We introduce the Multiplicative Quasi-Instrumental Variable (MQIV) model, a framework for causal inference with unmeasured confounding that leverages an instrument that may be imperfectly exogenous. We allow the candidate quasi-instrument to have a direct effect on the outcome not mediated by the treatment, thus violating the standard IV exclusion restriction. We establish nonparametric identification of the population average treatment effect on the treated (ATT) under a treatment model that is multiplicative with respect to the quasi-IV and the hidden confounder (Hernan and Robins, 2006). Such a multiplicative treatment model may arise naturally either when treatment occurs only if two independent instrument-driven and confounder-driven causal mechanisms are present; or alternatively, when an instrument's effect on treatment uptake is inherently heterogeneous and scales with a person's latent propensity, best capturing settings in which it is challenging for a given instrument to overcome a person's inherent lack of preference for the treatment in view. Importantly, as we establish, the MQIV model is simultaneously agnostic to treatment-effect heterogeneity with respect to hidden confounders and violation of the core IV exclusion restriction condition. Identification is achieved via a modified Wald ratio estimand, which corrects the bias due to the exclusion restriction violation, and we propose a new class of estimators that are multiply robust and semiparametric efficient. Finally, we evaluate the approach in extensive simulations and an application to evaluate the causal effect of having three or more children on mothers' labor-market engagement.

stat.ME↗

arXiv2025

Quasi Instrumental Variable Methods for Stable Hidden Confounding and Binary Outcome

Instrumental variable (IV) methods are central to causal inference from observational data, particularly when a randomized experiment is not feasible. However, of the three conventional core IV identification conditions, only one, IV relevance, is empirically verifiable; often one or both of the other conditions, exclusion restriction and IV independence from unmeasured confounders, are unmet in real-world applications. These challenges are compounded when the outcome is binary, a setting for which robust IV methods remain underdeveloped. A fundamental contribution of this paper is the development of a general identification strategy justified under a structural equilibrium dynamic generative model of so-called stable confounding and a quasi instrumental variable (QIV), i.e. a variable that is only assumed to be predictive of the outcome. Such a model implies (a) stability of confounding on the multiplicative scale, and (b) stability of the additive average treatment effect among the treated (ATT), across levels of that QIV. The former is all that is necessary to ensure a valid test of the causal null hypothesis; together those two conditions establish nonparametric identification and estimation of the conditional and marginal ATT. To address the statistical challenges posed by the need for boundedness in binary outcomes, we introduce a generalized odds product re-parametrization of the observed data distribution, and we develop both a principled maximum likelihood estimator and a triply robust semiparametric locally efficient estimator, which we evaluate through simulations and an empirical application to the UK Biobank.

stat.ME↗

arXiv2023

Single Proxy Control

Negative control variables are sometimes used in non-experimental studies to detect the presence of confounding by hidden factors. A negative control outcome (NCO) is an outcome that is influenced by unobserved confounders of the exposure effects on the outcome in view, but is not causally impacted by the exposure. Tchetgen Tchetgen (2013) introduced the Control Outcome Calibration Approach (COCA) as a formal NCO counterfactual method to detect and correct for residual confounding bias. For identification, COCA treats the NCO as an error-prone proxy of the treatment-free counterfactual outcome of interest, and involves regressing the NCO on the treatment-free counterfactual, together with a rank-preserving structural model which assumes a constant individual-level causal effect. In this work, we establish nonparametric COCA identification for the average causal effect for the treated, without requiring rank-preservation, therefore accommodating unrestricted effect heterogeneity across units. This nonparametric identification result has important practical implications, as it provides single proxy confounding control, in contrast to recently proposed proximal causal inference, which relies for identification on a pair of confounding proxies. For COCA estimation we propose three separate strategies: (i) an extended propensity score approach, (ii) an outcome bridge function approach, and (iii) a doubly-robust approach. Finally, we illustrate the proposed methods in an application evaluating the causal impact of a Zika virus outbreak on birth rate in Brazil.

stat.ME↗

arXiv2023

Universal Difference-in-Differences for Causal Inference in Epidemiology

Difference-in-differences is undoubtedly one of the most widely used methods for evaluating the causal effect of an intervention in observational (i.e., nonrandomized) settings. The approach is typically used when pre- and post-exposure outcome measurements are available, and one can reasonably assume that the association of the unobserved confounder with the outcome has the same absolute magnitude in the two exposure arms, and is constant over time; a so-called parallel trends assumption. The parallel trends assumption may not be credible in many practical settings, including if the outcome is binary, a count, or polytomous, as well as when an uncontrolled confounder exhibits non-additive effects on the distribution of the outcome, even if such effects are constant over time. We introduce an alternative approach that replaces the parallel trends assumption with an odds ratio equi-confounding assumption under which an association between treatment and the potential outcome under no-treatment is identified with a well-specified generalized linear model relating the pre-exposure outcome and the exposure. Because the proposed method identifies any causal effect that is conceivably identified in the absence of confounding bias, including nonlinear effects such as quantile treatment effects, the approach is aptly called Universal Difference-in-differences (UDiD). Both fully parametric and more robust semiparametric UDiD estimators are described and illustrated in a real-world application concerning the causal effects of a Zika virus outbreak on birth rate in Brazil.

stat.ME↗

arXiv2022

Alternative approaches for analysing repeated measures data that are missing not at random

We consider studies where multiple measures on an outcome variable are collected over time, but some subjects drop out before the end of follow up. Analyses of such data often proceed under either a 'last observation carried forward' or 'missing at random' assumption. We consider two alternative strategies for identification; the first is closely related to the difference-in-differences methodology in the causal inference literature. The second enables correction for violations of the parallel trend assumption, so long as one has access to a valid 'bespoke instrumental variable'. These are compared with existing approaches, first conceptually and then in an analysis of data from the Framingham Heart Study.

stat.ME↗

arXiv2022

Structural Nested Mean Models Under Parallel Trends Assumptions

We link and extend two approaches to estimating time-varying treatment effects on repeated continuous outcomes--time-varying Difference in Differences (DiD; see Roth et al. (2023) and Chaisemartin et al. (2023) for reviews) and Structural Nested Mean Models (SNMMs; see Vansteelandt and Joffe (2014) for a review). In particular, we show that SNMMs, previously known to be nonparametrically identified under a no unobserved confounding assumption, are also identified under a conditional parallel trends assumption similar to those typically used to justify time-varying DiD methods (but more amenable to time-varying confounding). Because SNMMs model a broader set of causal estimands, our results allow practitioners of time-varying DiD approaches to address additional types of substantive questions under similar assumptions. SNMMs enable estimation of time-varying effect heterogeneity, lasting effects of a `blip' of treatment at a single time point, effects of sustained interventions (possibly on continuous or multi-dimensional treatments) when treatment repeatedly changes value in the data, controlled direct effects, effects of dynamic treatment strategies that depend on covariate history, and more. We provide a method for sensitivity analysis to violations of our parallel trends assumption. We further explain how to estimate optimal treatment regimes via optimal regime SNMMs under parallel trends assumptions plus an assumption that there is no effect modification by unobserved confounders. Finally, we illustrate our methods with real data applications estimating effects of Medicaid expansion on uninsurance rates, effects of floods on flood insurance take-up, and effects of sustained changes in temperature on crop yields.

stat.ME↗

arXiv2022

DV-QKD Coexistence With 1.6 Tbps Classical Channels Over Hollow Core Fibre

The feasibility of coexisting a quantum channel with carrier-grade classical optical channels over Hollow Core Nested Antiresonant Nodeless Fibre (HC-NANF) is experimentally explored for the first time in terms of achievable quantum bit error rate (QBER), secret key rate (SKR) as well as classical signal bit error rates (BER). A coexistence transmission of 1.6 Tbps is achieved for the classical channels simultaneously with a quantum channel over a 2 km-long HC-NANF with a total coexistence power of 0 dBm. To find the best and worst wavelength position for the classical channels, we simulated different classical channels bands with different spacing between the quantum and classical channels considering the crosstalk generated from both Raman scattering and four-wave-mixing (FWM) on the quantum channel. Following our simulation, we numerically estimate the best (Raman spectrum dip) and worst locations (Raman spectrum peak) of the classical channel with respect to its impact on the performance on the quantum channel in terms of SKR and QBER. We further implemented a testbed to experimentally test both single mode fibre (SMF) and HC-NANF in the best and worst-case scenarios. In the best-case scenario, the spacing between quantum and classical is 200 GHz (1.6 nm) with 50 GHz (0.4 nm) spacing between each classical channel. The SKR was preserved without any noticeable changes when coexisting the quantum channel with eight classical channels at 0 dBm total coexistence power in HC-NANF compared to a significant drop of 73% when using SMF at -24 dBm total coexistence power which is 250 times lower than the power used in HC-NANF. In the worst-case scenario using the same powers, and with 1 THz (8 nm) spacing between quantum and classical channels, the SKR dropped 10% using the HC-NANF, whereas in the SMF the SKR plummeted to zero.

quant-ph↗

arXiv2022

Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects

We study identifying and estimating the causal effect of a treatment variable on a long-term outcome using data from an observational and an experimental domain. The observational data are subject to unobserved confounding. Furthermore, subjects in the experiment are only followed for a short period; thus, long-term effects are unobserved, though short-term effects are available. Consequently, neither data source alone suffices for causal inference on the long-term outcome, necessitating a principled fusion of the two. We propose three approaches for data fusion for the purpose of identifying and estimating the causal effect. The first assumes equal confounding bias for short-term and long-term outcomes. The second weakens this assumption by leveraging an observed confounder for which the short-term and long-term potential outcomes share the same partial additive association with this confounder. The third approach employs proxy variables of the latent confounder of the treatment-outcome relationship, extending the proximal causal inference framework to the data fusion setting. For each approach, we develop influence function-based estimators and analyze their robustness properties. We illustrate our methods by estimating the effect of class size on 8th-grade SAT scores using data from the Project STAR experiment combined with observational data from the Early Childhood Longitudinal Study.

stat.ME↗

arXiv2021

Odds Ratios are far from "portable": A call to use realistic models for effect variation in meta-analysis

Objective: Recently Doi et al. argued that risk ratios should be replaced with odds ratios in clinical research. We disagreed, and empirically documented the lack of portability of odds ratios, while Doi et al. defended their position. In this response we highlight important errors in their position. Study Design and Setting: We counter Doi et al.'s arguments by further examining the correlations of odds ratios, and risk ratios, with baseline risks in 20,198 meta-analyses from the Cochrane Database of Systematic Reviews. Results: Doi et al.'s claim that odds ratios are portable is invalid because 1) their reasoning is circular: they assume a model under which the odds ratio is constant and show that under such a model the odds ratio is portable; 2) the method they advocate to convert odds ratios to risk ratios is biased; 3) their empirical example is readily-refuted by counter-examples of meta-analyses in which the risk ratio is portable but the odds ratio isn't; and 4) they fail to consider the causal determinants of meta-analytic inclusion criteria: Doi et al. mistakenly claim that variation in odds ratios with different baseline risks in meta-analyses is due to collider bias. Empirical comparison between the correlations of odds ratios, and risk ratios, with baseline risks show that the portability of odds ratios and risk ratios varies across settings. Conclusion: The suggestion to replace risk ratios with odds ratios is based on circular reasoning and a confusion of mathematical and empirical results. It is especially misleading for meta-analyses and clinical guidance. Neither the odds ratio nor the risk ratio is universally portable. To address this lack of portability, we reinforce our suggestion to report variation in effect measures conditioning on modifying factors such as baseline risk; understanding such variation is essential to patient-centered practice.

stat.AP↗

arXiv2017

Fibre-optic metadevice for all-optical signal modulation based on coherent absorption

Recently, coherent control of the optical response of thin films of matter in standing waves has attracted considerable attention, ranging from applications in excitation-selective spectroscopy and nonlinear optics to demonstrations of all-optical image processing. Here we show that integration of metamaterial and optical fibre technologies allows the use of coherently controlled absorption in a fully fiberized and packaged switching metadevice. With this metadevice, that controls light with light in a nanoscale plasmonic metamaterial film on an optical fibre tip, we provide proof-of-principle demonstrations of logical functions XOR, NOT and AND that are performed within a coherent fully fiberized network at wavelengths between 1530 nm and 1565 nm. The metadevice performance has been tested with optical signals equivalent to a bitrate of up to 40 Gbit/s and sub-milliwatt power levels. Since coherent absorption can operate at the single photon level and also with 100 THz bandwidth, we argue that the demonstrated all-optical switch concept has potential applications in coherent and quantum information networks.

physics.optics↗

arXiv2017

Anisotropic super-attenuation of capillary waves on driven glass interfaces

Metrological AFM measurements are performed on the silica glass interfaces of photonic band-gap fibres and hollow capillaries. The freezing of attenuated out-of-equilibrium capillary waves during the drawing process is shown to result in a reduced surface roughness. The roughness attenuation with respect to the expected thermodynamical limit is determined to vary with the drawing stress following a power law. A striking anisotropic character of the height correlation is observed: glass surfaces thus retain a structural record of the direction of the flow to which the liquid was submitted.

cond-mat.soft↗

arXiv1999

HeXLN: A 2-Dimensional nonlinear photonic crystal

We report on the fabrication of what we believe is the first example of a two dimensional nonlinear periodic crystal\cite{berger}, where the refractive index is constant but in which the 2nd order nonlinear susceptibility is spatially periodic. Such a crystal allows for efficient quasi-phase matched 2nd harmonic generation using multiple reciprocal lattice vectors of the crystal lattice. External 2nd harmonic conversion efficiencies > 60% were measured with picosecond pulses. The 2nd harmonic light can be simultaneously phase matched by multiple reciprocal lattice vectors, resulting in the generation of multiple coherent beams. The fabrication technique is extremely versatile and allows for the fabrication of a broad range of 2-D crystals including quasi-crystals.

physics.optics↗