arXiv subjects

Richard Post

Publications and source records attributed to Richard Post.

7 recordsLinked to original sources

arXiv2026

Bernhard-1: An Eccentric Binary Periodically Obscured by its Misaligned Circumbinary Disk

Bernhard-1 is a proposed KH 15D-like circumbinary disk occultation (CBO) system, but its binary nature and disk geometry have not previously been confirmed. We present new optical and near-infrared spectroscopy together with multi-band photometric monitoring of the system. The radial velocities confirm that Bernhard-1 hosts a highly eccentric binary with $e = 0.80 \pm 0.09$, confirming that the periodic photometric variability arises from occultation by a misaligned circumbinary disk. Joint modeling of the spectra and phase-dependent spectral energy distributions yields pre-main-sequence components with masses of $\sim 1.1\,M_\odot$ and $\sim 0.8\,M_\odot$. Combining stellar isochrones with the measured lithium abundance yields a system age of $\sim$ 10 Myr. Together with the spatial, astrometric, and metallicity properties of Bernhard-1, this suggests that Bernhard-1 is probably a member of the open cluster Dolidze 42. By combining the RV orbit with a semi-transparent occultation-screen model, we infer a disk--binary mutual inclination of roughly $50^\circ$ or $130^\circ$, with the degeneracy arising from the unknown disk rotation direction. This geometric method can be applied to any CBO system once radial velocity monitoring yields an orbital solution. The new light curves deviate from earlier model predictions, consistent with ongoing disk precession, while the phase-dependent H$\alpha$ profiles indicate pulsed accretion near periastron. Bernhard-1 therefore joins KH 15D and Bernhard-2 as a rare spectroscopically confirmed CBO system.

astro-ph.SR↗

arXiv2026

Decision-analytical models as causal models

Health economic evaluations are fundamentally concerned with answering causal questions by targeting estimands that contrast the costs and health consequences that would be observed under at least two different interventions. This requires the joint distribution of potential outcomes under each level of intervention, which, with appropriate causal assumptions, can in principle be identified from the joint distribution of observed health outcomes. Such data, however, are rarely available from a single source. This limitation has motivated the use of decision-analytical models to approximate the joint distribution of outcomes under each intervention directly, informed by causal parameters drawn and synthesized from multiple sources, so that the potential outcomes of interest can be approximated as an expectation over the model-implied outcome trajectories. The validity of this approach, however, depends on the credibility of the underlying assumptions. In this work, we formalize this procedure explicitly as a task of causal inference, thereby defining and decomposing decision-analytical model bias into components arising from model structure (model bias) and input parameters (target bias). Because decision-analytical models often rely on unconventional target parameters lacking straightforward observable analogues, and because bias in these parameters can propagate through the model, target bias may arise even in simple settings, a point of central focus in this work. More broadly, this work provides a unifying foundation for medical decision-analytical modelling and causal inference, making explicit the potential for decision-analytical model bias and the role of causal assumptions contributing to it. Ultimately, the resulting clinical decision is only as credible as the assumptions underlying it.

stat.ME↗

arXiv2022

The built-in selection bias of hazard ratios formalized

It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from built-in selection bias as, over time, the individuals at risk in the exposed and unexposed are no longer exchangeable. In this work, we formalize how the observed hazard ratio evolves and deviates from the causal hazard ratio of interest in the presence of heterogeneity of the hazard of unexposed individuals (frailty) and heterogeneity in effect (individual modification). For the case of effect heterogeneity, we define the causal hazard ratio. We show that the observed hazard ratio equals the ratio of expectations of the latent variables (frailty and modifier) conditionally on survival in the world with and without exposure, respectively. Examples with gamma, inverse Gaussian and compound Poisson distributed frailty, and categorical (harming, beneficial or neutral) effect modifiers are presented for illustration. This set of examples shows that an observed hazard ratio with a particular value can arise for all values of the causal hazard ratio. Therefore, the hazard ratio can not be used as a measure of the causal effect without making untestable assumptions, stressing the importance of using more appropriate estimands such as contrasts of the survival probabilities.

math.ST↗

arXiv2022

Bias of the additive hazard model in the presence of causal effect heterogeneity

Hazard ratios are prone to selection bias, compromising their use as causal estimands. On the other hand, the hazard difference has been shown to remain unaffected by the selection of frailty factors over time. Therefore, observed hazard differences can be used as an unbiased estimator for the causal hazard differences in the absence of confounding. However, in the presence of effect (on the hazard) heterogeneity, the hazard difference is also affected by selection. In this work, we formalize how the observed hazard difference (from a randomized controlled trial) evolves by selecting favourable levels of effect modifiers in the exposed group and thus deviates from the causal hazard difference of interest. Such selection may result in a non-linear integrated hazard difference curve even when the individual causal effects are time-invariant. Therefore, a homogeneous time-varying causal additive effect on the hazard can not be distinguished from a constant but heterogeneous causal effect. We illustrate this causal issue by studying the effect of chemotherapy on the survival time of patients suffering from carcinoma of the oropharynx using data from a clinical trial. The hazard difference can thus not be used as an appropriate measure of the causal effect without making untestable assumptions.

math.ST↗

arXiv2022

Beyond Conditional Averages: Estimating The Individual Causal Effect Distribution

In recent years, the field of causal inference from observational data has emerged rapidly. The literature has focused on (conditional) average causal effect estimation. When (remaining) variability of individual causal effects (ICEs) is considerable, average effects may be uninformative for an individual. The fundamental problem of causal inference precludes estimating the joint distribution of potential outcomes without making assumptions. In this work, we show that the ICE distribution is identifiable under (conditional) independence of the individual effect and the potential outcome under no exposure, in addition to the common assumptions of consistency, positivity, and conditional exchangeability. Moreover, we present a family of flexible latent variable models that can be used to study individual effect modification and estimate the ICE distribution from cross-sectional data. How such latent variable models can be applied and validated in practice is illustrated in a case study on the effect of Hepatic Steatosis on a clinical precursor to heart failure. Under the assumptions presented, we estimate that 20.6% (95% Bayesian credible interval: 8.9%, 33.6%) of the population has a harmful effect greater than twice the average causal effect.

stat.ME↗

arXiv2022

Flexible machine learning estimation of conditional average treatment effects: a blessing and a curse

Causal inference from observational data requires untestable identification assumptions. If these assumptions apply, machine learning (ML) methods can be used to study complex forms of causal effect heterogeneity. Recently, several ML methods were developed to estimate the conditional average treatment effect (CATE). If the features at hand cannot explain all heterogeneity, the individual treatment effects (ITEs) can seriously deviate from the CATE. In this work, we demonstrate how the distributions of the ITE and the CATE can differ when a causal random forest (CRF) is applied. We extend the CRF to estimate the difference in conditional variance between treated and controls. If the ITE distribution equals the CATE distribution, this estimated difference in variance should be small. If they differ, an additional causal assumption is necessary to quantify the heterogeneity not captured by the CATE distribution. The conditional variance of the ITE can be identified when the individual effect is independent of the outcome under no treatment given the measured features. Then, in the cases where the ITE and CATE distributions differ, the extended CRF can appropriately estimate the variance of the ITE distribution while the CRF fails to do so.

stat.ME↗

arXiv2021

Individual causal effects from observational longitudinal studies with time-varying exposures

Causal effects may vary among individuals and can even be of opposite signs. When significant effect heterogeneity exists, the population average causal effect might be uninformative for an individual. Due to the fundamental problem of causality, individual causal effects (ICEs) cannot be retrieved from cross-sectional data. However, in crossover studies, it is accepted that ICEs can be estimated under the assumptions of no carryover effects and time invariance of potential outcomes. A generic potential-outcome formulation with appropriate statistical assumptions to identify ICEs is lacking for other longitudinal data with time-varying exposures. We present a general framework for causal effect heterogeneity in which individual-specific effect modification is parameterized with a latent variable, the receptiveness factor. If the exposure varies over time, then the repeated measurements contain information on an individual's level of this receptiveness factor. Therefore, we study the conditional distribution of the ICE given all an individual's factual information. This novel conditional random variable is called the cross-world causal effect (CWCE). For known causal structures and time-varying exposures, the variability of the CWCE reduces with an increasing number of repeated measurements. The CWCE becomes identifiable from observational data under the causal assumption of cross-world similarity of individual-effect modification (i.e. there exists an exposure strategy whose effect is affected by all latent causes). We illustrate the theory with examples in which the cause-effect relations can be parameterized as generalized linear mixed assignments.

stat.ME↗