arXiv subjects

Alex Lewin

Publications and source records attributed to Alex Lewin.

8 recordsLinked to original sources

arXiv2024

BayesFBHborrow: An R Package for Bayesian borrowing for time-to-event data from a flexible baseline hazard

Statistical methods that leverage external trial information to help accelerate drug development are becoming increasingly popular. Bayesian methods facilitate dynamic borrowing, where the similarity of the response guides how much information is used. We have proposed a semiparametric Bayesian borrowing model for time-to-event data, with smoothing priors that allows the baseline hazard to take any form via an ensemble average. By accurately modelling the baseline hazard, rather than approximating its form via fixed piecewise intervals, power is improved and bias of the estimated treatment effect reduced when the borrowing assumption of parameter exchangeability holds. A ``lump-and-smear'' borrowing prior makes the model robust to non-exchangeable historical data by increasing the sensitivity of borrowing to the presence of prior-data conflict, reducing the potential for type I error inflation. We present BayesFBHborrow, an R package that implements our semiparametric Bayesian borrowing model with a historical control. We demonstrate how to select the optimal borrowing hyperparameters. The model supports covariate-adjusted borrowing, which can reduce prior-data conflict and improve power when differences in outcomes are attributable to changes in the covariate distribution. As the treatment effect estimator is non-collapsible, the marginal hazard ratio can be estimated via Bayesian G-computation, while still permitting an adjusted analysis to account for control group drift. We illustrate the Bayesian flexible baseline hazard model on a simulated and real dataset with a marginal estimand, for both an unadjusted and adjusted analyses.

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arXiv2024

Borrowing from historical control data in a Bayesian time-to-event model with flexible baseline hazard function

There is currently a focus on statistical methods which can use historical trial information to help accelerate the discovery, development and delivery of medicine. Bayesian methods can be constructed so that the borrowing is "dynamic" in the sense that the similarity of the data helps to determine how much information is used. In the time to event setting with one historical data set, a popular model for a range of baseline hazards is the piecewise exponential model where the time points are fixed and a borrowing structure is imposed on the model. Although convenient for implementation this approach effects the borrowing capability of the model. We propose a Bayesian model which allows the time points to vary and a dependency to be placed between the baseline hazards. This serves to smooth the posterior baseline hazard improving both model estimation and borrowing characteristics. We explore a variety of prior structures for the borrowing within our proposed model and assess their performance against established approaches. We demonstrate that this leads to improved type I error in the presence of prior data conflict and increased power. We have developed accompanying software which is freely available and enables easy implementation of the approach.

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arXiv2021

BayesSUR: An R package for high-dimensional multivariate Bayesian variable and covariance selection in linear regression

In molecular biology, advances in high-throughput technologies have made it possible to study complex multivariate phenotypes and their simultaneous associations with high-dimensional genomic and other omics data, a problem that can be studied with high-dimensional multi-response regression, where the response variables are potentially highly correlated. To this purpose, we recently introduced several multivariate Bayesian variable and covariance selection models, e.g., Bayesian estimation methods for sparse seemingly unrelated regression for variable and covariance selection. Several variable selection priors have been implemented in this context, in particular the hotspot detection prior for latent variable inclusion indicators, which results in sparse variable selection for associations between predictors and multiple phenotypes. We also propose an alternative, which uses a Markov random field (MRF) prior for incorporating prior knowledge about the dependence structure of the inclusion indicators. Inference of Bayesian seemingly unrelated regression (SUR) by Markov chain Monte Carlo methods is made computationally feasible by factorisation of the covariance matrix amongst the response variables. In this paper we present BayesSUR, an R package, which allows the user to easily specify and run a range of different Bayesian SUR models, which have been implemented in C++ for computational efficiency. The R package allows the specification of the models in a modular way, where the user chooses the priors for variable selection and for covariance selection separately. We demonstrate the performance of sparse SUR models with the hotspot prior and spike-and-slab MRF prior on synthetic and real data sets representing eQTL or mQTL studies and in vitro anti-cancer drug screening studies as examples for typical applications.

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arXiv2021

Multivariate Bayesian structured variable selection for pharmacogenomic studies

Precision cancer medicine aims to determine the optimal treatment for each patient. In-vitro cancer drug sensitivity screens combined with multi-omics characterization of the cancer cells have become an important tool to achieve this aim. Analyzing such pharmacogenomic studies requires flexible and efficient joint statistical models for associating drug sensitivity with high-dimensional multi-omics data. We propose a multivariate Bayesian structured variable selection model for sparse identification of omics features associated with multiple correlated drug responses. Since many anti-cancer drugs are designed for specific molecular targets, our approach makes use of known structure between responses and predictors, e.g. molecular pathways and related omics features targeted by specific drugs, via a Markov random field (MRF) prior for the latent indicator variables of the coefficients in sparse seemingly unrelated regression. The structure information included in the MRF prior can improve the model performance, i.e. variable selection and response prediction, compared to other common priors. In addition, we employ random effects to capture heterogeneity between cancer types in a pan-cancer setting. The proposed approach is validated by simulation studies and applied to the Genomics of Drug Sensitivity in Cancer data, which includes pharmacological profiling and multi-omics characterization of a large set of heterogeneous cell lines.

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arXiv2015

Optimal whitening and decorrelation

Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example based on principal component analysis (PCA), Cholesky matrix decomposition and zero-phase component analysis (ZCA), among others. Here we provide an overview of the underlying theory and discuss five natural whitening procedures. Subsequently, we demonstrate that investigating the cross-covariance and the cross-correlation matrix between sphered and original variables allows to break the rotational invariance and to identify optimal whitening transformations. As a result we recommend two particular approaches: ZCA-cor whitening to produce sphered variables that are maximally similar to the original variables, and PCA-cor whitening to obtain sphered variables that maximally compress the original variables.

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arXiv2001

Can inflationary models of cosmic perturbations evade the secondary oscillation test?

We consider the consequences of an observed Cosmic Microwave Background (CMB) temperature anisotropy spectrum containing no secondary oscillations. While such a spectrum is generally considered to be a robust signature of active structure formation, we show that such a spectrum {\em can} be produced by (very unusual) inflationary models or other passive evolution models. However, we show that for all these passive models the characteristic oscillations would show up in other observable spectra. Our work shows that when CMB polarization and matter power spectra are taken into account secondary oscillations are indeed a signature of even these very exotic passive models. We construct a measure of the observability of secondary oscillations in a given experiment, and show that even with foregrounds both the MAP and \pk satellites should be able to distinguish between models with and without oscillations. Thus we conclude that inflationary and other passive models can {\em not} evade the secondary oscillation test.

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arXiv1999

A new statistic for picking out Non-Gaussianity in the CMB

In this paper we propose a new statistic capable of detecting non-Gaussianity in the CMB. The statistic is defined in Fourier space, and therefore naturally separates angular scales. It consists of taking another Fourier transform, in angle, over the Fourier modes within a given ring of scales. Like other Fourier space statistics, our statistic outdoes more conventional methods when faced with combinations of Gaussian processes (be they noise or signal) and a non-Gaussian signal which dominates only on some scales. However, unlike previous efforts along these lines, our statistic is successful in recognizing multiple non-Gaussian patterns in a single field. We discuss various applications, in which the Gaussian component may be noise or primordial signal, and the non-Gaussian component may be a cosmic string map, or some geometrical construction mimicking, say, small scale dust maps.

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arXiv1997

Non-Gaussian spectra and the search for cosmic strings

We present a new tool for relating theory and experiment suited for non-Gaussian theories: non-Gaussian spectra. It does for non-Gaussian theories what the angular power spectrum $C_\ell$ does for Gaussian theories. We then show how previous studies of cosmic strings have over rated their non-Gaussian signature. More realistic maps are not visually stringy. However non-Gaussian spectra will accuse their stringiness. We finally summarise the steps of an undergoing experimental project aiming at searching for cosmic strings by means of this technique.

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