Volume 19, Issue 2

SMAC 2021 was a webconference organized in June 2021. The aim of this conference was to bring together data scientists, (bio)statisticians, philosophers, and any person interested in the questions of causality and Bayesian statistics, ranging from technical to philosophical aspects. This webconference consisted of keynote speakers and contributed speakers, and closed with a round-table organized in an unusual fashion. Indeed, organisers asked world renowned scientists to prepare two videos: a short video presenting a question of interest to them and a longer one presenting their point of view on the question. The first video served as a “teaser” for the conference and the second were presented during the conference as an introduction to the round-table. These videos and this round-table generated original scientific insights and discussion worthy of being shared with the community which we do by means of this paper.

In this paper, we review some important early developments on causal inference in medical statistics and epidemiology that were inspired by questions in oncology. We examine two classical examples from the literature and point to a current area of ongoing methodological development, namely the estimation of optimal adaptive treatment strategies. While causal approaches to analysis have become more routine in oncology research, many exciting challenges and open problems remain, particularly in the context of censored outcomes.

In this paper, I provide an introduction for biostatisticians and others to some recent work in the philosophy of medicine. Firstly, I give an overview of some philosophical arguments that are thought to create problems for a prominent approach towards establishing causal claims in medicine, namely, the Evidence-Based Medicine (EBM) approach. Secondly, I provide an overview of further recent work in the philosophy of medicine, which argues that mechanistic studies can help to address these problems. Lastly, I describe a novel approach for establishing causal claims in medicine that has been informed by this recent work in the philosophy of medicine, namely, the EBM+ approach.

Bayesian philosophy and Bayesian statistics have diverged in recent years, because Bayesian philosophers have become more interested in philosophical problems other than the foundations of statistics and Bayesian statisticians have become less concerned with philosophical foundations. One way in which this divergence manifests itself is through the use of direct inference principles: Bayesian philosophers routinely advocate principles that require calibration of degrees of belief to available non-epistemic probabilities, while Bayesian statisticians rarely invoke such principles. As I explain, however, the standard Bayesian framework cannot coherently employ direct inference principles. Direct inference requires a shift towards a non-standard Bayesian framework, which further increases the gap between Bayesian philosophy and Bayesian statistics. This divergence does not preclude the application of Bayesian philosophical methods to real-world problems. Data consolidation is a key challenge for present-day systems medicine and other systems sciences. I show that data consolidation requires direct inference and that the non-standard Bayesian methods outlined here are well suited to this task.

In this work, we examine recently developed methods for Bayesian inference of optimal dynamic treatment regimes (DTRs). DTRs are a set of treatment decision rules aimed at tailoring patient care to patient-specific characteristics, thereby falling within the realm of precision medicine. In this field, researchers seek to tailor therapy with the intention of improving health outcomes; therefore, they are most interested in identifying optimal DTRs. Recent work has developed Bayesian methods for identifying optimal DTRs in a family indexed by ψ via Bayesian dynamic marginal structural models (MSMs) (Rodriguez Duque D, Stephens DA, Moodie EEM, Klein MB. Semiparametric Bayesian inference for dynamic treatment regimes via dynamic regime marginal structural models. Biostatistics; 2022. (In Press)); we review the proposed estimation procedure and illustrate its use via the new BayesDTR R package. Although methods in Rodriguez Duque D, Stephens DA, Moodie EEM, Klein MB. (Semiparametric Bayesian inference for dynamic treatment regimes via dynamic regime marginal structural models. Biostatistics; 2022. (In Press)) can estimate optimal DTRs well, they may lead to biased estimators when the model for the expected outcome if everyone in a population were to follow a given treatment strategy, known as a value function, is misspecified or when a grid search for the optimum is employed. We describe recent work that uses a Gaussian process ( G P ) $(\mathcal{G}\mathcal{P})$ prior on the value function as a means to robustly identify optimal DTRs (Rodriguez Duque D, Stephens DA, Moodie EEM. Estimation of optimal dynamic treatment regimes using Gaussian processes; 2022. Available from: https://doi.org/10.48550/arXiv.2105.12259). We demonstrate how a G P $\mathcal{G}\mathcal{P}$ approach may be implemented with the BayesDTR package and contrast it with other value-search approaches to identifying optimal DTRs. We use data from an HIV therapeutic trial in order to illustrate a standard analysis with these methods, using both the original observed trial data and an additional simulated component to showcase a longitudinal (two-stage DTR) analysis.

Simulation studies are promising in medical research in particular to improve drug development. For instance, one can aim to develop In Silico Clinical Trial in order to challenge trial’s design parameters in terms of feasibility and probability of success of the trial. Approaches based on agent-based models draw on a particularly useful framework to simulate patients evolution. In this paper, an approach based on agent-based modeling is described and discussed in the context of medical research. An R-vine copula model is used to represent the multivariate distribution of the data. A baseline data cohort can then be simulated and execution models can be developed to simulate the evolution of patients. R-vine copula models are very flexible tools which allow researchers to consider different marginal distributions than the ones observed in the data. It is then possible to perform data augmentation to explore a new population by simulating baseline data which are slightly different than those of the original population. A simulation study illustrates the efficiency of copula modeling to generate data according to specific marginal distributions but also highlights difficulties inherent to data augmentation.

Although they remain little used in the field of Health Care Economics, Agent Based Models (ABM) are potentially powerful decision-making tools that open up great prospects. The reasons for this lack of popularity are essentially to be found in a methodology that should be further clarified. This article hence aims to illustrate the methodology by means of two applications to medical examples. The first example of ABM illustrates the construction of a Baseline Data Cohort by means of a Virtual Baseline Generator. The aim is to describe the prevalence of thyroid cancer in the French population over the long term according to different scenarios of evolution of this population. The second study considers a setting where the Baseline Data Cohort is an established cohort of (real) patients: the EVATHYR cohort. The aim of the ABM is to describe the long-term costs associated with different scenarios of thyroid cancer management. The results are evaluated using several simulation runs in order to observe the variability of simulations and to derive prediction intervals. The ABM approach is very flexible since several sources of data can be involved and a large variety of simulation models can be calibrated to generate observations according to different evolution scenarios.

In genome wide association studies (GWAS), researchers are often dealing with dichotomous and non-normally distributed traits, or a mixture of discrete-continuous traits. However, most of the current region-based methods rely on multivariate linear mixed models (mvLMMs) and assume a multivariate normal distribution for the phenotypes of interest. Hence, these methods are not applicable to disease or non-normally distributed traits. Therefore, there is a need to develop unified and flexible methods to study association between a set of (possibly rare) genetic variants and non-normal multivariate phenotypes. Copulas are multivariate distribution functions with uniform margins on the [0, 1] interval and they provide suitable models to deal with non-normality of errors in multivariate association studies. We propose a novel unified and flexible copula-based multivariate association test (CBMAT) for discovering association between a genetic region and a bivariate continuous, binary or mixed phenotype. We also derive a data-driven analytic p -value procedure of the proposed region-based score-type test. Through simulation studies, we demonstrate that CBMAT has well controlled type I error rates and higher power to detect associations compared with other existing methods, for discrete and non-normally distributed traits. At last, we apply CBMAT to detect the association between two genes located on chromosome 11 and several lipid levels measured on 1477 subjects from the ASLPAC study.

Many health care professionals and institutions manage longitudinal databases, involving follow-ups for different patients over time. Longitudinal data frequently manifest additional complexities such as high variability, correlated measurements and missing data. Mixed effects models have been widely used to overcome these difficulties. This work proposes the use of linear mixed effects models as a tool that allows to search conceptually different types of anomalies in the data simultaneously.

Current research suggests that hundreds to thousands of single nucleotide polymorphisms (SNPs) with small to modest effect sizes contribute to the genetic basis of many disorders, a phenomenon labeled as polygenicity. Additionally, many such disorders demonstrate polygenic overlap, in which risk alleles are shared at associated genetic loci. A simple strategy to detect polygenic overlap between two phenotypes is based on rank-ordering the univariate p -values from two genome-wide association studies (GWASs). Although high-dimensional variable selection strategies such as Lasso and elastic nets have been utilized in other GWAS analysis settings, they are yet to be utilized for detecting shared polygenicity. In this paper, we illustrate how elastic nets, with polygenic scores as the dependent variable and with appropriate adaptation in selecting the penalty parameter, may be utilized for detecting a subset of SNPs involved in shared polygenicity. We provide theory to better understand our approaches, and illustrate their utility using synthetic datasets. Results from extensive simulations are presented comparing the elastic net approaches with the rank ordering approach, in various scenarios. Results from simulations studies exhibit one of the elastic net approaches to be superior when the correlations among the SNPs are high. Finally, we apply the methods on two real datasets to illustrate further the capabilities, limitations and differences among the methods.

Third generation sequencing technologies such as Pacific Biosciences and Oxford Nanopore provide faster, cost-effective and simpler assembly process generating longer reads than the ones in the next generation sequencing. However, the error rates of these long reads are higher than those of the short reads, resulting in an error correcting process before the assembly such as using the Circular Consensus Sequencing (CCS) reads in PacBio sequencing machines. In this paper, we propose a probabilistic model for the error occurrence along the CCS reads. We obtain the error probability of any arbitrary nucleotide as well as the base calling Phred quality score of the nucleotides along the CCS reads in terms of the number of sub-reads. Furthermore, we derive the error rate distribution of the reads in relation to the pass number. It follows the binomial distribution which can be approximated by the normal distribution for long reads. Finally, we evaluate our proposed model by comparing it with three real PacBio datasets, namely, Lambda, and E. coli genomes, and Alzheimer’s disease targeted experiment.

Bivariate random-effects models represent an established approach for meta-analysis of accuracy measures of a diagnostic test, which are typically given by sensitivity and specificity. A recent formulation of the classical model describes the test accuracy in terms of study-specific Receiver Operating Characteristics curves. In this way, the resulting summary curve can be thought of as an average of the study-specific Receiver Operating Characteristics curves. Within this framework, the paper shows that the standard likelihood approach for inference is prone to several issues. Small sample size can give rise to unreliable conclusions and convergence problems deeply affect the analysis. The proposed alternative is a simulation-extrapolation method, called SIMEX, developed within the measurement error literature. It suits the meta-analysis framework, as the accuracy measures provided by the studies are estimates rather than true values, and thus are prone to error. The methods are compared in a series of simulation studies, covering different scenarios of interest, including deviations from normality assumptions. SIMEX reveals a satisfactory strategy, providing more accurate inferential results if compared to the likelihood approach, while avoiding convergence failure. The approaches are applied to a meta-analysis of the accuracy of the ultrasound exam for diagnosing abdominal tuberculosis in HIV-positive subjects.

In this paper, we propose the first-order stationary integer-valued autoregressive process with the cosine Poisson innovation, based on the negative binomial thinning operator. It can be equi-dispersed, under-dispersed and over-dispersed. Therefore, it is flexible for modelling integer-valued time series. Some statistical properties of the process are derived. The parameters of the process are estimated by two methods of estimation and the performances of the estimators are evaluated via some simulation studies. Finally, we demonstrate the usefulness of the proposed model by modelling and analyzing some practical count time series data on the daily deaths of COVID-19 and the drug calls data.

This paper proposes a new flexible discrete triplet Lindley model that is constructed from the balanced discretization principle of the extended Lindley distribution. This model has several appealing statistical properties in terms of providing exact and closed form moment expressions and handling all forms of dispersion. Due to these, this paper explores further the usage of the discrete triplet Lindley as an innovation distribution in the simple integer-valued autoregressive process (INAR(1)). This subsequently allows for the modeling of count time series observations. In this context, a novel INAR(1) process is developed under mixed Binomial and the Pegram thinning operators. The model parameters of the INAR(1) process are estimated using the conditional maximum likelihood and Yule-Walker approaches. Some Monte Carlo simulation experiments are executed to assess the consistency of the estimators under the two estimation approaches. Interestingly, the proposed INAR(1) process is applied to analyze the COVID-19 cases and death series of different countries where it yields reliable parameter estimates and suitable forecasts via the modified Sieve bootstrap technique. On the other side, the new INAR(1) with discrete triplet Lindley innovations competes comfortably with other established INAR(1)s in the literature.