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Modelling and computation for multivariate longitudinal surveys have proven challenging, particularly when data are not all continuous and Gaussian but contain discrete measurements. In many social science surveys, study participants are selected via complex survey designs such as stratified random sampling, leading to discrepancies between the sample and population, which are further compounded by missing data and loss to follow-up. Survey weights are typically constructed to address these issues, but it is not clear how to include them in models. Motivated by data on sexual development, we propose a novel non-parametric approach for mixed scale longitudinal data in surveys. In the approach proposed, the mixed scale multivariate response is expressed through an underlying continuous variable with dynamic latent factors inducing time varying associations. Bias from the survey design is adjusted for in posterior computation relying on a Markov chain Monte Carlo algorithm. The approach is assessed in simulation studies and applied to the National Longitudinal Study of Adolescent to Adult Health.

Aims/hypothesis A precision medicine approach in type 2 diabetes could enhance targeting specific glucose-lowering therapies to individual patients most likely to benefit. We aimed to use the recently developed Bayesian causal forest (BCF) method to develop and validate an individualised treatment selection algorithm for two major type 2 diabetes drug classes, sodium–glucose cotransporter 2 inhibitors (SGLT2i) and glucagon-like peptide-1 receptor agonists (GLP1-RA). Methods We designed a predictive algorithm using BCF to estimate individual-level conditional average treatment effects for 12-month glycaemic outcome (HbA 1c ) between SGLT2i and GLP1-RA, based on routine clinical features of 46,394 people with type 2 diabetes in primary care in England (Clinical Practice Research Datalink; 27,319 for model development, 19,075 for hold-out validation), with additional external validation in 2252 people with type 2 diabetes from Scotland (SCI-Diabetes [Tayside & Fife]). Differences in glycaemic outcome with GLP1-RA by sex seen in clinical data were replicated in clinical trial data (HARMONY programme: liraglutide [ n =389] and albiglutide [ n =1682]). As secondary outcomes, we evaluated the impacts of targeting therapy based on glycaemic response on weight change, tolerability and longer-term risk of new-onset microvascular complications, macrovascular complications and adverse kidney events. Results Model development identified marked heterogeneity in glycaemic response, with 4787 (17.5%) of the development cohort having a predicted HbA 1c benefit >3 mmol/mol (>0.3%) with SGLT2i over GLP1-RA and 5551 (20.3%) having a predicted HbA 1c benefit >3 mmol/mol with GLP1-RA over SGLT2i. Calibration was good in hold-back validation, and external validation in an independent Scottish dataset identified clear differences in glycaemic outcomes between those predicted to benefit from each therapy. Sex, with women markedly more responsive to GLP1-RA, was identified as a major treatment effect modifier in both the UK observational datasets and in clinical trial data: HARMONY-7 liraglutide (GLP1-RA): 4.4 mmol/mol (95% credible interval [95% CrI] 2.2, 6.3) (0.4% [95% CrI 0.2, 0.6]) greater response in women than men. Targeting the two therapies based on predicted glycaemic response was also associated with improvements in short-term tolerability and long-term risk of new-onset microvascular complications. Conclusions/interpretation Precision medicine approaches can facilitate effective individualised treatment choice between SGLT2i and GLP1-RA therapies, and the use of routinely collected clinical features for treatment selection could support low-cost deployment in many countries. Graphical Abstract

There is an innate human tendency, one might call it the “league table mentality,” to construct rankings. Schools, hospitals, sports teams, movies, and myriad other objects are ranked even though their inherent multi-dimensionality would suggest that—at best—only partial orderings were possible. We consider a large class of elementary ranking problems in which we observe noisy, scalar measurements of merit for n objects of potentially heterogeneous precision and are asked to select a group of the objects that are “most meritorious.” The problem is naturally formulated in the compound decision framework of Robbins’s (1956) empirical Bayes theory, but it also exhibits close connections to the recent literature on multiple testing. The nonparametric maximum likelihood estimator for mixture models (Kiefer and Wolfowitz (1956)) is employed to construct optimal ranking and selection rules. Performance of the rules is evaluated in simulations and an application to ranking U.S. kidney dialysis centers.

Population pharmacokinetic (PK) modeling methods can be statistically classified as either parametric or nonparametric (NP). Each classification can be divided into maximum likelihood (ML) or Bayesian (B) approaches. In this paper we discuss the nonparametric case using both maximum likelihood and Bayesian approaches. We present two nonparametric methods for estimating the unknown joint population distribution of model parameter values in a pharmacokinetic/pharmacodynamic (PK/PD) dataset. The first method is the NP Adaptive Grid (NPAG). The second is the NP Bayesian (NPB) algorithm with a stick-breaking process to construct a Dirichlet prior. Our objective is to compare the performance of these two methods using a simulated PK/PD dataset. Our results showed excellent performance of NPAG and NPB in a realistically simulated PK study. This simulation allowed us to have benchmarks in the form of the true population parameters to compare with the estimates produced by the two methods, while incorporating challenges like unbalanced sample times and sample numbers as well as the ability to include the covariate of patient weight. We conclude that both NPML and NPB can be used in realistic PK/PD population analysis problems. The advantages of one versus the other are discussed in the paper. NPAG and NPB are implemented in R and freely available for download within the Pmetrics package from www.lapk.org .

We develop a Bayesian method for nonparametric model-based quantile regression. The approach involves flexible Dirichlet process mixture models for the joint distribution of the response and the covariates, with posterior inference for different quantile curves emerging from the conditional response distribution given the covariates. An extension to allow for partially observed responses leads to a novel Tobit quantile regression framework. We use simulated data sets and two data examples from the literature to illustrate the capacity of the model to uncover nonlinearities in quantile regression curves, as well as nonstandard features in the response distribution.

It is well known that store-level brand sales may not only depend on contemporaneous influencing factors like current own and competitive prices or other marketing activities, but also on past prices representing customer response to price dynamics. On the other hand, non- or semiparametric regression models have been proposed in order to accommodate potential nonlinearities in price response, and related empirical findings for frequently purchased consumer goods indicate that price effects may show complex nonlinearities, which are difficult to capture with parametric models. In this contribution, we combine nonparametric price response modeling and behavioral pricing theory. In particular, we propose a semiparametric approach to flexibly estimating price-change or reference price effects based on store-level sales data. We compare different representations for capturing symmetric vs. asymmetric and proportional vs. disproportionate price-change effects following adaptation-level and prospect theory, and further compare our flexible autoregressive model specifications to parametric benchmark models. Functional flexibility is accommodated via P-splines, and all models are estimated within a fully Bayesian framework. In an empirical study, we demonstrate that our semiparametric dynamic models provide more accurate sales forecasts for most brands considered compared to competing benchmark models that either ignore price dynamics or just include them in a parametric way.

Inferring underlying cooperative and competitive strategies from human behaviour in repeated games is important for accurately characterizing human behaviour and understanding how people reason strategically. Finite automata, a bounded model of computation, have been extensively used to compactly represent strategies for these games and are a standard tool in game theoretic analyses. However, inference over these strategies in repeated games is challenging since the number of possible strategies grows exponentially with the number of repetitions yet behavioural data are often sparse and noisy. As a result, previous approaches start by specifying a finite hypothesis space of automata that does not allow for flexibility. This limitation hinders the discovery of novel strategies that may be used by humans but are not anticipated a priori by current theory. Here we present a new probabilistic model for strategy inference in repeated games by exploiting non-parametric Bayesian modelling. With simulated data, we show that the model is effective at inferring the true strategy rapidly and from limited data, which leads to accurate predictions of future behaviour. When applied to experimental data of human behaviour in a repeated prisoner's dilemma, we uncover strategies of varying complexity and diversity.

Energy markets are typically characterized by high complexity due to several reasons such as the large number of occurring variables, different in nature, and their associative structure. Estimating a statistical model that properly represents the dependencies among the variables is crucial for managing such a complexity. In this paper, a simple energy market influenced by hydroelectric availability is studied by using Bayesian networks. Since the variables of interest are quantitative but non Gaussian, non-parametric strategies are used to infer the Colombian energy market association structure. We propose a comparison between the UniNet learning algorithm and the Rank PC algorithm, both based on normal copula assumption and Spearman correlation measure, in order to explore differences in the estimated models. Finally, model usability for energy managers is shown through the discussion of some scenarios.

PurposeThe purpose this paper is to review some of the statistical methods used in the field of social sciences.Design/methodology/approachA review of some of the statistical methodologies used in areas like survey methodology, official statistics, sociology, psychology, political science, criminology, public policy, marketing research, demography, education and economics.FindingsSeveral areas are presented such as parametric modeling, nonparametric modeling and multivariate methods. Focus is also given to time series modeling, analysis of categorical data and sampling issues and other useful techniques for the analysis of data in the social sciences. Indicative references are given for all the above methods along with some insights for the application of these techniques.Originality/valueThis paper reviews some statistical methods that are used in social sciences and the authors draw the attention of researchers on less popular methods. The purpose is not to give technical details and also not to refer to all the existing techniques or to all the possible areas of statistics. The focus is mainly on the applied aspect of the techniques and the authors give insights about techniques that can be used to answer problems in the abovementioned areas of research.

This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We develop an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent normal-Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two-equation structural model drawn from the labour and returns to schooling literatures.