Mechanistic curiosity will not kill the Bayesian cat

Meta-analyses are frequently performed on adverse event data and are primarily used for improving statistical power to detect safety signals. However, in the evaluation of drug safety for New Drug Applications, simple pooling of adverse event data from multiple clinical trials is still commonly used. We sought to propose a new Bayesian hierarchical meta-analytic approach based on consideration of a hierarchical structure of reported individual adverse event data from multiple randomized clinical trials. To develop our meta-analysis model, we extended an existing three-stage Bayesian hierarchical model by including an additional stage of the clinical trial level in the hierarchical model; this generated a four-stage Bayesian hierarchical model. We applied the proposed Bayesian meta-analysis models to published adverse event data from three premarketing randomized clinical trials of tadalafil and to a simulation study motivated by the case example to evaluate the characteristics of three alternative models. Comparison of the results from the Bayesian meta-analysis model with those from Fisher's exact test after simple pooling showed that 6 out of 10 adverse events were the same within a top 10 ranking of individual adverse events with regard to association with treatment. However, more individual adverse events were detected in the Bayesian meta-analysis model than in Fisher's exact test under the body system "Musculoskeletal and connective tissue disorders." Moreover, comparison of the overall trend of estimates between the Bayesian model and the standard approach (odds ratios after simple pooling methods) revealed that the posterior median odds ratios for the Bayesian model for most adverse events shrank toward values for no association. Based on the simulation results, the Bayesian meta-analysis model could balance the false detection rate and power to a better extent than Fisher's exact test. For example, when the threshold value of the posterior probability for signal detection was set to 0.8, the false detection rate was 41% and power was 88% in the Bayesian meta-analysis model, whereas the false detection rate was 56% and power was 86% in Fisher's exact test. Adverse events under the same body system were not necessarily positively related when we used "system organ class" and "preferred term" in the Medical Dictionary for Regulatory Activities as a hierarchical structure of adverse events. For the Bayesian meta-analysis models to be effective, the validity of the hierarchical structure of adverse events and the grouping of adverse events are critical. Our proposed meta-analysis models considered trial effects to avoid confounding by trial and borrowed strength from both within and across body systems to obtain reasonable and stable estimates of an effect measure by considering a hierarchical structure of adverse events.

Random effects regression models are routinely used for clustered data in etiological and intervention research. However, in prediction models, the random effects are either neglected or conventionally substituted with zero for new clusters after model development. In this study, we applied a Bayesian prediction modelling method to the subclinical ketosis data previously collected by Van der Drift et al. (2012). Using a dataset of 118 randomly selected Dutch dairy farms participating in a regular milk recording system, the authors proposed a prediction model with milk measures as well as available test-day information as predictors for the diagnosis of subclinical ketosis in dairy cows. While their original model included random effects to correct for the clustering, the random effect term was removed for their final prediction model. With the Bayesian prediction modelling approach, we first used non-informative priors for the random effects for model development as well as for prediction. This approach was evaluated by comparing it to the original frequentist model. In addition, herd level expert opinion was elicited from a bovine health specialist using three different scales of precision and incorporated in the prediction as informative priors for the random effects, resulting in three more Bayesian prediction models. Results showed that the Bayesian approach could naturally take the clustering structure of clusters into account by keeping the random effects in the prediction model. Expert opinion could be explicitly combined with individual level data for prediction. However in this dataset, when elicited expert opinion was incorporated, little improvement was seen at the individual level as well as at the herd level. When the prediction models were applied to the 118 herds, at the individual cow level, with the original frequentist approach we obtained a sensitivity of 82.4% and a specificity of 83.8% at the optimal cutoff, while with the three Bayesian models with elicited expert opinion, we obtained sensitivities ranged from 78.7% to 84.6% and specificities ranged from 75.0% to 83.6%. At the herd level, 30 out of 118 within herd prevalences were correctly predicted by the original frequentist approach, and 31 to 44 herds were correctly predicted by the three Bayesian models with elicited expert opinion. Further investigation in expert opinion and distributional assumption for the random effects was carried out and discussed.

Health utilities from value sets for the EQ-5D-5L are commonly used in economic evaluations. We examined whether modeling spatial correlation among health states could improve the precision of the value sets. Using data from 7 EQ-5D-5L valuation studies, we compared the predictive precision of the published linear model, a recently proposed cross-attribute level effects (CALE) model, and 2 Bayesian models with spatial correlation. Predictive precision was quantified through the root mean squared error (RMSE) for out-of-sample predictions of state-level mean utilities on omitting individual states, as well as omitting blocks of states. In all 7 countries, on omitting single health states, Bayesian models with spatial correlation improved upon the published linear model: the RMSEs for the originally published models, 0.050, 0.051, 0.060, 0.061, 0.039, 0.050, and 0.087 for Canada, China, Germany, Indonesia, Japan, Korea, and the Netherlands, respectively, could be reduced to 0.043, 0.042, 0.051, 0.054, 0.037, 0.037, and 0.085, respectively. On omitting blocks of health states, Bayesian models with spatial correlation led to smaller RMSEs in 3 countries, while the CALE model led to smaller RMSEs in the remaining 4 countries. Bayesian models incorporating spatial correlation and CALE models are promising for improving the precision of value sets for the EQ-5D-5L. The differential performance of the Bayesian models on omitting single states versus blocks of states suggests that designing valuation studies to capture more health states may further improve precision. We suggest that Bayesian and CALE models be considered as candidates when creating value sets and that alternative designs be explored; this is vital as the prediction errors in value sets need to be smaller than the minimal important difference of the instrument. The accuracy of value sets of multi-attribute utility instruments is typically of the same order of magnitude as the instrument's minimal important difference and would benefit from improvement.Bayesian models with spatial correlation have been shown to improve value set accuracy in isolated cases.We showed that Bayesian approaches with spatial correlation improved predictive precision in 7 EQ-5D-5L valuation studies.We recommend that Bayesian models incorporating spatial correlation be considered when creating value sets and have provided code for fitting them.

Climate change is a pervasive global issue that threatens the livelihoods and wellbeing of billions living globally. Climate change is a risk multiplier impacting all ecosystems, society, and sectors of the economy. The agriculture sector is one such sector that is highly vulnerable to changes in climate. In a country like Nepal where rainfed agriculture is a dominant occupation and a key pillar of the country’s economy, climate change brings risks and negative consequences for on-farm production, farmers' livelihoods as well as on the country’s development. The impacts of climate change including rising temperatures, an increase in the frequency or intensity of extreme weather events such as drought, and shifts in the rainfall seasonality, can cause a decline in food production and threaten the quality of food supplies, leading to reduced food security. The rise in the global population will increase global demand for food which implies that agriculture needs to boost production and increase yields, among other things. The unprecedented risks posed by climate change potentially undermine the ability of farms and farm holders to grow adequate and quality food. The severity of these risks varies due to a range of underlying factors including low economic development, their location, existing biophysical and socioeconomic conditions, and institutional arrangements. While the impacts of climate change on food production as well as agricultural practices in Nepal have been documented, there is a dearth in scholarly literature that has assessed the impacts of climate change on household food security in Nepal incorporating farmers’ perspectives and in particular smallholder subsistence farmers. Furthermore, there is only modest literature that has examined geographical variations in those experiences and understandings. This PhD study aimed, therefore, to investigate the effects of climate change on agricultural practices and food security, with a focus on subsistence smallholder farmers in three main agro- ecological zones of Nepal known as The Mountains, Hills, and the Terai. The study aimed to respond to the primary research question: How are Nepalese farming communities being impacted by climate change and how are they responding to ensure their continued food security? To answer this main research, question the study posed the following secondary research questions: Q1. How is climate changing and how is it impacting subsistence agriculture? Q2. What are the farmers experiencing and what is their understanding? a. Are there gender differences in understanding and experiencing? Q3. What is the state of food insecurity among these farmers? a. How is it being impacted by climate change? Q4. What adaptation strategies have been adopted by smallholder farmers to address threats to agricultural practices and food security from climate change and other pressures? Both the qualitative and qualitative data were collected using multiple methods to address the identified research questions. Methods included a narrative literature review, systematic review, face to face interviews with farmers, individual interviews with key informants and focus groups with the women's group. Climate data on temperature between 1971-2013 and rainfall between 1967-2013 were analysed. Additionally, secondary data on crop yield from 1980 to 2016 were also analysed to gain a better empirical understanding of the relations between climate change and yield pattern and to triangulate and validate the findings from the interviews. Quantitative data on cereal crop yields and climate data were systematically tabulated and further statistically analysed using software R. This study employed the Bayesian approach to statistical modelling. Besides, this study undertook an integrated risk assessment of food insecurity using the Bayesian Belief Network model to reflect how the risk of food insecurity is influenced under two scenarios: (1) current climate conditions and (2) the influences of different adaptation strategies employed. NVivo was used for content analysis for qualitative data obtained from the key informant interview and focus group data and analysis of transcripts from farmers' structured interviews. The findings showed that agricultural practices have undergone various changes over the past 30 years. Climate change impacts were experienced by farmers in all three agro-ecological zones of Nepal. However, the impacts varied between these zones in terms of frequency and intensity. The effect of climate change was highly pronounced in the Mountains zone followed by the Hills and the Terai. The results confirmed that rural subsistence smallholder farmers dependent on rainfed agriculture are vulnerable to climate change impacts. Moreover, it disproportionately affects the poor farmers whose income hinges solely on agriculture and associated activities. Boosting agricultural production and empowering these smallholders is key to enhancing their food security. The experiences reported by farmers are well aligned with the trend of the climatic variables obtained from climate data analysis, highlighting the importance of perception-based survey in complementing climate research. The study demonstrated both the climatic and non-climatic factors are affecting agricultural practices as well as household food security of these farming communities. It is, therefore, difficult to isolate the influence of any of these factors. This was supported by the findings from the risk assessment undertaken by Bayesian modelling. Based on Bayesian modelling, the smallholder farmers mainly at the Mountain zone were at the risk of food insecurity. The measures to increase the adaptive capacity of these smallholders were found to help them manage the risk of food insecurity. Addressing the complicated and multifaceted concerns of climate change and food security needs multidisciplinary and multisectoral adaptation interventions acknowledging underlying biophysical, social, economic, geographical and environmental circumstances. Farmers have taken some actions to adapt and reduce the worsening impacts of climate change. Nevertheless, farmers encountered several barriers in effectively adapting to climate change. This study concluded there is an urgent need for a transformative level of intervention that warrants a coordinated action and collaboration between relevant stakeholders working in this field, including governments and non-governmental organizations, to target the most vulnerable and the needy smallholder farmers addressing the constraints and pressures they face. Policy and decision-makers should work extensively and sensitively with smallholders to ensure the maintenance of their livelihood and to guarantee their food security. Combining local and scientific knowledge is needed to help direct research and tailor adaptation solutions that meet local conditions and needs.

Behavior is often plastic and the study of the functional basis of behavior should provide insights into the adaptive role of the mechanisms responsible for behavioral flexibility. Cognitive biases provide a window into the psychological mechanisms of behavior and a functional theory of behavioral mechanisms should be able to explain also the evolutionary significance of cognitive biases, that is, whether they should be seen as a solution to environmental problems or more as a by-product of adaptive rules. But how should such a theory be developed? In behavioral ecology, the "heuristics" approach has been prevailing. It proposes the rule first and then it investigates how the rule should be optimally modified to solve the problems posed by the environment, cognitive biases being a possible solution. Here, I explore an alternative approach, which derives rules from formal models of optimality. By focusing on mate choice, I present an optimal Bayesian decision-making model, based on the computation of the cumulative sums of the log-likelihood ratios that the quality of a prospective mate is either higher or lower than average. When uncertainty is high, log-likelihood ratios can be approximated to a linear function of mate quality; specifically, they may be expressed as deviations of the perceived quality from the population mean, weighted by the perceived assessment accuracy. I use this model to illustrate the different origins and, possibly, the different functional role of decision-making biases. More generally, I propose the model as an attempt to develop an evolutionary theory of behavioral mechanisms.

Bayesian models of cognition provide a powerful way to understand the behavior and goals of individuals from a computational point of view. Much of the focus in the Bayesian cognitive modeling approach has been on qualitative model evaluations, where predictions from the models are compared to data that is often averaged over individuals. In many cognitive tasks, however, there are pervasive individual differences. We introduce an approach to directly infer individual differences related to subjective mental representations within the framework of Bayesian models of cognition. In this approach, Bayesian data analysis methods are used to estimate cognitive parameters and motivate the inference process within a Bayesian cognitive model. We illustrate this integrative Bayesian approach on a model of memory. We apply the model to behavioral data from a memory experiment involving the recall of heights of people. A cross-validation analysis shows that the Bayesian memory model with inferred subjective priors predicts withheld data better than a Bayesian model where the priors are based on environmental statistics. In addition, the model with inferred priors at the individual subject level led to the best overall generalization performance, suggesting that individual differences are important to consider in Bayesian models of cognition.

Bayesian statistics have been used in various health physics applications, but only limited material exists on the development of a decision threshold for simple gross count measurements using Bayesian statistics. Bayesian modeling specifies a logical procedure for processing information and provides the means to obtain abstract statistical knowledge about the data in question. A Bayesian interaction model was developed to analyze gross count measurements. This linear regression model studies the relationship between a gross count measurement and the standard deviation of the gross counts obtained in the current and the previous four measurements, and conditions the analysis on whether the data originate from background measurements or from measurements with a source present. The measure of that relationship is expressed statistically by the constructed parameter ζ, which in the Bayesian framework possesses a probability distribution that can be used to achieve detection decisions. The model was validated statistically and under operationally equivalent conditions. Specifically, it was applied to analyze sequential data obtained from continuous gross count measurements at fixed time intervals. The Bayesian analysis used five sequential measurements per detection decision. The model performs optimally for weaker source detections, and presents promising operational application. Its usefulness derives from the facts that an established training data set is not necessary, long-run background measurements are not required to establish parameter estimates, and ζ and the model are universally applicable such that their use is not limited to the predictor variable presented here.

Network meta-analysis (NMA) is an increasingly popular statistical method of synthesising evidence to assess the comparative benefits and harms of multiple treatments in a single analysis. Several automated software packages...

Bayesian Model Selection Approaches are flexible methods that can be utilised to investigate Genetic Association studies in greater detail; enabling us to more accurately pin-point locations of disease genes in complex regions such as the MHC, as well as investigate possible causal pathways between genes, disease and intermediate phenotypes. This thesis is split into two distinct parts. The first uses a Bayesian Multivariate Adaptive Regression Spline Model to search across many highly correlated variants to try to determine which are likely to be the truly causal variants within complex genetic regions and also how each of these variants influences disease status. Specifically, I consider the role of genetic variants within the MHC region on SLE. The second part of the thesis aims to model possible disease pathways between genes, disease, intermediate phenotypes and environmental factors using Bayesian Networks, in particular focussing upon Coronary Heart disease and numerous blood biomarkers and related genes. Bayesian Multivariate Adaptive Regression Spline Model: Genetic association studies have the problem that often many genotypes in strong linkage disequilibrium (LD) are found to be associated with the outcome of interest. This makes it difficult to establish the actual SNP responsible. The aim of this part of the thesis is to investigate Bayesian variable selection methods in regions of high LD. In particular, to investigate SNPs in the major histocompatibility complex (MHC) region associated with systematic lupus erythematosus (SLE). Past studies have found several SNPs in this region to be highly associated with SLE but these SNPs are in high LD with one another. It is desirable to search over all possible regression models in order to find those SNPs that are most important in the prediction of SLE. The Bayesian Multivariate Adapative Regression Splines (BMARS) model used should automatically correct for nearby associated SNPs, and only those directly associated should be included in the model. The BMARS approach will also automatically select the most appropriate disease model for each directly associated variant. It was found that there appear to be 3 separate SNP signals in the MHC region that show association with SLE. The rest of the associations found using simple Frequentist tests are likely to be due to LD with the true signal. Bayesian Networks for Genetic Association Studies: Coronary Heart Disease (CHD) is one of many diseases that result from complicated relationships between both genetic and environmental factors. Identifying causal factors and developing new treatments that target these factors is very difficult. Changes in intermediate phenotypes, or biomarkers, could suggest potential causal pathways, although these have a tendency to group amongst those patients with higher risk of CHD making to difficult to distinguish independent causal relationships. I aim to model disease pathways allowing for intermediate phenotypes as well as genetic and environmental factors. Statistical methodology was developed using directed acyclic graphs (DAGs). Disease outcomes, genes, intermediate phenotypes and possible explanatory variables were represented as nodes in a DAG. Possible models were investigated using Bayesian regression models, based upon the underlying DAG, in a reversible jump MCMC framework. Modelling the data this way allows us to distinguish between direct and indirect effects as well as explore possible directionality of relationships. Since different DAGs can belong to the same equivalence class, some directions of association may become indistinguishable and I am interested in the implications of this. I investigated the integrated associations of genotypes with multiple blood biomarkers linked to CHD risk, focusing particularly on relationships between APOE, CETP and APOB genotypes; HDL- and LDL- cholesterol, triglycerides, C-reactive protein, fibrogen and apolipoproteins A and B. Overview: I will begin by introducing the topics of genetics, statistics and directed acyclic graphs with a background on each (Chapters 2,3 and 4 respectively). Chapter 5 will then detail the analysis and results of the BMARS model. The analysis and results of Bayesian networks for genetic association studies will then be covered in Chapter 6.

The general question of our paper concerns the relationship between Bayesian models of cognition and predictive processing, and whether predictive processing can provide explanatory insight over and above Bayesian models. Bayesian models have been gaining influence in neuroscience and the cognitive sciences since they are able to predict human behavior with high accuracy. Models based on a Bayesian optimal observer are fitted on behavioral data. A good fit is hence interpreted as human subjects “behaving” in a Bayes’ optimal fashion. However, these models are performance-oriented and do not specify which processes could give rise to the observed behavior. Here, David Marr’s (Marr 1982) levels of analysis can help understand the relationship between performance- and process-oriented models or explanations. Bayesian models are situated at the computational level since they specify what the system (in this case the brain) does and why it does it in this manner. Although Bayesian models can constrain the search space for hypotheses at the algorithmic level, they do not provide a precise solution about how a system realizes the observed behavior. Here predictive processing can shed more light on the underlying principles. Predictive processing provides a unifying functional theory of cognition and can thus i) provide an answer at the algorithmic level by answering how the brain realizes cognition, ii) can aid in the interpretation of neurophysiological findings at the implementational level.

Improving the accuracy of brain activation maps in the group-level analysis of fMRI data utilizing spatiotemporal Gaussian process model

One practical challenge in observational studies and quasi-experimental designs is selection bias. The issue of selection bias becomes more concerning when data are non-normal and contain missing values. Recently, a Bayesian robust two-stage causal modeling with instrumental variables was developed and has the advantages of addressing selection bias and handle non-normal data and missing data simultaneously in one model. The method provides reliable parameter and standard error estimates when missing data and outliers exist. The modeling technique can be widely applied to empirical studies particularly in social, psychological and behavioral areas where any of the three issues (e.g., selection bias, data with outliers and missing data) is commonly seen. To implement this method, we developed an R package named ALMOND (Analysis of LATE (Local Average Treatment Effect) for Missing Or/and Nonnormal Data). Package users have the flexibility to directly apply the Bayesian robust two-stage causal models or write their own Bayesian models from scratch within the package. To facilitate the application of the Bayesian robust two-stage causal modeling technique, we provide a tutorial for the ALMOND package in this article, and illustrate the application with two examples from empirical research.

Fässler, S. M. M., Brierley, A. S., and Fernandes, P. G. 2009. A Bayesian approach to estimating target strength. – ICES Journal of Marine Science, 66: 1197–1204. Currently, conventional models of target strength (TS) vs. fish length, based on empirical measurements, are used to estimate fish density from integrated acoustic data. These models estimate a mean TS, averaged over variables that modulate fish TS (tilt angle, physiology, and morphology); they do not include information about the uncertainty of the mean TS, which could be propagated through to estimates of fish abundance. We use Bayesian methods, together with theoretical TS models and in situ TS data, to determine the uncertainty in TS estimates of Atlantic herring (Clupea harengus). Priors for model parameters (surface swimbladder volume, tilt angle, and s.d. of the mean TS) were used to estimate posterior parameter distributions and subsequently build a probabilistic TS model. The sensitivity of herring abundance estimates to variation in the Bayesian TS model was also evaluated. The abundance of North Sea herring from the area covered by the Scottish acoustic survey component was estimated using both the conventional TS–length formula (5.34×109 fish) and the Bayesian TS model (mean = 3.17×109 fish): this difference was probably because of the particular scattering model employed and the data used in the Bayesian model. The study demonstrates the relative importance of potential bias and precision of TS estimation and how the latter can be so much less important than the former.

Civil registration and vital statistics (CRVS) systems should be the primary source of mortality data for governments. Accurate measurement of the completeness of death registration helps inform interventions to improve CRVS systems and to generate reliable mortality indicators. In this work we propose a Bayesian extension to the empirical completeness method to estimate the completeness of death registration in a population. The Bayesian models were developed using death registration data from 120 countries and 2748 country-years in 1970–2019 from the Global Burden of Disease (GBD) 2019 database. According to our findings, the credible intervals obtained under the proposed Bayesian models suggest that the covariates are reliable predictors of the logit of the completeness of death registration. To illustrate the effectiveness of our proposal, we applied the Bayesian models to estimate the completeness of death registration in the departments of Colombia in 2017. We found that most posterior mean estimates closely approximate to the observed value of completeness across the departments of Colombia and that, for nearly all departments, the observed completeness is within the credible intervals. The proposed Bayesian demographic models allow institutions to produce distributional estimates (e.g., posterior mean, quantiles, credible intervals, posterior probabilities) of the completeness of death registration at the subnational level, which can be used as evidence to strengthen their CRVS system.

We propose a Bayesian semiparametric joint regression model for a recurrent event process and survival time. Assuming independent latent subject frailties, we define marginal models for the recurrent event process intensity and survival distribution as functions of the subject's frailty and baseline covariates. A robust Bayesian model, called Joint-DP, is obtained by assuming a Dirichlet process for the frailty distribution. We present a simulation study that compares posterior estimates under the Joint-DP model to a Bayesian joint model with lognormal frailties, a frequentist joint model, and marginal models for either the recurrent event process or survival time. The simulations show that the Joint-DP model does a good job of correcting for treatment assignment bias, and has favorable estimation reliability and accuracy compared with the alternative models. The Joint-DP model is applied to analyze an observational dataset from esophageal cancer patients treated with chemo-radiation, including the times of recurrent effusions of fluid to the heart or lungs, survival time, prognostic covariates, and radiation therapy modality.