Bayesian estimation of two-part joint models for a longitudinal semicontinuous biomarker and a terminal event with INLA: Interests for cancer clinical trial evaluation

Two-part joint models for a longitudinal semicontinuous biomarker and a terminal event have been recently introduced based on frequentist estimation. The biomarker distribution is decomposed into a probability of positive value and the expected value among positive values. Shared random effects can represent the association structure between the biomarker and the terminal event. The computational burden increases compared to standard joint models with a single regression model for the biomarker. In this context, the frequentist estimation implemented in the R package frailtypack can be challenging for complex models (i.e., a large number of parameters and dimension of the random effects). As an alternative, we propose a Bayesian estimation of two-part joint models based on the Integrated Nested Laplace Approximation (INLA) algorithm to alleviate the computational burden and fit more complex models. Our simulation studies confirm that INLA provides accurate approximation of posterior estimates and to reduced computation time and variability of estimates compared to frailtypack in the situations considered. We contrast the Bayesian and frequentist approaches in the analysis of two randomized cancer clinical trials (GERCOR and PRIME studies), where INLA has a reduced variability for the association between the biomarker and the risk of event. Moreover, the Bayesian approach was able to characterize subgroups of patients associated with different responses to treatment in the PRIME study. Our study suggests that the Bayesian approach using the INLA algorithm enables to fit complex joint models that might be of interest in a wide range of clinical applications.     

Detection of significant disease risks using a spatial conditional autoregressive model

SUMMARY: The conditional autoregressive (CAR) model is widely used to describe the geographical distribution of a specific disease risk in lattice mapping. Successful developments based on frequentist and Bayesian procedures have been extensively applied to obtain two-stage disease risk predictions at the subregional level. Bayesian procedures are preferred for making inferences, as the posterior standard errors (SE) of the two-stage prediction account for the variability in the variance component estimates; however, some recent work based on frequentist procedures and the use of bootstrap adjustments for the SE has been undertaken. In this article we investigate the suitability of an analytical adjustment for disease risk inference that provides accurate interval predictions by using the penalized quasilikelihood (PQL) technique to obtain model parameter estimates. The method is a first-order approximation of the naive SE based on a Taylor expansion and is interpreted as a conditional measure of variability providing conditional calibrated prediction intervals, given the data. We conduct a simulation study to demonstrate how the method can be used to estimate the specific subregion risk by interval. We evaluate the proposed methodology by analyzing the commonly used example data set of lip cancer incidence in the 56 counties of Scotland for the period 1975-1980. This evaluation reveals a close similarity between the solutions provided by the method proposed here and those of its fully Bayesian counterpart.     

ABCtoolbox: a versatile toolkit for approximate Bayesian computations

Background  

The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations.     

Properties of cell death models calibrated and compared using Bayesian approaches

Using models to simulate and analyze biological networks requires principled approaches to parameter estimation and model discrimination. We use Bayesian and Monte Carlo methods to recover the full probability distributions of free parameters (initial protein concentrations and rate constants) for mass‐action models of receptor‐mediated cell death. The width of the individual parameter distributions is largely determined by non‐identifiability but covariation among parameters, even those that are poorly determined, encodes essential information. Knowledge of joint parameter distributions makes it possible to compute the uncertainty of model‐based predictions whereas ignoring it (e.g., by treating parameters as a simple list of values and variances) yields nonsensical predictions. Computing the Bayes factor from joint distributions yields the odds ratio (～20‐fold) for competing ‘direct’ and ‘indirect’ apoptosis models having different numbers of parameters. Our results illustrate how Bayesian approaches to model calibration and discrimination combined with single‐cell data represent a generally useful and rigorous approach to discriminate between competing hypotheses in the face of parametric and topological uncertainty.     

Maximum likelihood and Bayesian methods for estimating the distribution of selective effects among classes of mutations using DNA polymorphism data

Maximum likelihood and Bayesian approaches are presented for analyzing hierarchical statistical models of natural selection operating on DNA polymorphism within a panmictic population. For analyzing Bayesian models, we present Markov chain Monte-Carlo (MCMC) methods for sampling from the joint posterior distribution of parameters. For frequentist analysis, an Expectation-Maximization (EM) algorithm is presented for finding the maximum likelihood estimate of the genome wide mean and variance in selection intensity among classes of mutations. The framework presented here provides an ideal setting for modeling mutations dispersed through the genome and, in particular, for the analysis of how natural selection operates on different classes of single nucleotide polymorphisms (SNPs).     

Likelihood and Bayesian analyses reveal major genes affecting body composition,carcass, meat quality and the number of false teats in a Chinese European pig line

Segregation analyses were performed using both maximum likelihood – via a Quasi Newton algorithm – (ML-QN) and Bayesian – via Gibbs sampling – (Bayesian-GS) approaches in the Chinese European Tiameslan pig line. Major genes were searched for average ultrasonic backfat thickness (ABT), carcass fat (X2 and X4) and lean (X5) depths, days from 20 to 100 kg ({"type":"entrez-nucleotide","attrs":{"text":"D20100","term_id":"500997","term_text":"D20100"}}D20100), Napole technological yield (NTY), number of false (FTN) and good (GTN) teats, as well as total teat number (TTN). The discrete nature of FTN was additionally considered using a threshold model under ML methodology. The results obtained with both methods consistently suggested the presence of major genes affecting ABT, X2, NTY, GTN and FTN. Major genes were also suggested for X4 and X5 using ML-QN, but not the Bayesian-GS, approach. The major gene affecting FTN was confirmed using the threshold model. Genetic correlations as well as gene effect and genotype frequency estimates suggested the presence of four different major genes. The first gene would affect fatness traits (ABT, X2 and X4), the second one a leanness trait (X5), the third one NTY and the last one GTN and FTN. Genotype frequencies of breeding animals and their evolution over time were consistent with the selection performed in the Tiameslan line.     

The use of artificial neural networks to reduce data collection demands in determining spine loading: a laboratory based analysis

The extensive data requirements of three-dimensional inverse dynamics and joint modelling to estimate spinal loading prevent the implementation of these models in industry and may hinder development of advanced injury prevention standards. This work examines the potential of feed forward artificial neural networks (ANNs) as a data reduction approach and compared predictions to rigid link and EMG-assisted models. Ten males and ten females performed dynamic lifts, all approaches were applied and comparisons of predicted joint moments and joint forces were evaluated. While the ANN under- predicted peak extension moments (p = 0.0261) and joint compression (p < 0.0001), predictions of cumulative extension moments (p = 0.8293) and cumulative joint compression (p = 0.9557) were not different. Therefore, the ANNs proposed may be used to obtain estimates of cumulative exposure variables with reduced input demands; however they should not be applied to determine peak demands of a worker's exposure.     

Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture

Shared random effects joint models are becoming increasingly popular for investigating the relationship between longitudinal and time‐to‐event data. Although appealing, such complex models are computationally intensive, and quick, approximate methods may provide a reasonable alternative. In this paper, we first compare the shared random effects model with two approximate approaches: a naïve proportional hazards model with time‐dependent covariate and a two‐stage joint model, which uses plug‐in estimates of the fitted values from a longitudinal analysis as covariates in a survival model. We show that the approximate approaches should be avoided since they can severely underestimate any association between the current underlying longitudinal value and the event hazard. We present classical and Bayesian implementations of the shared random effects model and highlight the advantages of the latter for making predictions. We then apply the models described to a study of abdominal aortic aneurysms (AAA) to investigate the association between AAA diameter and the hazard of AAA rupture. Out‐of‐sample predictions of future AAA growth and hazard of rupture are derived from Bayesian posterior predictive distributions, which are easily calculated within an MCMC framework. Finally, using a multivariate survival sub‐model we show that underlying diameter rather than the rate of growth is the most important predictor of AAA rupture.     

Parameter estimation in a generalized discrete-time model of density dependence

Flexible discrete-time per-capita-growth-rate models accommodating a variety of density-dependent relationships offer parsimonious explanations for the variation of population abundance through time. However, the accuracy of standard approaches to parameter estimation and confidence interval construction for such models has not been explored in a generalized setting or with consideration of limited sample sizes typical for ecology. Here, we use simulated data to quantify the relative effects of sample size, population perturbations, and environmental stochasticity on statistical inference. We focus on the key parameters that inform population dynamic predictions in a generalized Beverton–Holt model. We find that reliable parameter estimation requires data spanning ranges where both low and high density dependence act. However, the asymptotic distribution of the likelihood ratio test statistic can be fairly accurate for constructing confidence regions even when point estimation is poor. Consideration of the joint profile likelihood surface is shown to be useful for assessing reliability of point estimates and dynamical population predictions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Multi-trait and multi-environment QTL analyses of yield and a set of physiological traits in pepper

Key message

A mixed model framework was defined for QTL analysis of multiple traits across multiple environments for a RIL population in pepper. Detection power for QTLs increased considerably and detailed study of QTL by environment interactions and pleiotropy was facilitated.

Abstract

For many agronomic crops, yield is measured simultaneously with other traits across multiple environments. The study of yield can benefit from joint analysis with other traits and relations between yield and other traits can be exploited to develop indirect selection strategies. We compare the performance of three multi-response QTL approaches based on mixed models: a multi-trait approach (MT), a multi-environment approach (ME), and a multi-trait multi-environment approach (MTME). The data come from a multi-environment experiment in pepper, for which 15 traits were measured in four environments. The approaches were compared in terms of number of QTLs detected for each trait, the explained variance, and the accuracy of prediction for the final QTL model. For the four environments together, the superior MTME approach delivered a total of 47 regions containing putative QTLs. Many of these QTLs were pleiotropic and showed quantitative QTL by environment interaction. MTME was superior to ME and MT in the number of QTLs, the explained variance and accuracy of predictions. The large number of model parameters in the MTME approach was challenging and we propose several guidelines to help obtain a stable final QTL model. The results confirmed the feasibility and strengths of novel mixed model QTL methodology to study the architecture of complex traits.     

Prediction of dry-cured ham weight loss and prospects of use in a pig breeding program

Large ham weight losses (WL) in dry-curing are undesired as they lead to a loss of marketable product and penalise the quality of the dry-cured ham. The availability of early predictions of WL may ease the adaptation of the dry-curing process to the characteristics of the thighs and increase the effectiveness of selective breeding in enhancing WL. Aims of this study were (i) to develop Bayesian and Random Forests (RFs) regression models for the prediction of ham WL during dry-curing using on-site infrared spectra of raw ham subcutaneous fat, carcass and raw ham traits as predictors and (ii) to estimate genetic parameters for WL and their predictions (P-WL). Visible-near infrared spectra were collected on the transversal section of the subcutaneous fat of raw hams. Carcass traits were carcass weight, carcass backfat depth, lean meat content and weight of raw hams. Raw ham traits included measures of ham subcutaneous fat depth and linear scores for round shape, subcutaneous fat thickness and marbling of the visible muscles of the thigh. Measures of WL were available for 1672 hams. The best prediction accuracies were those of a Bayesian regression model including the average spectrum, carcass and raw ham traits, with R² values in validation of 0.46, 0.55 and 0.62, for WL at end of salting (23 days), resting (90 days) and curing (12 months), respectively. When WL at salting was used as an additional predictor of total WL, the R² in validation was 0.67. Bayesian regressions were more accurate than RFs models in predicting all the investigated traits. Restricted maximum likelihood (REML) estimates of genetic parameters for WL and P-WL at the end of curing were estimated through a bivariate animal model including 1672 measures of WL and 8819 P-WL records. Results evidenced that the traits are heritable (h² ± SE was 0.27 ± 0.04 for WL and 0.39 ± 0.04 for P-WL), and the additive genetic correlation is positive and high (r_a = 0.88 ± 0.03). Prediction accuracy of ham WL is high enough to envisage a future use of prediction models in identifying batches of hams requiring an adaptation of the processing conditions to optimise results of the manufacturing process. The positive and high genetic correlation detected between WL and P-WL at the end of dry-curing, as well as the estimated heritability for P-WL, suggests that P-WL can be successfully used as an indicator trait of the measured WL in pig breeding programs.     

Investigating meta-approaches for reconstructing gene networks in a mammalian cellular context

The output of state-of-the-art reverse-engineering methods for biological networks is often based on the fitting of a mathematical model to the data. Typically, different datasets do not give single consistent network predictions but rather an ensemble of inconsistent networks inferred under the same reverse-engineering method that are only consistent with the specific experimentally measured data. Here, we focus on an alternative approach for combining the information contained within such an ensemble of inconsistent gene networks called meta-analysis, to make more accurate predictions and to estimate the reliability of these predictions. We review two existing meta-analysis approaches; the Fisher transformation combined coefficient test (FTCCT) and Fisher's inverse combined probability test (FICPT); and compare their performance with five well-known methods, ARACNe, Context Likelihood or Relatedness network (CLR), Maximum Relevance Minimum Redundancy (MRNET), Relevance Network (RN) and Bayesian Network (BN). We conducted in-depth numerical ensemble simulations and demonstrated for biological expression data that the meta-analysis approaches consistently outperformed the best gene regulatory network inference (GRNI) methods in the literature. Furthermore, the meta-analysis approaches have a low computational complexity. We conclude that the meta-analysis approaches are a powerful tool for integrating different datasets to give more accurate and reliable predictions for biological networks.     

Inference for meta‐analysis with a suspected temporal trend

There is sometimes a clear evidence of a strong secular trend in the treatment effect of studies included in a meta‐analysis. In such cases, estimating the present‐day treatment effect by meta‐regression is both reasonable and straightforward. We however consider the more common situation where a secular trend is suspected, but is not strongly statistically significant. Typically, this lack of significance is due to the small number of studies included in the analysis, so that a meta‐regression could give wild point estimates. We introduce an empirical Bayes meta‐analysis methodology, which shrinks the secular trend toward zero. This has the effect that treatment effects are adjusted for trend, but where the evidence from data is weak, wild results are not obtained. We explore several frequentist approaches and a fully Bayesian method is also implemented. A measure of trend analogous to I² is described, and exact significance tests for trend are given. Our preferred method is one based on penalized or h‐likelihood, which is computationally simple, and allows invariance of predictions to the (arbitrary) choice of time origin. We suggest that a trendless standard random effects meta‐analysis should routinely be supplemented with an h‐likelihood analysis as a sensitivity analysis.     

Inference for the Ratio of Two Normal Means with Unspecified Variances

Mendoza and Gutiérrez‐Peña (1999) presented a Bayesian analysis of the ratio of two normal means when the ratio of the means determines the ratio of the variances, X ～ N(βμ, β²σ²), Y ～ N(μ, σ²). They claimed the superiority of the Bayesian analysis, based on the whole likelihood function with non‐informative priors, by comparing it with a non‐Bayesian analysis based only on the Fieller pivotal. The purpose here is to show that the Fieller pivotal constitutes only part of the likelihood function of β in this model, so that any analysis, including Bayesian, based solely on the Fieller pivotal is highly inefficient, possibly to the extent of discarding most of the information in the sample. A non‐Bayesian analysis based on the structure of the whole likelihood function exhibits this and rectifies such an oversight. The role of the variance ratio is discussed and exemplified. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A design criterion for symmetric model discrimination based on flexible nominal sets

Experimental design applications for discriminating between models have been hampered by the assumption to know beforehand which model is the true one, which is counter to the very aim of the experiment. Previous approaches to alleviate this requirement were either symmetrizations of asymmetric techniques, or Bayesian, minimax, and sequential approaches. Here we present a genuinely symmetric criterion based on a linearized distance between mean-value surfaces and the newly introduced tool of flexible nominal sets. We demonstrate the computational efficiency of the approach using the proposed criterion and provide a Monte-Carlo evaluation of its discrimination performance on the basis of the likelihood ratio. An application for a pair of competing models in enzyme kinetics is given.     

Calculating the evolutionary rates of different genes: a fast, accurate estimator with applications to maximum likelihood phylogenetic analysis

In phylogenetic analyses with combined multigene or multiprotein data sets, accounting for differing evolutionary dynamics at different loci is essential for accurate tree prediction. Existing maximum likelihood (ML) and Bayesian approaches are computationally intensive. We present an alternative approach that is orders of magnitude faster. The method, Distance Rates (DistR), estimates rates based upon distances derived from gene/protein sequence data. Simulation studies indicate that this technique is accurate compared with other methods and robust to missing sequence data. The DistR method was applied to a fungal mitochondrial data set, and the rate estimates compared well to those obtained using existing ML and Bayesian approaches. Inclusion of the protein rates estimated from the DistR method into the ML calculation of trees as a branch length multiplier resulted in a significantly improved fit as measured by the Akaike Information Criterion (AIC). Furthermore, bootstrap support for the ML topology was significantly greater when protein rates were used, and some evident errors in the concatenated ML tree topology (i.e., without protein rates) were corrected. [Bayesian credible intervals; DistR method; multigene phylogeny; PHYML; rate heterogeneity.].     

A joint fairness model with applications to risk predictions for underrepresented populations

In data collection for predictive modeling, underrepresentation of certain groups, based on gender, race/ethnicity, or age, may yield less accurate predictions for these groups. Recently, this issue of fairness in predictions has attracted significant attention, as data-driven models are increasingly utilized to perform crucial decision-making tasks. Existing methods to achieve fairness in the machine learning literature typically build a single prediction model in a manner that encourages fair prediction performance for all groups. These approaches have two major limitations: (i) fairness is often achieved by compromising accuracy for some groups; (ii) the underlying relationship between dependent and independent variables may not be the same across groups. We propose a joint fairness model (JFM) approach for logistic regression models for binary outcomes that estimates group-specific classifiers using a joint modeling objective function that incorporates fairness criteria for prediction. We introduce an accelerated smoothing proximal gradient algorithm to solve the convex objective function, and present the key asymptotic properties of the JFM estimates. Through simulations, we demonstrate the efficacy of the JFM in achieving good prediction performance and across-group parity, in comparison with the single fairness model, group-separate model, and group-ignorant model, especially when the minority group's sample size is small. Finally, we demonstrate the utility of the JFM method in a real-world example to obtain fair risk predictions for underrepresented older patients diagnosed with coronavirus disease 2019 (COVID-19).     

Computational protein biomarker prediction: a case study for prostate cancer

Background  

Recent technological advances in mass spectrometry pose challenges in computational mathematics and statistics to process the mass spectral data into predictive models with clinical and biological significance. We discuss several classification-based approaches to finding protein biomarker candidates using protein profiles obtained via mass spectrometry, and we assess their statistical significance. Our overall goal is to implicate peaks that have a high likelihood of being biologically linked to a given disease state, and thus to narrow the search for biomarker candidates.