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Shear wave elastography is an emerging diagnostic tool used to assess for changes in the stiffness of muscle. Each region of the muscle may have a different stiffness; therefore, the anatomical region should be carefully selected. Machine vendors each have unique methods for calculating the returned stiffness values and, consequently, a high level of agreement in measurement between machines (quantified using the intraclass correlation coefficient [ICC] and Bland-Altman analysis) will allow research findings to be translated to the clinic. This study assessed three locations within the biceps muscle (50% and 75% of the distance between the acromioclavicular joint and antecubital fossa, and superior to distal myotendinous junction [MTJ]) of 32 healthy volunteers with two different machines, the Canon Aplio i600 and SuperSonic Imagine Aixplorer (SSI), to compare the reported shear wave velocities and the variability by coefficient of variation (CV) and ICC. There was no difference in the CV between machines, but a significant difference in the CV at muscle regions, with the 75% location having a 40.2% reduction in CV. The 75% location had the highest ICC values with good posterior mean ICCs of 0.84 on the Canon and 0.83 on the SSI. The 50% and MTJ locations had poor ICC values. The 75% location provided the lowest CV and highest ICC and should be used for future stiffness assessments.

Ultrasound elastography shows diagnostic promise via the non-invasive determination of placental elastic properties. A limitation is a potential for inadequate measurements from posterior placentae. This study aimed to analyse placental position's influence on measures of shear wave elastography (SWV).SWV elastography measurements were obtained via ultrasound at 24, 28 and 36 weeks gestation from 238 pregnancies. . The placental position was labelled as either anterior, posterior or fundal/lateral. Average SWV measurements (m/s) and the corresponding standard deviations (SD) were used for data analysis.There was a statistically significant difference between SWV recorded from anterior (1.33 ± 0.19)m/s and posterior (1.39 ± 0.18)m/s placentae (p 0.001). However, the average sampling depth between these groups was significantly different (3.98 cm vs. 5.38 cm, p 0.001). There was no statistically significant difference between SWV when measurements were compared at similar depths, regardless of placental location. The addition of placental position to a previously developed mixed-effects model confirmed placental position did not result in improved SWV measurements. In this model, sampling depth remained the best predictor for SWV.This study showed that placental position does not influence the accuracy or reliability of SWV.

When effective vaccines are available, vaccination programs are typically one of the best defences against the spread of an infectious disease. Unfortunately, vaccination rates may be suboptimal for a prolonged duration as a result of slow uptake of vaccines by the public. Key factors driving slow vaccination uptake can be a complex interaction of vaccine roll-out policies and logistics, and vaccine hesitancy behaviours potentially caused by an inflated sense of risk in adverse reactions in some populations or community complacency in communities that have not yet experienced a large outbreak. In the recent COVID-19 pandemic, public health responses around the world began to include vaccination programs from late 2020 to early 2021 with an aim of relaxing non-pharmaceutical interventions such as lockdowns and travel restrictions. For many jurisdictions there have been challenges in getting vaccination rates high enough to enable the relaxation of restrictions based on non-pharmaceutical interventions. A key concern during this time was vaccine hestitancy behaviours potentially caused by vaccine safety concerns fuelled by misinformation and community complacency in jurisdictions that had seen very low COVID-19 case numbers throughout 2020, such as Australia and New Zealand. We develop a novel stochastic epidemiological model of COVID-19 transmission that incorporates changes in population behaviour relating to responses based on non-pharmaceutical interventions and community vaccine uptake as functions of the reported COVID-19 cases, deaths, and vaccination rates. Through a simulation study, we develop a Bayesian analysis approach to demonstrate that different factors inhibiting the uptake of vaccines by the population can be isolated despite key model parameters being subject to substantial uncertainty. In particular, we are able to identify the presence of vaccine hesitancy in a population using reported case, death and vaccination count data alone. Furthermore, our approach provides insight as to whether the dominant concerns driving hesitancy are related to vaccine safety or complacency. While our simulation study is inspired by the COVID-19 pandemic, our tools and techniques are general and could be enable vaccination programs of various infectious diseases to be adapted rapidly in response to community behaviours moving forward into the future.

We consider predictions in longitudinal studies, and investigate the well known statistical mixed-effects model, piecewise linear mixed-effects model and six different popular machine learning approaches: decision trees, bagging, random forest, boosting, support-vector machine and neural network. In order to consider the correlated data in machine learning, the random effects is combined into the traditional tree methods and random forest. Our focus is the performance of statistical modelling and machine learning especially in the cases of the misspecification of the fixed effects and the random effects. Extensive simulation studies have been carried out to evaluate the performance using a number of criteria. Two real datasets from longitudinal studies are analysed to demonstrate our findings. The R code and dataset are freely available at https://github.com/shuwen92/MEML.

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

This randomized cross-over study tested the hypothesis that heat acclimation training would detrimentally affect sleep variables and alter incidental physical activity compared to a thermoneutral training control condition. Eight recreationally trained males (V̇ O2peak 49±4.9 mL. kg-1.min-1) completed two separate interventions separated by at least 31 days: 5 consecutive day training blocks of moderate-intensity cycling (60 min·day-1 at 50% peak power output) in a hot (34.9±0.7 °C and 53±4 % relative humidity) and a temperate (22.2±2.6 °C; 65±8 % relative humidity) environment. Wrist-mounted accelerometers were worn continuously for the length of the training blocks and recorded physical activity, sleep quality and quantity. Data were analysed in a Bayesian framework, with the results presented as the posterior probability that a coefficient was greater or less than zero. Compared to the temperate training environment, heat acclimation impaired sleep efficiency (Pr β0 = .917). Daily sedentary time was, on average, 35 min longer (Pr β>0 = .973) and light physical activity time 18 min shorter (Pr β>0 = .960) during the heat acclimation period. No differences were observed between conditions in sleep duration, subjective sleep quality, or moderate or vigorous physical activity. These findings may suggest that athletes and coaches need to be cognisant that heat acclimation training may alter sleep quality and increase sedentary behaviour.

Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models can pose a challenge in terms of their ability to be validated with experimental measurements. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. The ability of this type of model to capture tumour growth accurately remains unknown. In this paper, a likelihood-free method is employed to calibrate a VCBM to breast, ovarian and pancreatic cancer measurements in vivo. Our approach involves estimating the distribution of parameters that govern cancer cell proliferation and recovering the output from the model based on estimated parameters so that the outputs match the experimental data. Our results show that the VCBM can accurately model monophasic tumour growth but lacks the ability to capture biphasic or multiphasic tumour growth. Furthermore, we find that the time taken for a daughter cell to become a mature adult cell is highly informed by the data. Moving forward, this allows us to propose future refinements to the model to improve accuracy, whilst also making conclusions about the differences in cancer cell characteristics.

Likelihood-free methods are useful for parameter estimation of complex models with intractable likelihood functions for which it is easy to simulate data. Such models are prevalent in many disciplines including genetics, biology, ecology and cosmology. Likelihood-free methods avoid explicit likelihood evaluation by finding parameter values of the model that generate data close to the observed data. The general consensus has been that it is most efficient to compare datasets on the basis of a low dimensional informative summary statistic, incurring information loss in favour of reduced dimensionality. More recently, researchers have explored various approaches for efficiently comparing empirical distributions in the likelihood-free context in an effort to avoid data summarisation. This article provides a review of these full data distance based approaches, and conducts the first comprehensive comparison of such methods, both qualitatively and empirically. We also conduct a substantive empirical comparison with summary statistic based likelihood-free methods. The discussion and results offer guidance to practitioners considering a likelihood-free approach. Whilst we find the best approach to be problem dependent, we also find that the full data distance based approaches are promising and warrant further development. We discuss some opportunities for future research in this space. Computer code to implement the methods discussed in this paper can be found at https://github.com/cdrovandi/ABC-dist-compare., To appear in Statistics and Computing

Parameter estimation for mathematical models of biological processes is often difficult and depends significantly on the quality and quantity of available data. We introduce an efficient frame-work using Gaussian processes to discover mechanisms underlying delay, migration, and proliferation in a cell invasion experiment. Gaussian processes are leveraged with bootstrapping to provide uncertainty quantification for the mechanisms that drive the invasion process. Our frame-work is efficient, parallelisable, and can be applied to other biological problems. We illustrate our methods using a canonical scratch assay experiment, demonstrating how simply we can explore different functional forms and develop and test hypotheses about underlying mechanisms, such as whether delay is present. All code and data to reproduce this work are available at https://github.com/DanielVandH/EquationLearning.jl.1Author summaryIn this work we introduce uncertainty quantification into equation learning methods, such as physics-informed and biologically-informed neural networks. Our framework is computationally efficient and applicable to problems with unknown nonlinear mechanisms that we wish to learn from experiments where only sparse noisy data are available. We demonstrate our methods on a canonical scratch assay experiment from cell biology and show the underlying mechanisms can be learned, providing confidence intervals for functional forms and for solutions to partial differential equation models believed to describe the experiment.

Biological heterogeneity is a primary contributor to the variation observed in experiments that probe dynamical processes, such as the internalization of material by cells. Given that internalization is a critical process by which many therapeutics and viruses reach their intracellular site of action, quantifying cell-to-cell variability in internalization is of high biological interest. Yet, it is common for studies of internalization to neglect cell-to-cell variability. We develop a simple mathematical model of internalization that captures the dynamical behaviour, cell-to-cell variation, and extrinsic noise introduced by flow cytometry. We calibrate our model through a novel distribution-matching approximate Bayesian computation algorithm to flow cytometry data of internalization of anti-transferrin receptor antibody in a human B-cell lymphoblastoid cell line. This approach provides information relating to the region of the parameter space, and consequentially the nature of cell-to-cell variability, that produces model realizations consistent with the experimental data. Given that our approach is agnostic to sample size and signal-to-noise ratio, our modelling framework is broadly applicable to identify biological variability in single-cell data from internalization assays and similar experiments that probe cellular dynamical processes.

Performing optimal Bayesian design for discriminating between competing models is computationally intensive as it involves estimating posterior model probabilities for thousands of simulated data sets. This issue is compounded further when the likelihood functions for the rival models are computationally expensive. A new approach using supervised classification methods is developed to perform Bayesian optimal model discrimination design. This approach requires considerably fewer simulations from the candidate models than previous approaches using approximate Bayesian computation. Further, it is easy to assess the performance of the optimal design through the misclassification error rate. The approach is particularly useful in the presence of models with intractable likelihoods but can also provide computational advantages when the likelihoods are manageable., Biotechnology and Biological Sciences Research Council grant BB/M020193/1

During the COVID-19 pandemic, many countries implemented international travel restrictions that aimed to contain viral spread while still allowing necessary cross-border travel for social and economic reasons. The relative effectiveness of these approaches for controlling the pandemic has gone largely unstudied. Here we developed a flexible network meta-population model to compare the effectiveness of international travel policies, with a focus on evaluating the benefit of policy coordination. Because country-level epidemiological parameters are unknown, they need to be estimated from data; we accomplished this using approximate Bayesian computation, given the nature of our complex stochastic disease transmission model. Based on simulation and theoretical insights we find that, under our proposed policy, international airline travel may resume up to 58% of the pre-pandemic level with pandemic control comparable to that of a complete shutdown of all airline travel. Our results demonstrate that global coordination is necessary to allow for maximum travel with minimum effect on viral spread.

Building on a strong foundation of philosophy, theory, methods and computation over the past three decades, Bayesian approaches are now an integral part of the toolkit for most statisticians and data scientists. Whether they are dedicated Bayesians or opportunistic users, applied professionals can now reap many of the benefits afforded by the Bayesian paradigm. In this paper, we touch on six modern opportunities and challenges in applied Bayesian statistics: intelligent data collection, new data sources, federated analysis, inference for implicit models, model transfer and purposeful software products., Comment: 27 pages, 8 figures

Sequential Monte Carlo squared (SMC$$^2$$ 2 ) methods can be used for parameter inference of intractable likelihood state-space models. These methods replace the likelihood with an unbiased particle filter estimate, similarly to particle Markov chain Monte Carlo (MCMC). As with particle MCMC, the efficiency of SMC$$^2$$ 2 greatly depends on the variance of the likelihood estimator, and therefore on the number of state particles used within the particle filter. We introduce novel methods to adaptively select the number of state particles within SMC$$^2$$ 2 using the expected squared jumping distance to trigger the adaptation, and modifying the exchange importance sampling method of Chopin et al. (J R Stat Soc: Ser B (Stat Method) 75(3):397–426, 2012) to replace the current set of state particles with the new set of state particles. The resulting algorithm is fully automatic, and can significantly improve current methods. Code for our methods is available at https://github.com/imkebotha/adaptive-exact-approximate-smc.

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data., Comment: Minor changes to text. Additional results in supplementary material. Additional statistics regarding results given in main and supplementary material

Australian football goal kicking is vital to team success, but its study is limited. Develop and apply Bayesian models incorporating temporal, spatial and situational variables to predict shot outcomes. The models aim to (i) rank players on their goal kicking and (ii) create clusters of statistically similar players and rank these clusters to provide generalised recommendations about player types.Retrospective longitudinal study with goal kicking data from three seasons, 2018-2020, 576 official Australian Football League matches, containing 26,818 attempts at goal from 778 players.The Bayesian ordinal regression model enables descriptive analysis of goal kicking performance. The models include spatial variables of distance and kick angle, situational variables of shot type and player or cluster with interaction terms. Alternative models included situational variables of weather and player characteristics, spatial variables of stadium location and temporal variables of time and quarter. Approximate leave-one-out cross validation was used to test the model.Overall goal rate of 47% (12,600), behind rate of 35% (9373) with misses the remaining 18% (4845). Accuracy of both player and cluster model achieved 0.51 against an uninformed (predict goal) model result of 0.47. The models allow for analysis of goal kicking accuracy by distance and angle and analysis of player and player-type performance.While credible intervals for all players for set shots and general play were relatively large, some 95% credible intervals excluded zero. Therefore, it may be concluded that some players' goal kicking skill can be quantified and differentiated from other players.

Maternal obesity is a significant risk factor for poor pregnancy outcomes. Obesity is linked to abnormalities in placental tissue at term. The purpose of this study was to correlate changes in placental stiffness, measured via ultrasound elastography, with maternal pre-pregnancy body mass index and gestational weight gain.Body Mass Index and gestation weight gain data was collected from 238 women. Elastography measurements were obtained via ultrasound at 24-, 28- and 36-weeks' gestation. An analysis using a linear mixed regression model assessed for the statistical significance of pre-pregnancy BMI, pregnancy weight gain and placental SWV (Shear Wave Velocity).Pre-pregnancy weight status has a significant impact on placental tissue stiffness detectable via ultrasound elastography. Placental tissue stiffness was highest in obese women, followed by overweight women. Obese women, on average, had a MeanSWV 0.11 m/s (95% CI (0.061-0.15) m/s, p 0.001) above the healthy group throughout the 3rd trimester. Weight gain during pregnancy had a small impact on placental stiffness at the end of pregnancy. MeanSWV was 0.06 m/s (95% CI (0.03-0.10) m/s, p 0.001) higher in the excessive weight gain group.Structural changes of the placenta detected via ultrasound elastography techniques are not exclusive to placental dysfunction conditions (pre-eclampsia and growth restriction) but are also associated with maternal obesity.

Purpose: Sport-science research consistently contains repeated measures and imbalanced data sets. This study calls for further adoption of mixed models when analyzing longitudinal sport-science data sets. Mixed models were used to understand whether the level of competition affected the intensity of women’s rugby league match play. Methods: A total of 472 observations were used to compare the mean speed of female rugby league athletes recorded during club-, state-, and international-level competition. As athletes featured in all 3 levels of competition and there were multiple matches within each competition (ie, repeated measures), the authors demonstrated that mixed models are the appropriate statistical approach for these data. Results: The authors determined that if a repeated-measures analysis of variance (ANOVA) were used for the statistical analysis in the present study, at least 48.7% of the data would have been omitted to meet ANOVA assumptions. Using a mixed model, the authors determined that mean speed recorded during Trans-Tasman Test matches was 73.4 m·min−1, while the mean speeds for National Rugby League Women and State of Origin matches were 77.6 and 81.6 m·min−1, respectively. Random effects of team, athlete, and match all accounted for variations in mean speed, which otherwise could have concealed the main effects of position and level of competition had less flexible ANOVAs been used. Conclusion: These data clearly demonstrate the appropriateness of applying mixed models to typical data sets acquired in the professional sport setting. Mixed models should be more readily used within sport science, especially in observational, longitudinal data sets such as movement pattern analyses.

This exploratory study investigated whether performance in a behavioural inhibition task followed the shape proposed by the Maximum Adaptability Model during progressive exertional heat stress-that is, an initial improvement in cognitive performance is followed by a plateau, and subsequent decline once body temperature continues to rise unabated.Seventeen adult males walked on a treadmill at 4 km hWe did not find any evidence that core body temperature had an effect on congruent or incongruent inverse efficiency scores, and no evidence that the relationship between these variables followed the shaped described by the Maximum Adaptability Model. There was, however, evidence that higher pre-exercise serum osmolality values were associated with slower congruent (β = 9.19) and incongruent (β = 8.67) inverse efficiency scores. The posterior probability that these effects were greater than zero was 0.971 and 0.952, respectively.In young, fit men, performance in the behavioural inhibition task was unaffected by increases in body temperature up to 39 °C and did not follow the shape proposed by the Maximum Adaptability Model. A secondary finding of the study was that pre-exercise hydration status affected performance in the inhibition task. Future studies are needed to confirm this result.

This commentary discusses data and code sharing in sport and exercise science research.