Blouch: Bayesian Linear Ornstein-Uhlenbeck Models for Comparative Hypotheses.

Relationships among species in the tree of life can complicate comparative methods and testing adaptive hypotheses. Models based on the Ornstein-Uhlenbeck process permit hypotheses about adaptation to be tested by allowing traits to either evolve towards fixed adaptive optima (e.g., regimes or niches) or track continuously changing optima that can be influenced by other traits. These models allow estimation of the effects of both adaptation and phylogenetic inertia - resistance to adaptation due to any source - on trait evolution, an approach known as the "adaptation-inertia" framework. However, previous applications of this framework, and most approaches suggested to deal with the issue of species non-independence, are based on a maximum likelihood approach and thus it is difficult to include information based on prior biological knowledge in the analysis, which can affect resulting inferences. Here I present Blouch, (Bayesian Linear Ornstein-Uhlenbeck Models for Comparative Hypotheses), which fits allometric and adaptive models of continuous trait evolution in a Bayesian framework based on fixed or continuous predictors and incorporates measurement error. I first briefly discuss the models implemented in Blouch, and then the new applications for these models provided by a Bayesian framework. This includes the advantages of assigning biologically meaningful priors when compared to non-Bayesian approaches, allowing for varying effects (intercepts and slopes), and multilevel modeling. Validations on simulated data show good performance in recovering the true evolutionary parameters for all models. To demonstrate the workflow of Blouch on an empirical dataset, I test the hypothesis that the relatively larger antlers of larger bodied deer are the result of more intense sexual selection that comes along with their tendency to live in larger breeding groups. While results show that larger bodied deer that live in larger breeding groups have relatively larger antlers, deer living in the smallest groups appear to have a different and steeper scaling pattern of antler size to body size than other groups. These results are contrary to previous findings and may argue that a different type of sexual selection or other selective pressures govern optimum antler size in the smallest breeding groups.

A modeling framework for the analysis of the SARS-CoV2 transmission dynamics.

Despite the progress in medical data collection the actual burden of SARS-CoV-2 remains unknown due to under-ascertainment of cases. This was apparent in the acute phase of the pandemic and the use of reported deaths has been pointed out as a more reliable source of information, likely less prone to under-reporting. Since daily deaths occur from past infections weighted by their probability of death, one may infer the total number of infections accounting for their age distribution, using the data on reported deaths. We adopt this framework and assume that the dynamics generating the total number of infections can be described by a continuous time transmission model expressed through a system of nonlinear ordinary differential equations where the transmission rate is modeled as a diffusion process allowing to reveal both the effect of control strategies and the changes in individuals behavior. We develop this flexible Bayesian tool in Stan and study 3 pairs of European countries, estimating the time-varying reproduction number ( R t $$ {R}_t $$ ) as well as the true cumulative number of infected individuals. As we estimate the true number of infections we offer a more accurate estimate of R t $$ {R}_t $$ . We also provide an estimate of the daily reporting ratio and discuss the effects of changes in mobility and testing on the inferred quantities.

A comparison of computational algorithms for the Bayesian analysis of clinical trials.

BACKGROUND: Clinical trials are increasingly using Bayesian methods for their design and analysis. Inference in Bayesian trials typically uses simulation-based approaches such as Markov Chain Monte Carlo methods. Markov Chain Monte Carlo has high computational cost and can be complex to implement. The Integrated Nested Laplace Approximations algorithm provides approximate Bayesian inference without the need for computationally complex simulations, making it more efficient than Markov Chain Monte Carlo. The practical properties of Integrated Nested Laplace Approximations compared to Markov Chain Monte Carlo have not been considered for clinical trials. Using data from a published clinical trial, we aim to investigate whether Integrated Nested Laplace Approximations is a feasible and accurate alternative to Markov Chain Monte Carlo and provide practical guidance for trialists interested in Bayesian trial design. METHODS: Data from an international Bayesian multi-platform adaptive trial that compared therapeutic-dose anticoagulation with heparin to usual care in non-critically ill patients hospitalized for COVID-19 were used to fit Bayesian hierarchical generalized mixed models. Integrated Nested Laplace Approximations was compared to two Markov Chain Monte Carlo algorithms, implemented in the software JAGS and stan, using packages available in the statistical software R. Seven outcomes were analysed: organ-support free days (an ordinal outcome), five binary outcomes related to survival and length of hospital stay, and a time-to-event outcome. The posterior distributions for the treatment and sex effects and the variances for the hierarchical effects of age, site and time period were obtained. We summarized these posteriors by calculating the mean, standard deviations and the 95% equitailed credible intervals and presenting the results graphically. The computation time for each algorithm was recorded. RESULTS: The average overlap of the 95% credible interval for the treatment and sex effects estimated using Integrated Nested Laplace Approximations was 96% and 97.6% compared with stan, respectively. The graphical posterior densities for these effects overlapped for all three algorithms. The posterior mean for the variance of the hierarchical effects of age, site and time estimated using Integrated Nested Laplace Approximations are within the 95% credible interval estimated using Markov Chain Monte Carlo but the average overlap of the credible interval is lower, 77%, 85.6% and 91.3%, respectively, for Integrated Nested Laplace Approximations compared to stan. Integrated Nested Laplace Approximations and stan were easily implemented in clear, well-established packages in R, while JAGS required the direct specification of the model. Integrated Nested Laplace Approximations was between 85 and 269 times faster than stan and 26 and 1852 times faster than JAGS. CONCLUSION: Integrated Nested Laplace Approximations could reduce the computational complexity of Bayesian analysis in clinical trials as it is easy to implement in R, substantially faster than Markov Chain Monte Carlo methods implemented in JAGS and stan, and provides near identical approximations to the posterior distributions for the treatment effect. Integrated Nested Laplace Approximations was less accurate when estimating the posterior distribution for the variance of hierarchical effects, particularly for the proportional odds model, and future work should determine if the Integrated Nested Laplace Approximations algorithm can be adjusted to improve this estimation.

Is the fetus fit for labor? Introducing fast-and-frugal trees (FFTrees) to simplify triage of women for STAN monitoring: An interobserver agreement comparison with traditional classification.

INTRODUCTION: It is a shortcoming of traditional cardiotocography (CTG) classification table formats that CTG traces are frequently classified differently by different users, resulting in poor interobserver agreements. A fast-and-frugal tree (FFTree) flow chart may help provide better concordance because it is straightforward and has clearly structured binary questions with understandable "yes" or "no" responses. The initial triage to determine whether a fetus is suitable for labor when utilizing fetal ECG ST analysis (STAN) is very important, since a fetus with restricted capacity to respond to hypoxic stress may not generate STAN events and therefore may become falsely negative. This study aimed to compare physiology-focused FFTree CTG interpretation with FIGO classification for assessing the suitability for STAN monitoring. MATERIAL AND METHODS: A retrospective study of 36 CTG traces with a high proportion of adverse outcomes (17/36) selected from a European multicenter study database. Eight experienced European obstetricians evaluated the initial 40 minutes of the CTG recordings and judged whether STAN was a suitable fetal surveillance method and whether intervention was indicated. The experts rated the CTGs using the FFTree and FIGO classifications at least 6 weeks apart. Interobserver agreements were calculated using proportions of agreement and Fleiss' kappa (κ). RESULTS: The proportions of agreement for "not suitable for STAN" were for FIGO 47% (95% confidence interval [CI] 42%-52%) and for FFTree 60% (95% CI 56-64), ie a significant difference; the corresponding figures for "yes, suitable" were 74% (95% CI 71-77) and 70% (95% CI 67-74). For "intervention needed" the figures were 52% (95% CI 47-56) vs 58% (95% CI 54-62) and for "expectant management" 74% (95% CI 71-77) vs 72% (95% CI 69-75). Fleiss' κ agreement on "suitability for STAN" was 0.50 (95% CI 0.44-0.56) for the FIGO classification and 0.57 (95% CI 0.51-0.63) for the FFTree classification; the corresponding figures for "intervention or expectancy" were 0.53 (95% CI 0.47-0.59) and 0.57 (95% CI 0.51-0.63). CONCLUSIONS: The proportion of agreement among expert obstetricians using the FFTree physiological approach was significantly higher compared with the traditional FIGO classification system in rejecting cases not suitable for STAN monitoring. That might be of importance to avoid false negative STAN recordings. Other agreement figures were similar. It remains to be shown whether the FFTree simplicity will benefit less experienced users and how it will work in real-world clinical scenarios.

A Stan tutorial on Bayesian IRTree models: Conventional models and explanatory extension.

IRTree models have been receiving increasing attention. However, to date, there are limited sources that provide a systematic introduction to Bayesian modeling techniques using modern probabilistic programming frameworks for the implementation of IRTree models. To facilitate the research and application of IRTree models, this paper introduces how to perform two families of Bayesian IRTree models (i.e., response tree models and latent tree models) in Stan and how to extend them in an explanatory way. Some suggestions on executing Stan codes and checking convergence are also provided. An empirical study based on the Oxford Achieving Resilience during COVID-19 data was conducted as an example to further illustrate how to apply Bayesian IRTree models to address research questions. Finally, strengths and future directions are discussed.

Customizing Bayesian multivariate generalizability theory to mixed-format tests.

Mixed-format tests, which typically include dichotomous items and polytomously scored tasks, are employed to assess a wider range of knowledge and skills. Recent behavioral and educational studies have highlighted their practical importance and methodological developments, particularly within the context of multivariate generalizability theory. However, the diverse response types and complex designs of these tests pose significant analytical challenges when modeling data simultaneously. Current methods often struggle to yield reliable results, either due to the inappropriate treatment of different types of response data separately or the imposition of identical covariates across various response types. Moreover, there are few software packages or programs that offer customized solutions for modeling mixed-format tests, addressing these limitations. This tutorial provides a detailed example of using a Bayesian approach to model data collected from a mixed-format test, comprising multiple-choice questions and free-response tasks. The modeling was conducted using the Stan software within the R programming system, with Stan codes tailored to the structure of the test design, following the principles of multivariate generalizability theory. By further examining the effects of prior distributions in this example, this study demonstrates how the adaptability of Bayesian models to diverse test formats, coupled with their potential for nuanced analysis, can significantly advance the field of psychometric modeling.

Comparison of effect of CTG + STan with CTG alone on emergency Cesarean section rate: STan Australian Randomized controlled Trial (START).

OBJECTIVE: To investigate whether use of ST analysis of the fetal electrocardiogram (STan) as an adjunct to continuous cardiotocography (CTG) reduces the rate of emergency Cesarean section (EmCS) compared with CTG alone. METHODS: This was a randomized controlled trial of patients with a singleton fetus in cephalic presentation at ≥ 36 weeks' gestation, requiring continuous electronic fetal monitoring during labor at a tertiary maternity hospital in Adelaide, Australia, between January 2018 and July 2021. Participants were randomized to undergo CTG + STan or CTG alone. The calculated sample size was 1818 participants. The primary outcome was EmCS. Secondary outcomes included metabolic acidosis, a composite adverse perinatal outcome, and other maternal and neonatal morbidity and safety outcomes. RESULTS: The present study enrolled 970 women, of whom 967 were included in the primary analysis. EmCS occurred in 107/482 (22.2%) deliveries in the CTG + STan arm and in 107/485 (22.1%) in the CTG arm (adjusted relative risk, 1.02 (95% CI, 0.81-1.27); P = 0.89). There was no difference in the rate of adverse maternal or neonatal outcomes between arms. CONCLUSIONS: The addition of STan as an adjunct to continuous CTG did not reduce the EmCS rate. The smaller-than-anticipated sample size meant that this study was underpowered to detect absolute differences of ≤ 5% and, therefore, this negative finding could be due to a Type-2 error. © 2023 The Authors. Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of International Society of Ultrasound in Obstetrics and Gynecology.

The Seven-parameter Diffusion Model: an Implementation in Stan for Bayesian Analyses.

Diffusion models have been widely used to obtain information about cognitive processes from the analysis of responses and response-time data in two-alternative forced-choice tasks. We present an implementation of the seven-parameter diffusion model, incorporating inter-trial variabilities in drift rate, non-decision time, and relative starting point, in the probabilistic programming language Stan. Stan is a free, open-source software that gives the user much flexibility in defining model properties such as the choice of priors and the model structure in a Bayesian framework. We explain the implementation of the new function and how it is used in Stan. We then evaluate its performance in a simulation study that addresses both parameter recovery and simulation-based calibration. The recovery study shows generally good recovery of the model parameters in line with previous findings. The simulation-based calibration study validates the Bayesian algorithm as implemented in Stan.

Anthocyanin regulatory networks in Solanum tuberosum L. leaves elucidated via integrated metabolomics, transcriptomics, and StAN1 overexpression.

BACKGROUND: Anthocyanins, which account for color variation and remove reactive oxygen species, are widely synthesized in plant tissues and organs. Using targeted metabolomics and nanopore full-length transcriptomics, including differential gene expression analysis, we aimed to reveal potato leaf anthocyanin biosynthetic pathways in different colored potato varieties. RESULTS: Metabolomics analysis revealed 17 anthocyanins. Their levels varied significantly between the different colored varieties, explaining the leaf color differences. The leaves of the Purple Rose2 (PurpleR2) variety contained more petunidin 3-O-glucoside and malvidin 3-O-glucoside than the leaves of other varieties, whereas leaves of Red Rose3 (RedR3) contained more pelargonidin 3-O-glucoside than the leaves of other varieties. In total, 114 genes with significantly different expression were identified in the leaves of the three potato varieties. These included structural anthocyanin synthesis-regulating genes such as F3H, CHS, CHI, DFR, and anthocyanidin synthase and transcription factors belonging to multiple families such as C3H, MYB, ERF, NAC, bHLH, and WRKY. We selected an MYB family transcription factor to construct overexpression tobacco plants; overexpression of this factor promoted anthocyanin accumulation, turning the leaves purple and increasing their malvidin 3-o-glucoside and petunidin 3-o-glucoside content. CONCLUSIONS: This study elucidates the effects of anthocyanin-related metabolites on potato leaves and identifies anthocyanin metabolic network candidate genes.

Stan and BART for Causal Inference: Estimating Heterogeneous Treatment Effects Using the Power of Stan and the Flexibility of Machine Learning.

A wide range of machine-learning-based approaches have been developed in the past decade, increasing our ability to accurately model nonlinear and nonadditive response surfaces. This has improved performance for inferential tasks such as estimating average treatment effects in situations where standard parametric models may not fit the data well. These methods have also shown promise for the related task of identifying heterogeneous treatment effects. However, the estimation of both overall and heterogeneous treatment effects can be hampered when data are structured within groups if we fail to correctly model the dependence between observations. Most machine learning methods do not readily accommodate such structure. This paper introduces a new algorithm, stan4bart, that combines the flexibility of Bayesian Additive Regression Trees (BART) for fitting nonlinear response surfaces with the computational and statistical efficiencies of using Stan for the parametric components of the model. We demonstrate how stan4bart can be used to estimate average, subgroup, and individual-level treatment effects with stronger performance than other flexible approaches that ignore the multilevel structure of the data as well as multilevel approaches that have strict parametric forms.

Flowering time and the identification of floral marker genes in Solanum tuberosum ssp. andigena.

Solanaceae is a family of flowering plants that includes agricultural species such as tomato (Solanum lycopersicum), eggplant (S. melongena), pepper (Capsicum annuum), and potato (S. tuberosum). The transition from the vegetative to reproductive stage has been extensively investigated in tomato as it affects fruit yield. While potato has mainly been studied with regards to the formation of storage organs, control of flowering time is a subject of increasing interest as development of true seeds is becoming more important for future breeding strategies. Here, we describe a robust growth regime for synchronized development of S. tuberosum ssp. andigena. Using SEM to analyse the developmental stages of the shoot apical meristem (SAM) throughout the floral transition, we show that andigena is a facultative long-day plant with respect to flowering. In addition, we identify the flower meristem identity gene MACROCALYX (StMC) as a marker to distinguish between the vegetative and reproductive stages. We show that the expression of WUSCHEL HOMEOBOX 9 (StWOX9) and ANANTHA (StAN) are specific to the inflorescence meristem and flower meristems in the cyme, respectively. The expression patterns of homologs of Arabidopsis flowering-time regulators were studied, and indicated that SUPPRESSOR OF OVEREXPRESSION OF CONSTANS1 (StSOC1) and StFD might regulate flowering similar to other plant species.

A temporally stratified extension of space-for-time Cormack-Jolly-Seber for migratory animals.

Understanding drivers of temporal variation in demographic parameters is a central goal of mark-recapture analysis. To estimate the survival of migrating animal populations in migration corridors, space-for-time mark-recapture models employ discrete sampling locations in space to monitor marked populations as they move past monitoring sites, rather than the standard practice of using fixed sampling points in time. Because these models focus on estimating survival over discrete spatial segments, model parameters are implicitly integrated over the temporal dimension. Furthermore, modeling the effect of time-varying covariates on model parameters is complicated by unknown passage times for individuals that are not detected at monitoring sites. To overcome these limitations, we extended the Cormack-Jolly-Seber (CJS) framework to estimate temporally stratified survival and capture probabilities by including a discretized arrival time process in a Bayesian framework. We allow for flexibility in the model form by including temporally stratified covariates and hierarchical structures. In addition, we provide tools for assessing model fit and comparing among alternative structural models for the parameters. We demonstrate our framework by fitting three competing models to estimate daily survival, capture, and arrival probabilities at four hydroelectric dams for over 200 000 individually tagged migratory juvenile salmon released into the Snake River, USA.

A Bayesian time-to-event pharmacokinetic model for phase I dose-escalation trials with multiple schedules.

Phase I dose-escalation trials must be guided by a safety model in order to avoid exposing patients to unacceptably high risk of toxicities. Traditionally, these trials are based on one type of schedule. In more recent practice, however, there is often a need to consider more than one schedule, which means that in addition to the dose itself, the schedule needs to be varied in the trial. Hence, the aim is finding an acceptable dose-schedule combination. However, most established methods for dose-escalation trials are designed to escalate the dose only and ad hoc choices must be made to adapt these to the more complicated setting of finding an acceptable dose-schedule combination. In this article, we introduce a Bayesian time-to-event model which takes explicitly the dose amount and schedule into account through the use of pharmacokinetic principles. The model uses a time-varying exposure measure to account for the risk of a dose-limiting toxicity over time. The dose-schedule decisions are informed by an escalation with overdose control criterion. The model is formulated using interpretable parameters which facilitates the specification of priors. In a simulation study, we compared the proposed method with an existing method. The simulation study demonstrates that the proposed method yields similar or better results compared with an existing method in terms of recommending acceptable dose-schedule combinations, yet reduces the number of patients enrolled in most of scenarios. The R and Stan code to implement the proposed method is publicly available from Github ( https://github.com/gunhanb/TITEPK_code).

idem: An R Package for Inferences in Clinical Trials with Death and Missingness.

In randomized controlled trials of seriously ill patients, death is common and often defined as the primary endpoint. Increasingly, non-mortality outcomes such as functional outcomes are co-primary or secondary endpoints. Functional outcomes are not defined for patients who die, referred to as "truncation due to death", and among survivors, functional outcomes are often unobserved due to missed clinic visits or loss to follow-up. It is well known that if the functional outcomes "truncated due to death" or missing are handled inappropriately, treatment effect estimation can be biased. In this paper, we describe the package idem that implements a procedure for comparing treatments that is based on a composite endpoint of mortality and the functional outcome among survivors. Among survivors, the procedure incorporates a missing data imputation procedure with a sensitivity analysis strategy. A web-based graphical user interface is provided in the idem package to facilitate users conducting the proposed analysis in an interactive and user-friendly manner. We demonstrate idem using data from a recent trial of sedation interruption among mechanically ventilated patients.

A Two-Stage Approach for Bayesian Joint Models of Longitudinal and Survival Data: Correcting Bias with Informative Prior.

Joint models of longitudinal and survival outcomes have gained much popularity in recent years, both in applications and in methodological development. This type of modelling is usually characterised by two submodels, one longitudinal (e.g., mixed-effects model) and one survival (e.g., Cox model), which are connected by some common term. Naturally, sharing information makes the inferential process highly time-consuming. In particular, the Bayesian framework requires even more time for Markov chains to reach stationarity. Hence, in order to reduce the modelling complexity while maintaining the accuracy of the estimates, we propose a two-stage strategy that first fits the longitudinal submodel and then plug the shared information into the survival submodel. Unlike a standard two-stage approach, we apply a correction by incorporating an individual and multiplicative fixed-effect with informative prior into the survival submodel. Based on simulation studies and sensitivity analyses, we empirically compare our proposal with joint specification and standard two-stage approaches. The results show that our methodology is very promising, since it reduces the estimation bias compared to the other two-stage method and requires less processing time than the joint specification approach.

Black swans in space: modeling spatiotemporal processes with extremes.

In ecological systems, extremes can happen in time, such as population crashes, or in space, such as rapid range contractions. However, current methods for joint inference about temporal and spatial dynamics (e.g., spatiotemporal modeling with Gaussian random fields) may perform poorly when underlying processes include extreme events. Here we introduce a model that allows for extremes to occur simultaneously in time and space. Our model is a Bayesian predictive-process GLMM (generalized linear mixed-effects model) that uses a multivariate-t distribution to describe spatial random effects. The approach is easily implemented with our flexible R package glmmfields. First, using simulated data, we demonstrate the ability to recapture spatiotemporal extremes, and explore the consequences of fitting models that ignore such extremes. Second, we predict tree mortality from mountain pine beetle (Dendroctonus ponderosae) outbreaks in the U.S. Pacific Northwest over the last 16 yr. We show that our approach provides more accurate and precise predictions compared to traditional spatiotemporal models when extremes are present. Our R package makes these models accessible to a wide range of ecologists and scientists in other disciplines interested in fitting spatiotemporal GLMMs, with and without extremes.

Population pharmacokinetic reanalysis of a Diazepam PBPK model: a comparison of Stan and GNU MCSim.

The aim of this study is to benchmark two Bayesian software tools, namely Stan and GNU MCSim, that use different Markov chain Monte Carlo (MCMC) methods for the estimation of physiologically based pharmacokinetic (PBPK) model parameters. The software tools were applied and compared on the problem of updating the parameters of a Diazepam PBPK model, using time-concentration human data. Both tools produced very good fits at the individual and population levels, despite the fact that GNU MCSim is not able to consider multivariate distributions. Stan outperformed GNU MCSim in sampling efficiency, due to its almost uncorrelated sampling. However, GNU MCSim exhibited much faster convergence and performed better in terms of effective samples produced per unit of time.

Development of a nonlinear hierarchical model to describe the disposition of deuterium in mother-infant pairs to assess exclusive breastfeeding practice.

The World Health Organization recommends exclusive breastfeeding (EBF) for the first 6 months after birth. The deuterium oxide dose-to-the-mother (DTM) technique is used to distinguish EBF based on a cut-off (< 25 g/day) of water intake from sources other than breastmilk. This value is based on a theoretical threshold and has not been verified in field studies. The aim of this study was to estimate the water intake cut-off value that can be used to define EBF practice. One hundred and twenty-one healthy infants, aged 2.5-5.5 months who were deemed to be EBF were recruited. After administration of deuterium to the mothers, saliva was sampled from mother and infant pairs over a 14-day period. Validation of infant feeding practices was conducted via home observation over six non-consecutive days with caregiver recall. A fully Bayesian framework using a gradient-based Markov chain Monte Carlo approach implemented in Stan was used to estimate the cut-off of non-milk water intake of EBF infants. From the original data set, 113 infants were determined to be EBF and provided 1500 paired mother-infant observations. The deuterium saliva concentrations were best described by two linked 1-compartment models (mother and infant), with body weight as a covariate on the mother's volume of distribution and infant's body weight on infant's water clearance rate. The cut-off value was based on the 90th percentile of the posterior distribution of non-milk water intake and was 86.6 g/day. This cut-off value can be used in future field studies in other geographic regions to determine exclusivity of breast feeding practices in order to determine their potential public health needs.

Using Hamiltonian Monte Carlo to estimate the log-linear cognitive diagnosis model via Stan.

The Bayesian literature has shown that the Hamiltonian Monte Carlo (HMC) algorithm is powerful and efficient for statistical model estimation, especially for complicated models. Stan, a software program built upon HMC, has been introduced as a means of psychometric modeling estimation. However, there are no systemic guidelines for implementing Stan with the log-linear cognitive diagnosis model (LCDM), which is the saturated version of many cognitive diagnostic model (CDM) variants. This article bridges the gap between Stan application and Bayesian LCDM estimation: Both the modeling procedures and Stan code are demonstrated in detail, such that this strategy can be extended to other CDMs straightforwardly.

Bayesian modelling of lung function data from multiple-breath washout tests.

Paediatric respiratory researchers have widely adopted the multiple-breath washout (MBW) test because it allows assessment of lung function in unsedated infants and is well suited to longitudinal studies of lung development and disease. However, a substantial proportion of MBW tests in infants fail current acceptability criteria. We hypothesised that a model-based approach to analysing the data, in place of traditional simple empirical summaries, would enable more efficient use of these tests. We therefore developed a novel statistical model for infant MBW data and applied it to 1197 tests from 432 individuals from a large birth cohort study. We focus on Bayesian estimation of the lung clearance index, the most commonly used summary of lung function from MBW tests. Our results show that the model provides an excellent fit to the data and shed further light on statistical properties of the standard empirical approach. Furthermore, the modelling approach enables the lung clearance index to be estimated by using tests with different degrees of completeness, something not possible with the standard approach. Our model therefore allows previously unused data to be used rather than discarded, as well as routine use of shorter tests without significant loss of precision. Beyond our specific application, our work illustrates a number of important aspects of Bayesian modelling in practice, such as the importance of hierarchical specifications to account for repeated measurements and the value of model checking via posterior predictive distributions.