Bayesian Hierarchical Modeling Approach Research Articles

Parallel Markov chain Monte Carlo for Bayesian hierarchical models with big data, in two stages

ABSTRACTDue to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for Bayesian nested hierarchical models, typically only a few parameters are common for the full data set, with most parameters being group specific. Thus, parallel Bayesian MCMC methods that take into account the structure of the model and split the full data set by groups rather than by observations are a more natural approach for analysis. Here, we adapt and extend a recently introduced two-stage Bayesian hierarchical modeling approach, and we partition complete data sets by groups. In stage 1, the group-specific parameters are estimated independently in parallel. The stage 1 posteriors are used as proposal distributions in stage 2, where the target distribution is the full model. Using three-level and four-level models, we show in both simulation and real data studies that results of our method agree closely with the full data analysis, with greatly increased MCMC efficiency and greatly reduced computation times. The advantages of our method versus existing parallel MCMC computing methods are also described.

Borrowing From Historical Control Data in Cancer Drug Development: A Cautionary Tale and Practical Guidelines

Some clinical trialists, especially those working in rare or pediatric disease, have suggested borrowing information from similar but already-completed clinical trials. This article begins with a case study in which relying solely on historical control information would have erroneously resulted in concluding a significant treatment effect. We then attempt to catalog situations where borrowing historical information may or may not be advisable using a series of carefully designed simulation studies. We use an MCMC-driven Bayesian hierarchical parametric survival modeling approach to analyze data from a sponsor’s colorectal cancer study. We also apply these same models to simulated data comparing the effective historical sample size, bias, 95% credible interval widths, and empirical coverage probabilities across the simulated cases. We find that even after accounting for variations in study design, baseline characteristics, and standard-of-care improvement, our approach consistently identifies Bayesianly significant differences between the historical and concurrent controls under a range of priors on the degree of historical data borrowing. Our simulation studies are far from exhaustive, but inform the design of future trials. When the historical and current controls are dissimilar, Bayesian methods can still moderate borrowing to a more appropriate level by adjusting for important covariates and adopting sensible priors.

Individual Differences in Cortical Processing Speed Predict Cognitive Abilities: a Model-Based Cognitive Neuroscience Account

Previous research has shown that individuals with greater cognitive abilities display a greater speed of higher-order cognitive processing. These results suggest that speeded neural information processing may facilitate evidence accumulation during decision making and memory updating and thus yield advantages in general cognitive abilities. We used a hierarchical Bayesian cognitive modeling approach to test the hypothesis that individual differences in the velocity of evidence accumulation mediate the relationship between neural processing speed and cognitive abilities. We found that a higher neural speed predicted both the velocity of evidence accumulation across behavioral tasks and cognitive ability test scores. However, only a negligible part of the association between neural processing speed and cognitive abilities was mediated by individual differences in the velocity of evidence accumulation. The model demonstrated impressive forecasting abilities by predicting 36% of individual variation in cognitive ability test scores in an entirely new sample solely based on their electrophysiological and behavioral data. Our results suggest that individual differences in neural processing speed might affect a plethora of higher-order cognitive processes, that only in concert explain the large association between neural processing speed and cognitive abilities, instead of the effect being entirely explained by differences in evidence accumulation speeds.

A Hierarchical Bayesian Modeling Approach for the Habitat Distribution of Smooth Dogfish by Sex and Season in Inshore Coastal Waters of the U.S. Northwest Atlantic

AbstractThe Smooth Dogfish Mustelus canis is an abundant, small coastal shark occurring along the U.S. Atlantic coast. Despite being targeted by a directed fishery and having recently undergone a stock assessment that found the population neither overfished nor experiencing overfishing, little is known about the spatial and temporal distribution of this species. Here, we used catch data from the spring and fall Northeast Area Monitoring and Assessment Program's fishery‐independent trawl surveys conducted between 2007 and 2016 and various environmental factors to perform hierarchical Bayesian modeling as a first attempt to spatially predict adult Smooth Dogfish CPUE in U.S. northwest Atlantic Ocean waters by sex and season. Relevant environmental variables differed between both sexes and seasons. Male and female CPUEs were similarly associated with lower salinity and shallower depth in the spring. During fall, male CPUE was associated with sea surface temperature and bottom rugosity, and female CPUE was associated with chlorophyll‐a concentration, bottom rugosity, and year. Habitat modeling results predicted that areas of high male and female CPUEs would overlap during spring but strongly diverge during fall, when greater predicted CPUEs for males were distributed considerably farther north. These results suggest sexual segregation among Smooth Dogfish during fall, with the springtime overlap in distribution coinciding with the pupping and mating season in this population. This difference in distribution during fall may allow for a male‐only directed fishery for Smooth Dogfish in the northern extent of the species’ range in waters near southern New England and Georges Bank.

Investigating varying effect of road-level factors on crash frequency across regions: A Bayesian hierarchical random parameter modeling approach

This study aims to quantitatively examine the variations in effect of road-level factors on crash frequency across different regions. Treating the hierarchical structure existing in the crash data that road entity nested within the geographic region, a hierarchical random parameter model, which allows the coefficients of road-level variables to vary with regions, is proposed. A Poisson lognormal model and a hierarchical random intercept model are also built for the purpose of comparison. A specific roadway facility type, urban two-lane two-way roadway segments in Florida, with crash and road level data including traffic volume, road length, surface condition, and access density for three-year period are used for a case study. The result shows that, in the hierarchical-random parameter model, the local regression coefficients and marginal effects of the road level factors vary over a wide range in the selected counties, which clearly illustrates the non-stationary in the relationships between road level factors and crash frequency across the counties. In regard to the model comparison, the hierarchical random parameter model outperforms the Poisson lognormal model and the hierarchical random intercept model in term of deviance information criterion (DIC). This further confirms the necessity of the use of hierarchical random parameter model in analyzing the crash frequency for road entities in different regions. This study provides a potential in guidance of model construction that considers regional variations (heterogeneities) in safety effects of road-level factors.

Topography and neighborhood crowding can interact to shape species growth and distribution in a diverse Amazonian forest.

Abiotic constraints and biotic interactions act simultaneously to shape communities. However, these community assembly mechanisms are often studied independently, which can limit understanding of how they interact to affect species dynamics and distributions. We develop a hierarchical Bayesian neighborhood modeling approach to quantify the simultaneous effects of topography and crowding by neighbors on the growth of 124,704 individual stems ≥1cm DBH for 1,047 tropical tree species in a 25-ha mapped rainforest plot in Amazonian Ecuador. We build multi-level regression models to evaluate how four key functional traits (specific leaf area, maximum tree size, wood specific gravity and seed mass) mediate tree growth response to topography and neighborhood crowding. Tree growth is faster in valleys than on ridges and is reduced by neighborhood crowding. Topography and crowding interact to influence tree growth in ~10% of the species. Specific leaf area, maximum tree size and seed mass are associated with growth responses to topography, but not with responses to neighborhood crowding or with the interaction between topography and crowding. In sum, our study reveals that topography and neighborhood crowding each influence tree growth in tropical forests, but act largely independently in shaping species distributions. While traits were associated with species response to topography, their role in species response to neighborhood crowding was less clear, which suggests that trait effects on neighborhood dynamics may depend on the direction (negative/positive) and degree of symmetry of biotic interactions. Our study emphasizes the importance of simultaneously assessing the individual and interactive role of multiple mechanisms in shaping species dynamics in high diversity tropical systems.

Integrative Bayesian analysis of brain functional networks incorporating anatomical knowledge

Recently, there has been increased interest in fusing multimodal imaging to better understand brain organization by integrating information on both brain structure and function. In particular, incorporating anatomical knowledge leads to desirable outcomes such as increased accuracy in brain network estimates and greater reproducibility of topological features across scanning sessions. Despite the clear advantages, major challenges persist in integrative analyses including an incomplete understanding of the structure-function relationship and inaccuracies in mapping anatomical structures due to inherent deficiencies in existing imaging technology. This calls for the development of advanced network modeling tools that appropriately incorporate anatomical structure in constructing brain functional networks. We propose a hierarchical Bayesian Gaussian graphical modeling approach which models the brain functional networks via sparse precision matrices whose degree of edge specific shrinkage is a random variable that is modeled using both anatomical structure and an independent baseline component. The proposed approach adaptively shrinks functional connections and flexibly identifies functional connections supported by structural connectivity knowledge. This enables robust brain network estimation even in the presence of misspecified anatomical knowledge, while accommodating heterogeneity in the structure-function relationship. We implement the approach via an efficient optimization algorithm which yields maximum a posteriori estimates. Extensive numerical studies involving multiple functional network structures reveal the clear advantages of the proposed approach over competing methods in accurately estimating brain functional connectivity, even when the anatomical knowledge is misspecified up to a certain degree. An application of the approach to data from the Philadelphia Neurodevelopmental Cohort (PNC) study reveals gender based connectivity differences across multiple age groups, and higher reproducibility in the estimation of network metrics compared to alternative methods.

Drivers of the summer-distribution of Northeast Atlantic mackerel (Scomber scombrus) in the Nordic Seas from 2011 to 2017; a Bayesian hierarchical modelling approach

Drivers of the summer-distribution of Northeast Atlantic mackerel (<i>Scomber scombrus</i>) in the Nordic Seas from 2011 to 2017; a Bayesian hierarchical modelling approach

Hierarchical Bayesian estimation of unobserved salmon passage through weirs

We developed a hierarchical Bayesian model (HBM) to estimate missing counts of Chinook salmon (Oncorhynchus tshawytscha (Walbaum in Artedi, 1792)) at a weir on the Kogrukluk River, Alaska, between 1976 and 2015. The model assumed that fish passage during a breach of the weir was typical of passage during normal operations. Counts of fish passing the weir were missing for some days during the runs, or only partial counts for a given 24-hour period were available. The HBM approach provided more defensible estimates of missing data and total escapement than ad hoc or year-by-year model estimates, because estimates of passage for a given year were informed not only by counts for the current year, but also by counts for all previous years. The results of the HBM yielded less variable estimates of escapement than did ad hoc or year-by-year model estimates. The HBM represents a standardized approach to estimate missing counts and total escapement and eliminates the need for ad hoc estimates of missing counts. The model also provides managers with a measure of uncertainty around estimates of escapement and around estimates of hyper-parameters to define run curves in subsequent years with incomplete fish counts.

Visual interpretation and time series modeling of Landsat imagery highlight drought's role in forest canopy declines

AbstractRemote sensing studies indicate that slow and subtle degradation of forest canopies, or forest canopy declines, has increased in extent during recent decades, possibly due to hotter and drier droughts. However, it is difficult to collect consistent, high‐quality time series of forest canopy decline occurrence observations needed for examining multi‐year drought contributions to forest canopy decline at an annual scale. In this research, we leveraged a tool for visual interpretation of annual Landsat satellite imagery (TimeSync) and a hierarchical Bayesian time series modeling approach (stochastic antecedent modeling, SAM) in five forest type groups located in the western United States to assess (1) what seasonal and interannual patterns in vapor pressure deficit (VPD) and precipitation preceded forest canopy decline events, (2) how drought effects on forest canopy decline events differed by forest type group, and (3) whether or not drought effects on forest canopy decline events were uniform within forest type groups. We examined observations of forest canopy decline over three decades (1985–2013) at 126 plots where we collected annual TimeSync observations. Stochastic antecedent modeling indicated that January–March VPD and July–September precipitation anomalies for the current year and 1–3 yr in the past contributed to defining drought conditions in relation to forest canopy decline dynamics. The probability of forest canopy decline decreased with summer precipitation for all forest type groups and increased with winter VPD for the warmest and the coldest forest type groups. However, the magnitude and direction of forest canopy decline sensitivity to drought varied substantially within forest type groups. The ubiquitous, but not uniform, effects of drought on forest canopy decline dynamics implied that local biotic (e.g., forest structure and composition, tree genetics) and abiotic (e.g., topography and soils) factors act to mediate effects of drought on forest change. The integration of the TimeSync satellite image interpretation tool with SAM provides a promising approach to link ecological understanding of tree drought responses to forest and landscape responses at regional and continental scales.

Cancer driver mutation prediction through Bayesian integration of multi-omic data.

Identification of cancer driver mutations is critical for advancing cancer research and personalized medicine. Due to inter-tumor genetic heterogeneity, many driver mutations occur at low frequencies, which make it challenging to distinguish them from passenger mutations. Here, we show that a novel Bayesian hierarchical modeling approach, named rDriver can achieve enhanced prediction accuracy by identifying mutations that not only have high functional impact scores but also are associated with systemic variation in gene expression levels. In examining 3,080 tumor samples from 8 cancer types in The Cancer Genome Atlas, rDriver predicted 1,389 driver mutations. Compared with existing tools, rDriver identified more low frequency mutations associated with lineage specific functional properties, timing of occurrence and patient survival. Evaluation of rDriver predictions using engineered cell-line models resulted in a positive predictive value of 0.94 in PIK3CA genes. Our study highlights the importance of integrating multi-omic data in predicting cancer driver mutations and provides a statistically rigorous solution for cancer target discovery and development.

A Bayesian basket trial design using a calibrated Bayesian hierarchical model

The basket trial evaluates the treatment effect of a targeted therapy in patients with the same genetic or molecular aberration, regardless of their cancer types. Bayesian hierarchical modeling has been proposed to adaptively borrow information across cancer types to improve the statistical power of basket trials. Although conceptually attractive, research has shown that Bayesian hierarchical models cannot appropriately determine the degree of information borrowing and may lead to substantially inflated type I error rates. We propose a novel calibrated Bayesian hierarchical model approach to evaluate the treatment effect in basket trials. In our approach, the shrinkage parameter that controls information borrowing is not regarded as an unknown parameter. Instead, it is defined as a function of a similarity measure of the treatment effect across tumor subgroups. The key is that the function is calibrated using simulation such that information is strongly borrowed across subgroups if their treatment effects are similar and barely borrowed if the treatment effects are heterogeneous. The simulation study shows that our method has substantially better controlled type I error rates than the Bayesian hierarchical model. In some scenarios, for example, when the true response rate is between the null and alternative, the type I error rate of the proposed method can be inflated from 10% up to 20%, but is still better than that of the Bayesian hierarchical model. The proposed design assumes a binary endpoint. Extension of the proposed design to ordinal and time-to-event endpoints is worthy of further investigation. The calibrated Bayesian hierarchical model provides a practical approach to design basket trials with more flexibility and better controlled type I error rates than the Bayesian hierarchical model. The software for implementing the proposed design is available at http://odin.mdacc.tmc.edu/~yyuan/index_code.html.

Climate warming drives invasion history of Ambrosia artemisiifolia in central Europe

It is thought that future climate change is likely to foster biological invasions, but effects of climate warming on invasions in recent decades are little explored. In this paper, we analyse the history of the spread of Ambrosia artemisiifolia (common ragweed) in central Europe in order to determine the effects of climate warming. In addition, we infer the likely history of this species’ spread and current distribution from incomplete documentation. The area studied in central Europe includes Austria, the Czech Republic, Germany, Hungary, Liechtenstein, Slovakia, Slovenia and Switzerland. These countries were represented by a lattice of grid cells of size 5' × 3' (~ 6 × 6 km2), and we modelled this species’ increase in range in this grid from 1900 to 2010 at an annual resolution. The spread was modelled to be driven by the spatio-temporal variation in environmental suitability of grid cells as determined by climatic conditions and land use, propagule production and dispersal from invaded cells, and ‘background’ introductions from unknown sources. A hierarchical Bayesian modelling approach accounted for lagged and incomplete records of occurrence and spatio-temporal variation in sampling intensity. We fitted models with different representations of climate variation over time, and further contrasted the hierarchical model to a simplified model, which assumed that records accurately reflected the species’ actual spread. Climatic conditions were the most important determinants of environmental suitability for invasion, and suitability also increased with increase in the proportion of urban area and length of railways in grid cells. Temperature was, on average, 2.7 °C higher in the environmentally more suitable cells than in the less suitable cells. The pattern in the spread was determined by local range expansion frommultiple, spatially scattered points of introduction. Assuming a linear trend in climate warming over the modelling period provided a better model fit than using annual weather conditions or the long-term average of the climate. The model estimated that by 2010 only about 60% of the actually invaded grid cells were recorded, and records lagged behind actual colonizations by years up to decades. Inferences of the hierarchical and simplified models differed quantitatively. We conclude that by using our modelling framework it is possible to separate spatial effects of climate on the spread of non-native species from temporal effects, and that climate warming has already promoted the spread of Ambrosia artemisiifolia in central Europe. The recorded distribution reflects only a part of this species’ actual distribution. Properly accounting for incomplete records hence improves inferences about the dynamics of spread.

Prescribed fire and natural recovery produce similar long-term patterns of change in forest structure in the Lake Tahoe basin, California

Abstract In the context of concerns about degrading forest health, increasing fire activity, and practical restoration alternatives, we analyzed 20 years of data on the response of mixed conifer forest stands in the Sierra Nevada, California to two distinctly different management approaches. Specifically, we used a Bayesian hierarchical modeling approach to evaluate the direction and magnitude of changes in forest structure and fuel variables in areas treated with prescribed fire as well as untreated forest stands in the Lake Tahoe basin. Counter to many regional studies, our results indicated that treated and long-unaltered, untreated areas may be moving in a similar direction. Treated and untreated areas experienced declines in tree density, increases in the size of the average individual, and losses of surface fuels in most size classes. The number of large trees increased in untreated areas, but decreased in treated areas. Our results suggested that untreated areas may be naturally recovering from the large disturbances associated with resource extraction and development in the late 1800s, and that natural recovery processes, including self thinning, are taking hold. Given the high cost and broad extent of treatment required to restore forest health, management approaches that promote naturally recovering landscapes may complement ongoing and planned fuel reduction treatments. Deliberately managing for natural processes to proceed unimpeded may also be important for maintaining or increasing forest heterogeneity, resilience, and biodiversity.

Bayesian analysis improves experimental studies about temporal patterning of aggression in fish

This study aims to describe a Bayesian Hierarchical Linear Model (HLM) approach for longitudinal designs in fish’s experimental aggressive behavior studies as an alternative to classical methods In particular, we discuss the advantages of Bayesian analysis in dealing with combined variables, non-statistically significant results and required sample size using an experiment of angelfish (Pterophyllum scalare) species as case study. Groups of 3 individuals were subjected to daily observations recorded for 10min during 5days. The frequencies of attacks, displays and the total attacks (attacks+displays) of each record were modeled using Monte Carlo Markov chains. In addition, a Bayesian HLM was performed for measuring the rate of increase/decrease of the aggressive behavior during the time and to assess the probability of difference among days. Results highlighted that using the combined variable of total attacks could lead to biased conclusions as displays and attacks showed an opposite pattern in the experiment. Moreover, depending of the study, this difference in pattern can happen more clearly or more subtly. Subtle changes cannot be detected when p-values are implemented. On the contrary, Bayesian methods provide a clear description of the changes even when patterns are subtle. Additionally, results showed that the number of replicates (15 or 11) invariant the study conclusions as well that using a small sample size could be more evident within the overlapping days, that includes the social rank stability. Therefore, Bayesian analysis seems to be a richer and an adequate statistical approach for fish’s aggressive behavior longitudinal designs.

Occupant-level injury severity analyses for taxis in Hong Kong: A Bayesian space-time logistic model

This study aimed to identify the factors affecting the crash-related severity level of injuries in taxis and quantify the associations between these factors and taxi occupant injury severity. Casualties resulting from taxi crashes from 2004 to 2013 in Hong Kong were divided into four categories: taxi drivers, taxi passengers, private car drivers and private car passengers. To avoid any biased interpretation caused by unobserved spatial and temporal effects, a Bayesian hierarchical logistic modeling approach with conditional autoregressive priors was applied, and four different model forms were tested. For taxi drivers and passengers, the model with space-time interaction was proven to most properly address the unobserved heterogeneity effects. The results indicated that time of week, number of vehicles involved, weather, point of impact and driver age were closely associated with taxi drivers’ injury severity level in a crash. For taxi passengers’ injury severity an additional factor, taxi service area, was influential. To investigate the differences between taxis and other traffic, similar models were established for private car drivers and passengers. The results revealed that although location in the network and driver gender significantly influenced private car drivers’ injury severity, they did not influence taxi drivers’ injury severity. Compared with taxi passengers, the injury severity of private car passengers was more sensitive to average speed and whether seat belts were worn. Older drivers, urban taxis and fatigued driving were identified as factors that increased taxi occupant injury severity in Hong Kong.

Backpack electrofishing effort and imperfect detection: Influence on riverine fish inventories and monitoring

Summary An increased electrofishing sampling effort will increase detection probabilities of riverine fishes. In this study, a repeat-sampling approach was used in small to medium-sized Ontario (Canada) rivers to estimate: (i) species-specific detection probabilities of freshwater fishes, (ii) the number of sampling events required to confidently detect species, and (iii) the power of timed-search surveys to detect future distribution (or occupancy) declines. Wadeable habitats at 36 sites were sampled with a backpack electrofisher on four separate dates during the summer low-flow period in 2013 and 2014. Forty-two species were collected, including three species of conservation concern (American eel Anguilla rostrata Lacepede, 1802, channel darter Percina copelandi Jordan, 1877, northern sunfish Lepomis peltastes Cope, 1870), and two recreationally important species (largemouth bass Micropterus salmoides Lacepede, 1802 and smallmouth bass Micropterus dolomieu Lacepede, 1802). A hierarchical Bayesian modelling approach was used to estimate detection probabilities and site occupancy for 18 species at four levels of effort: 250, 500, 750 and 1,000 s. In all cases, species detection was imperfect. Search effort had a positive effect on estimates of detection probability and site occupancy and the power to detect declines in future distribution. Detection probabilities ranged from 0.11 to 0.66 with an effort of 250 s, and 0.27 to 0.92 with an effort of 1,000 s. For 13 species, detection and power to detect changes in distribution were significantly improved by increasing sampling effort from 250 to 750 s or 1,000 s. For the channel darter and northern sunfish, three replicate sampling visits (of 750 or 1,000 s duration) are recommended for confident detection.

LATENT CLASS MODELING USING MATRIX COVARIATES WITH APPLICATION TO IDENTIFYING EARLY PLACEBO RESPONDERS BASED ON EEG SIGNALS.

Latent class models are widely used to identify unobserved subgroups (i.e., latent classes) based upon one or more manifest variables. The probability of belonging to each subgroup is typically modeled as a function of a set of measured covariates. In this paper, we extend existing latent class models to incorporate matrix covariates. This research is motivated by a randomized placebo-controlled depression clinical trial. One study goal is to identify a subgroup of subjects who experience symptoms improvement early on during antidepressant treatment, which is considered to be an indication of a placebo rather than a true pharmacological response. We want to relate the likelihood of belonging to this subgroup of early responders to baseline electroencephalography (EEG) measurement that takes the form of a matrix. The proposed method is built upon a low rank Candecomp/Parafac (CP) decomposition of the target coefficient matrix through low-dimensional latent variables, which effectively reduces the model dimensionality. We adopt a Bayesian hierarchical modeling approach to estimate the latent variables, which allows a flexible way to incorporate prior knowledge about covariate effect heterogeneity and offers a data-driven method of regularization. Simulation studies suggest that the proposed method is robust against potentially misspecified rank in the CP decomposition. With the motivating example we show how the proposed method can be applied to extract valuable information from baseline EEG measurements that explains the likelihood of belonging to the early responder subgroup, helping to identify placebo responders and suggesting new targets for the study of placebo response.

Increasing the efficiency of oncology basket trials using a Bayesian approach

With the rapid growth of targeted and immune-oncology therapies, novel statistical design approaches are needed to increase the flexibility and efficiency of early phase oncology trials.Basket trials enroll patients with defined biological deficiencies, but with multiple histologic tumor types (or indications), to discover in which indications the drug is active. In such designs different indications are typically analyzed independently. This, however, ignores potential biological similarities among the indications.Our research provides a statistical methodology to enhance such basket trials by assessing the homogeneity of the response rates among indications at an interim analysis, and applying a Bayesian hierarchical modeling approach in the second stage if the efficacy is deemed reasonably homogenous across indications. This increases the power of the study by allowing indications with similar response rates to borrow information from each other. Via simulations, we quantify the efficiency gain of our proposed approach relative to the conventional parallel approach. The operating characteristics of our method depend on the similarity of the response rates between the different indications. If the response rates are comparable in most or all indications after treatment with the investigational drug, a substantial increase in efficiency as compared to the conventional approach can be obtained as fewer patients are required or a higher power is attained. We also demonstrate that efficacy again decreases if the response rates vary considerably among tumor types but it is still better than the conventional approach.

Bias away from the null due to miscounted outcomes? A case study on the TORCH trial

Count outcomes occur in virtually all disciplines, such as medicine, epidemiology or biology, but they often contain error. Recently, it has been shown that self-reported numbers of exacerbations of Chronic Obstructive Pulmonary Disease patients can be considerably miscounted. Motivated by this result, we reanalysed data from the Towards a Revolution in Chronic Obstructive Pulmonary Disease Health trial, a large randomized controlled trial with the self-reported number of exacerbations of Chronic Obstructive Pulmonary Disease patients as outcome. To adjust for miscounting error in the response of Poisson and (zero-inflated) negative binomial models, we introduce novel, general methodology. The key idea is to formulate a zero-inflated negative binomial model to capture the error mechanism. This parametric approach automatically circumvents drawbacks of previously suggested methodology that treats miscounted outcomes in the misclassification framework. Prior information for the response error model parameters was elicited from validation data of an external study and adaptively weighted to account for potential prior-data conflict. The results of the Bayesian hierarchical modelling approach indicated that the treatment effect has been overestimated in the original study. However, closer inspection revealed that this unexpected result was an artefact of an unaccounted time dependency of the treatment effect.