Zero-inflated multiscale models for aggregated small area health data.

It is our primary focus to study the spatial distribution of disease incidence at different geographical levels. Often, spatial data are available in the form of aggregation at multiple scale levels such as census tract, county, state, and so on. When data are aggregated from a fine (e.g. county) to a coarse (e.g. state) geographical level, there will be loss of information. The problem is more challenging when excessive zeros are available at the fine level. After data aggregation, the excessive zeros at the fine level will be reduced at the coarse level. If we ignore the zero inflation and the aggregation effect, we could get inconsistent risk estimates at the fine and coarse levels. Hence, in this paper, we address those problems using zero inflated multiscale models that jointly describe the risk variations at different geographical levels. For the excessive zeros at the fine level, we use a zero inflated convolution model, whereas we consider a regular convolution model for the smoothed data at the coarse level. These methods provide a consistent risk estimate at the fine and coarse levels when high percentages of structural zeros are present in the data.

Spatial mixture multiscale modeling for aggregated health data.

One of the main goals in spatial epidemiology is to study the geographical pattern of disease risks. For such purpose, the convolution model composed of correlated and uncorrelated components is often used. However, one of the two components could be predominant in some regions. To investigate the predominance of the correlated or uncorrelated component for multiple scale data, we propose four different spatial mixture multiscale models by mixing spatially varying probability weights of correlated (CH) and uncorrelated heterogeneities (UH). The first model assumes that there is no linkage between the different scales and, hence, we consider independent mixture convolution models at each scale. The second model introduces linkage between finer and coarser scales via a shared uncorrelated component of the mixture convolution model. The third model is similar to the second model but the linkage between the scales is introduced through the correlated component. Finally, the fourth model accommodates for a scale effect by sharing both CH and UH simultaneously. We applied these models to real and simulated data, and found that the fourth model is the best model followed by the second model.

Empirical Bayes estimates for correlated hierarchical data with overdispersion.

An extension of the generalized linear mixed model was constructed to simultaneously accommodate overdispersion and hierarchies present in longitudinal or clustered data. This so-called combined model includes conjugate random effects at observation level for overdispersion and normal random effects at subject level to handle correlation, respectively. A variety of data types can be handled in this way, using different members of the exponential family. Both maximum likelihood and Bayesian estimation for covariate effects and variance components were proposed. The focus of this paper is the development of an estimation procedure for the two sets of random effects. These are necessary when making predictions for future responses or their associated probabilities. Such (empirical) Bayes estimates will also be helpful in model diagnosis, both when checking the fit of the model as well as when investigating outlying observations. The proposed procedure is applied to three datasets of different outcome types.

Model-based estimates of long-term persistence of induced HPV antibodies: a flexible subject-specific approach.

In infectious diseases, it is important to predict the long-term persistence of vaccine-induced antibodies and to estimate the time points where the individual titers are below the threshold value for protection. This article focuses on HPV-16/18, and uses a so-called fractional-polynomial model to this effect, derived in a data-driven fashion. Initially, model selection was done from among the second- and first-order fractional polynomials on the one hand and from the linear mixed model on the other. According to a functional selection procedure, the first-order fractional polynomial was selected. Apart from the fractional polynomial model, we also fitted a power-law model, which is a special case of the fractional polynomial model. Both models were compared using Akaike's information criterion. Over the observation period, the fractional polynomials fitted the data better than the power-law model; this, of course, does not imply that it fits best over the long run, and hence, caution ought to be used when prediction is of interest. Therefore, we point out that the persistence of the anti-HPV responses induced by these vaccines can only be ascertained empirically by long-term follow-up analysis.

Phase I Study of Taminadenant (PBF509/NIR178), an Adenosine 2A Receptor Antagonist, with or without Spartalizumab (PDR001), in Patients with Advanced Non-Small Cell Lung Cancer.

PURPOSE: The adenosine 2A receptor (A2AR) mediates the immunosuppressive effects of adenosine in the tumor microenvironment and is highly expressed in non-small cell lung cancer (NSCLC). Taminadenant (PBF509/NIR178) is an A2AR antagonist able to reactivate the antitumor immune response. PATIENTS AND METHODS: In this phase I/Ib, dose-escalation/expansion study, patients with advanced/metastatic NSCLC and ≥1 prior therapy received taminadenant (80-640 mg, orally, twice a day) with or without spartalizumab (anti-programmed cell death-1, 400 mg, i.v., every 4 weeks). Primary endpoints were safety, tolerability, and feasibility of the combination. RESULTS: During dose escalation, 25 patients each received taminadenant alone or with spartalizumab; 19 (76.0%) and 9 (36.0%) had received prior immunotherapy, respectively. Dose-limiting toxicities (all Grade 3) with taminadenant alone were alanine/aspartate aminotransferase increase and nausea [n = 1 (4.0%) each; 640 mg], and in the combination group were pneumonitis [n = 2 (8.0%); 160 and 240 mg] and fatigue and alanine/aspartate aminotransferase increase [n = 1 (4.0%) each; 320 mg]; pneumonitis cases responded to steroids rapidly and successfully. Complete and partial responses were observed in one patient each in the single-agent and combination groups; both were immunotherapy naïve. In the single-agent and combination groups, 7 and 14 patients experienced stable disease; 7 and 6 patients were immunotherapy pretreated, respectively. CONCLUSIONS: Taminadenant, with and without spartalizumab, was well tolerated in patients with advanced NSCLC. The maximum tolerated dose of taminadenant alone was 480 mg twice a day, and 240 mg twice a day plus spartalizumab. Efficacy was neither a primary or secondary endpoint; however, some clinical benefit was noted regardless of prior immunotherapy or programmed cell death ligand-1 status.

Spatially-dependent Bayesian model selection for disease mapping.

In disease mapping where predictor effects are to be modeled, it is often the case that sets of predictors are fixed, and the aim is to choose between fixed model sets. Model selection methods, both Bayesian model selection and Bayesian model averaging, are approaches within the Bayesian paradigm for achieving this aim. In the spatial context, model selection could have a spatial component in the sense that some models may be more appropriate for certain areas of a study region than others. In this work, we examine the use of spatially referenced Bayesian model averaging and Bayesian model selection via a large-scale simulation study accompanied by a small-scale case study. Our results suggest that BMS performs well when a strong regression signature is found.

Bayesian multi-scale modeling for aggregated disease mapping data.

In disease mapping, a scale effect due to an aggregation of data from a finer resolution level to a coarser level is a common phenomenon. This article addresses this issue using a hierarchical Bayesian modeling framework. We propose four different multiscale models. The first two models use a shared random effect that the finer level inherits from the coarser level. The third model assumes two independent convolution models at the finer and coarser levels. The fourth model applies a convolution model at the finer level, but the relative risk at the coarser level is obtained by aggregating the estimates at the finer level. We compare the models using the deviance information criterion (DIC) and Watanabe-Akaike information criterion (WAIC) that are applied to real and simulated data. The results indicate that the models with shared random effects outperform the other models on a range of criteria.

Space-time variation of respiratory cancers in South Carolina: a flexible multivariate mixture modeling approach to risk estimation.

PURPOSE: Many types of cancer have an underlying spatiotemporal distribution. Spatiotemporal mixture modeling can offer a flexible approach to risk estimation via the inclusion of latent variables. METHODS: In this article, we examine the application and benefits of using four different spatiotemporal mixture modeling methods in the modeling of cancer of the lung and bronchus as well as "other" respiratory cancer incidences in the state of South Carolina. RESULTS: Of the methods tested, no single method outperforms the other methods; which method is best depends on the cancer under consideration. The lung and bronchus cancer incidence outcome is best described by the univariate modeling formulation, whereas the "other" respiratory cancer incidence outcome is best described by the multivariate modeling formulation. CONCLUSIONS: Spatiotemporal multivariate mixture methods can aid in the modeling of cancers with small and sparse incidences when including information from a related, more common type of cancer.

Comparing multilevel and multiscale convolution models for small area aggregated health data.

In spatial epidemiology, data are often arrayed hierarchically. The classification of individuals into smaller units, which in turn are grouped into larger units, can induce contextual effects. On the other hand, a scaling effect can occur due to the aggregation of data from smaller units into larger units. In this paper, we propose a shared multilevel model to address the contextual effects. In addition, we consider a shared multiscale model to adjust for both scale and contextual effects simultaneously. We also study convolution and independent multiscale models, which are special cases of shared multilevel and shared multiscale models, respectively. We compare the performance of the models by applying them to real and simulated data sets. We found that the shared multiscale model was the best model across a range of simulated and real scenarios as measured by the deviance information criterion (DIC) and the Watanabe Akaike information criterion (WAIC).

Extensions to Multivariate Space Time Mixture Modeling of Small Area Cancer Data.

Oral cavity and pharynx cancer, even when considered together, is a fairly rare disease. Implementation of multivariate modeling with lung and bronchus cancer, as well as melanoma cancer of the skin, could lead to better inference for oral cavity and pharynx cancer. The multivariate structure of these models is accomplished via the use of shared random effects, as well as other multivariate prior distributions. The results in this paper indicate that care should be taken when executing these types of models, and that multivariate mixture models may not always be the ideal option, depending on the data of interest.

Disease mapping of zero-excessive mesothelioma data in Flanders.

PURPOSE: To investigate the distribution of mesothelioma in Flanders using Bayesian disease mapping models that account for both an excess of zeros and overdispersion. METHODS: The numbers of newly diagnosed mesothelioma cases within all Flemish municipalities between 1999 and 2008 were obtained from the Belgian Cancer Registry. To deal with overdispersion, zero inflation, and geographical association, the hurdle combined model was proposed, which has three components: a Bernoulli zero-inflation mixture component to account for excess zeros, a gamma random effect to adjust for overdispersion, and a normal conditional autoregressive random effect to attribute spatial association. This model was compared with other existing methods in literature. RESULTS: The results indicate that hurdle models with a random effects term accounting for extra variance in the Bernoulli zero-inflation component fit the data better than hurdle models that do not take overdispersion in the occurrence of zeros into account. Furthermore, traditional models that do not take into account excessive zeros but contain at least one random effects term that models extra variance in the counts have better fits compared to their hurdle counterparts. In other words, the extra variability, due to an excess of zeros, can be accommodated by spatially structured and/or unstructured random effects in a Poisson model such that the hurdle mixture model is not necessary. CONCLUSIONS: Models taking into account zero inflation do not always provide better fits to data with excessive zeros than less complex models. In this study, a simple conditional autoregressive model identified a cluster in mesothelioma cases near a former asbestos processing plant (Kapelle-op-den-Bos). This observation is likely linked with historical local asbestos exposures. Future research will clarify this.

Bayesian model selection methods in modeling small area colon cancer incidence.

PURPOSE: Many types of cancer have an underlying spatial incidence distribution. Spatial model selection methods can be useful when determining the linear predictor that best describes incidence outcomes. METHODS: In this article, we examine the applications and benefits of using two different types of spatial model selection techniques, Bayesian model selection and Bayesian model averaging, in relation to colon cancer incidence in the state of Georgia, United States. RESULTS: Both methods produce useful results that lead to the determination that median household income and percent African American population are important predictors of colon cancer incidence in the Northern counties of the state, whereas percent persons below poverty level and percent African American population are important in the Southern counties. CONCLUSIONS: Of the two presented methods, Bayesian model selection appears to provide more succinct results, but applying the two in combination offers even more useful information into the spatial preferences of the alternative linear predictors.

Multiscale measurement error models for aggregated small area health data.

Spatial data are often aggregated from a finer (smaller) to a coarser (larger) geographical level. The process of data aggregation induces a scaling effect which smoothes the variation in the data. To address the scaling problem, multiscale models that link the convolution models at different scale levels via the shared random effect have been proposed. One of the main goals in aggregated health data is to investigate the relationship between predictors and an outcome at different geographical levels. In this paper, we extend multiscale models to examine whether a predictor effect at a finer level hold true at a coarser level. To adjust for predictor uncertainty due to aggregation, we applied measurement error models in the framework of multiscale approach. To assess the benefit of using multiscale measurement error models, we compare the performance of multiscale models with and without measurement error in both real and simulated data. We found that ignoring the measurement error in multiscale models underestimates the regression coefficient, while it overestimates the variance of the spatially structured random effect. On the other hand, accounting for the measurement error in multiscale models provides a better model fit and unbiased parameter estimates.

Impact of Income on Small Area Low Birth Weight Incidence Using Multiscale Models.

Low birth weight (LBW) is an important public health issue in the US as well as worldwide. The two main causes of LBW are premature birth and fetal growth restriction. Socio-economic status, as measured by family income has been correlated with LBW incidence at both the individual and population levels. In this paper, we investigate the impact of household income on LBW incidence at different geographical levels. To show this, we choose to examine LBW incidences collected from the state of Georgia, in the US, at both the county and public health (PH) district. The data at the PH district are an aggregation of the data at the county level nested within the PH district. A spatial scaling effect is induced during data aggregation from the county to the PH level. To address the scaling effect issue, we applied a shared multiscale model that jointly models the data at two levels via a shared correlated random effect. To assess the benefit of using the shared multiscale model, we compare it with an independent multiscale model which ignores the scale effect. Applying the shared multiscale model for the Georgia LBW incidence, we have found that income has a negative impact at both the county and PH levels. On the other hand, the independent multiscale model shows that income has a negative impact only at the county level. Hence, if the scale effect is not properly accommodated in the model, a different interpretation of the findings could result.