Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through an empirical simulation study as well as an example of mortality estimation using NHANES data.
We develop a functional proportional hazards mixture cure (FPHMC) model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the EM algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness …
Survey data are often collected under multistage sampling designs where units are binned to clusters that are sampled in a first stage. The unit-indexed population variables of interest are typically dependent within cluster. We propose a Fully Bayesian method that constructs an exact likelihood for the observed sample to incorporate unit-level marginal sampling weights for performing unbiased inference for population parameters while simultaneously accounting for the dependence induced by sampling clusters of units to produce correct uncertainty quantification. Our approach parameterizes clus…
Age-specific mortality improvements are non-uniform, neither across ages nor across time. We propose a two-step procedure to estimate the rates of mortality improvement (RMI) in age-specific death rates (ASDR) at ages 85 and above for ten European countries from 1950 to 2019. In the first step, we smooth the raw death counts and estimate ASDR using four different methods: one parametric (gamma-Gompertz-Makeham), two non-parametric (P-splines and PCLM), and a novel Bayesian procedure to handle fluctuations resulting from ages with zero death counts. We compare the goodness of fit of the four sm…
Updating observations of a signal due to the delays in the measurement process is a common problem in signal processing, with prominent examples in a wide range of fields. An important example of this problem is the nowcasting of COVID-19 mortality: given a stream of reported counts of daily deaths, can we correct for the delays in reporting to paint an accurate picture of the present, with uncertainty? Without this correction, raw data will often mislead by suggesting an improving situation. We present a flexible approach using a latent Gaussian process that is capable of describing the chang…
Many data stewards collect confidential data that include fine geography. When sharing these data with others, data stewards strive to disseminate data that are informative for a wide range of spatial and non-spatial analyses while simultaneously protecting the confidentiality of data subjects' identities and attributes. Typically, data stewards meet this challenge by coarsening the resolution of the released geography and, as needed, perturbing the confidential attributes. When done with high intensity, these redaction strategies can result in released data with poor analytic quality. We prop…
Tuberculosis poses a global health risk and Brazil is among the top twenty countries by absolute mortality. However, this epidemiological burden is masked by under-reporting, which impairs planning for effective intervention. We present a comprehensive investigation and application of a Bayesian hierarchical approach to modelling and correcting under-reporting in tuberculosis counts, a general problem arising in observational count data. The framework is applicable to fully under-reported data, relying only on an informative prior distribution for the mean reporting rate to supplement the part…
In this work we present a statistical approach to distinguish and interpret the complex relationship between several predictors and a response variable at the small area level, in the presence of i) high correlation between the predictors and ii) spatial correlation for the response. Covariates which are highly correlated create collinearity problems when used in a standard multiple regression model. Many methods have been proposed in the literature to address this issue. A very common approach is to create an index which aggregates all the highly correlated variables of interest. For example,…
Weighting methods are popular tools for estimating causal effects; assessing their robustness under unobserved confounding is important in practice. In the following paper, we introduce a new set of sensitivity models called "variance-based sensitivity models". Variance-based sensitivity models characterize the bias from omitting a confounder by bounding the distributional differences that arise in the weights from omitting a confounder, with several notable innovations over existing approaches. First, the variance-based sensitivity models can be parameterized with respect to a simple $R^2$ pa…
When Method Choice Changes Statistical Inference: A Comparison of a Baseline Two-Stage Approach and Bayesian Joint Modeling for Longitudinal and Survival Data in an HIV Clinical Trial
Estimating marginal association between paired outcomes in clustered data with an application to analyzing caries and periodontal disease data from the National Health and Nutrition Examination Survey
A conditional expectation function (CEF) can at best be partially identified when the conditioning variable is interval censored. When the number of bins is small, existing methods often yield minimally informative bounds. We propose three innovations that make meaningful inference possible in interval data contexts. First, we prove novel nonparametric bounds for contexts where the distribution of the censored variable is known. Second, we show that a class of measures that describe the conditional mean across a fixed interval of the conditioning space can often be bounded tightly even when th…
Motivation: Although there is a rich literature on methods for assessing the impact of functional predictors, the focus has been on approaches for dimension reduction that can fail dramatically in certain applications. Examples of standard approaches include functional linear models, functional principal components regression, and cluster-based approaches, such as latent trajectory analysis. This article is motivated by applications in which the dynamics in a predictor, across times when the value is relatively extreme, are particularly informative about the response. For example, physicians a…
