Semiparametric Models for Missing Covariate and Response Data in Regression Models

Regularized approach for data missing not at random

It is common in longitudinal studies that missing data occur due to subjects' no response, missed visits, dropout, death or other reasons during the course of study. To perform valid analysis in this setting, data missing not at random (MNAR) have to be considered. However, models for data MNAR often suffer from the identifiability issue and hence result in difficulty in estimation and computational convergence. To ameliorate this issue, we propose the LASSO and ridge-regularized selection models that regularize the missing data mechanism model to handle data MNAR, with the regularization parameter selected via a cross-validation procedure. The proposed models can be also employed for sensitivity analysis to examine the effects on inference of different assumptions about the missing data mechanism. We illustrate the performance of the proposed models via simulation studies and the analysis of data from a randomized clinical trial.

Sequential BART for imputation of missing covariates

To conduct comparative effectiveness research using electronic health records (EHR), many covariates are typically needed to adjust for selection and confounding biases. Unfortunately, it is typical to have missingness in these covariates. Just using cases with complete covariates will result in considerable efficiency losses and likely bias. Here, we consider the covariates missing at random with missing data mechanism either depending on the response or not. Standard methods for multiple imputation can either fail to capture nonlinear relationships or suffer from the incompatibility and uncongeniality issues. We explore a flexible Bayesian nonparametric approach to impute the missing covariates, which involves factoring the joint distribution of the covariates with missingness into a set of sequential conditionals and applying Bayesian additive regression trees to model each of these univariate conditionals. Using data augmentation, the posterior for each conditional can be sampled simultaneously. We provide details on the computational algorithm and make comparisons to other methods, including parametric sequential imputation and two versions of multiple imputation by chained equations. We illustrate the proposed approach on EHR data from an affiliated tertiary care institution to examine factors related to hyperglycemia.

Merging multiple longitudinal studies with study-specific missing covariates: A joint estimating function approach

Merging multiple datasets collected from studies with identical or similar scientific objectives is often undertaken in practice to increase statistical power. This article concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics, such as different follow-up schedules and study-specific missing covariates (e.g., covariates observed in some studies but missing in other studies). The presence of study-specific missing covariates presents great statistical methodology challenge in data merging and analysis. We propose a joint estimating function approach to addressing this challenge, in which a novel nonparametric estimating function constructed via splines-based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates. Under mild regularity conditions, we show that the proposed estimator is consistent and asymptotically normal. We evaluate finite-sample performances of the proposed method through simulation studies. In comparison to the conventional multiple imputation approach, our method exhibits smaller estimation bias. We provide an illustrative data analysis using longitudinal cohorts collected in Mexico City to assess the effect of lead exposures on children's somatic growth.

A Bayesian Approach for the Cox Proportional Hazards Model with Covariates Subject to Detection Limit

The research on biomarkers has been limited in its effectiveness because biomarker levels can only be measured within the thresholds of assays and laboratory instruments, a challenge referred to as a detection limit (DL) problem. In this paper, we propose a Bayesian approach to the Cox proportional hazards model with explanatory variables subject to lower, upper, or interval DLs. We demonstrate that by formulating the time-to-event outcome using the Poisson density with counting process notation, implementing the proposed approach in the OpenBUGS and JAGS is straightforward. We have conducted extensive simulations to compare the proposed Bayesian approach to the other four commonly used methods and to evaluate its robustness with respect to the distribution assumption of the biomarkers. The proposed Bayesian approach and other methods were applied to an acute lung injury study, in which a panel of cytokine biomarkers was studied for the biomarkers’ association with ventilation-free survival.

A Bayesian Approach for Generalized Linear Models with Explanatory Biomarker Measurement Variables Subject to Detection Limit - an Application to Acute Lung Injury

Biomarkers have the potential to improve our understanding of disease diagnosis and prognosis. Biomarker levels that fall below the assay detection limits (DLs), however, compromise the application of biomarkers in research and practice. Most existing methods to handle non-detects focus on a scenario in which the response variable is subject to detection limit; only a few methods consider explanatory variables when dealing with DLs. We propose a Bayesian approach for generalized linear models with explanatory variables subject to lower, upper, or interval DLs. In simulation studies, we compared the proposed Bayesian approach to four commonly used methods in a logistic regression model with explanatory variable measurements subject to DL. We also applied the Bayesian approach and other four methods in a real study, in which a panel of cytokine biomarkers was studied for their association with acute lung injury (ALI). We found that IL8 was associated with a moderate increase in risk for ALI in the model based on the proposed Bayesian approach.

Geoadditive models to assess spatial variation of HIV infections among women in local communities of Durban, South Africa

BACKGROUND

The severity of the HIV/AIDS epidemic in South Africa varies between and within provinces, with differences noted even at the suburban scale. We investigated the geographical variability of HIV infection in rural areas of the eThekwini Metropolitan Municipality in KwaZulu-Natal province, South Africa.

METHOD

We used geoadditive models to assess nonlinear geographical variation in HIV prevalence while simultaneously controlling for important demographic and sexual risk factors. A total of 3,469 women who were screened for a Phase-III randomized trial were included in the current analysis.

RESULTS

We found significant spatial patterns that could not be explained by demographic and sexual risk behaviors. In particular, the epidemic was determined to be much worse 44 km south of Durban after controlling for all demographic and sexual risk behaviors.

CONCLUSION

The study revealed significant geographic variability in HIV infection in the eThekwini Metropolitan Municipality in KwaZulu-Natal, South Africa.

Changes in weather and the effects on pediatric asthma exacerbations

BACKGROUND

Pediatric asthma exacerbations may correlate with changes in weather, yet this relationship is not well defined.

OBJECTIVE

To determine the effects of fluctuations in climatic factors (temperature, humidity, and barometric pressure) on pediatric asthma exacerbations.

METHODS

A retrospective study was performed at 1 large urban hospital during a 2-year period (January 1, 2004, to December 31, 2005). Children presenting to the emergency department (ED) for an asthma exacerbation were included. Data on climactic factors, pollutants, and aeroallergens were collected daily. The relationship of daily (intraday) or between-day (interday) changes in climactic factors and asthma ED visits was evaluated using time series analysis, controlling for seasonality, air pollution, and aeroallergen exposure. The effects of climactic factors were evaluated on the day of admission (T=0) and up to 5 days before admission (T-5 through T-1).

RESULTS

There were 25,401 asthma ED visits. A 10% intraday increase in humidity on day T-1 or day T-2 was associated with approximately 1 additional ED visit for asthma (P < .001 and P = .01, respectively). Interday changes in humidity from day T - 3 to T-2 were also associated with more ED visits (P < .001). Interday changes in temperature from T-1 to T = 0 increased ED visits, with a 10 degrees F increase being associated with 1.8 additional visits (P = .006). No association was found with changes in barometric pressure.

CONCLUSION

Fluctuations in humidity and temperature, but not barometric pressure, appear to influence ED visits for pediatric asthma. The additional ED visits occur 1 to 2 days after the fluctuation.

Missing data methods in longitudinal studies: a review

Incomplete data are quite common in biomedical and other types of research, especially in longitudinal studies. During the last three decades, a vast amount of work has been done in the area. This has led, on the one hand, to a rich taxonomy of missing-data concepts, issues, and methods and, on the other hand, to a variety of data-analytic tools. Elements of taxonomy include: missing data patterns, mechanisms, and modeling frameworks; inferential paradigms; and sensitivity analysis frameworks. These are described in detail. A variety of concrete modeling devices is presented. To make matters concrete, two case studies are considered. The first one concerns quality of life among breast cancer patients, while the second one examines data from the Muscatine children's obesity study.

Semiparametric regression during 2003-2007

Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology - thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.

Assessing Sexual Attitudes and Behaviors of Young Women: A Joint Model with Nonlinear Time Effects, Time Varying Covariates, and Dropouts

Understanding human sexual behaviors is essential for the effective prevention of sexually transmitted infections. Analysis of longitudinally measured sexual behavioral data, however, is often complicated by zero-inflation of event counts, nonlinear time trend, time-varying covariates, and informative dropouts. Ignoring these complicating factors could undermine the validity of the study findings. In this paper, we put forth a unified joint modeling structure that accommodates these features of the data. Specifically, we propose a pair of simultaneous models for the zero-inflated event counts: Each of these models contains an auto-regressive structure for the accommodation of the effect of recent event history, and a nonparametric component for the modeling of nonlinear time effect. Informative dropout and time varying covariates are modeled explicitly in the process. Model fitting and parameter estimation are carried out in a Bayesian paradigm by the use of a Markov Chain Monte Carlo (MCMC) method. Analytical results showed that adolescent sexual behaviors tended to evolve nonlinearly over time and they were strongly influenced by the day-to-day variations in mood and sexual interests. These findings suggest that adolescent sex is to a large extent driven by intrinsic factors rather than being compelled by circumstances, thus highlighting the need of education on self protective measures against infection risks.

Theory and Inference for Regression Models with Missing Responses and Covariates

In this paper, we carry out an in-depth theoretical investigation for inference with missing response and covariate data for general regression models. We assume that the missing data are Missing at Random (MAR) or Missing Completely at Random (MCAR) throughout. Previous theoretical investigations in the literature have focused only on missing covariates or missing responses, but not both. Here, we consider theoretical properties of the estimates under three different estimation settings: complete case analysis (CC), a complete response analysis (CR) that involves an analysis of those subjects with only completely observed responses, and the all case analysis (AC), which is an analysis based on all of the cases. Under each scenario, we derive general expressions for the likelihood and devise estimation schemes based on the EM algorithm. We carry out a theoretical investigation of the three estimation methods in the normal linear model and analytically characterize the loss of information for each method, as well as derive and compare the asymptotic variances for each method assuming the missing data are MAR or MCAR. In addition, a theoretical investigation of bias for the CC method is also carried out. A simulation study and real dataset are given to illustrate the methodology.