Unified Computational Methods for Regression Analysis of Zero-Inflated and Bound-Inflated Data

Analysis of joint modeling of longitudinal zero-inflated power series and zero-inflated time to event data

In longitudinal studies measurements are often collected on different types of responses for each individual. These may contain several longitudinally measured responses (such as the CD4 count) and the time at which an event occurs (e.g., HIV, death, or dropout from the study). These outcomes are often separately analyzed. Compared to separate modeling, joint modeling and simultaneous analysis allows for more coherent, robust analysis and may produce a better insight into the process under study. However, there has always been difficulty to the analyst that finding a proper multi-variable joint distribution for linking responses. In this article, we survey the zero-inflated property for longitudinal count and time to event data. We apply a member of the family of power series distributions (PSDs) and the Cox proportional hazard regression model (Cox PH) with Weibull baseline hazard rate, respectively, for these correlated responses. Also we consider both right and left censoring mechanisms in time to event process. This modeling strategy leads to expand the class of joint models and presents some new joint models which, as far as we know, have not yet been investigated by other researchers. The parameters in the joint model are estimated by using likelihood techniques.

Meditation or exercise for preventing acute respiratory infection (MEPARI-2): A randomized controlled trial

Background

Practice of meditation or exercise may enhance health to protect against acute infectious illness.

Objective

To assess preventive effects of meditation and exercise on acute respiratory infection (ARI) illness.

Design

Randomized controlled prevention trial with three parallel groups.

Setting

Madison, Wisconsin, USA.

Participants

Community-recruited adults who did not regularly exercise or meditate.

Methods

1) 8-week behavioral training in mindfulness-based stress reduction (MBSR); 2) matched 8-week training in moderate intensity sustained exercise (EX); or 3) observational waitlist control. Training classes occurred in September and October, with weekly ARI surveillance through May. Incidence, duration, and area-under-curve ARI global severity were measured using daily reports on the WURSS-24 during ARI illness. Viruses were identified multiplex PCR. Absenteeism, health care utilization, and psychosocial health self-report assessments were also employed.

Results

Of 413 participants randomized, 390 completed the trial. In the MBSR group, 74 experienced 112 ARI episodes with 1045 days of ARI illness. Among exercisers, 84 had 120 episodes totaling 1010 illness days. Eighty-two of the controls had 134 episodes with 1210 days of ARI illness. Mean global severity was 315 for MBSR (95% confidence interval 244, 386), 256 (193, 318) for EX, and 336 (268, 403) for controls. A prespecified multivariate zero-inflated regression model suggested reduced incidence for MBSR (p = 0.036) and lower global severity for EX (p = 0.042), compared to control, not quite attaining the p<0.025 prespecified cut-off for null hypothesis rejection. There were 73 ARI-related missed-work days and 22 ARI-related health care visits in the MBSR group, 82 days and 21 visits for exercisers, and 105 days and 24 visits among controls. Viruses were identified in 63 ARI episodes in the MBSR group, compared to 64 for EX and 72 for control. Statistically significant (p<0.05) improvements in general mental health, self-efficacy, mindful attention, sleep quality, perceived stress, and depressive symptoms were observed in the MBSR and/or EX groups, compared to control.

Conclusions

Training in mindfulness meditation or exercise may help protect against ARI illness.

Limitations

This trial was likely underpowered.

Trial registration

Clinicaltrials.gov NCT01654289

Two-Part and Related Regression Models for Longitudinal Data

Statistical models that involve a two-part mixture distribution are applicable in a variety of situations. Frequently, the two parts are a model for the binary response variable and a model for the outcome variable that is conditioned on the binary response. Two common examples are zero-inflated or hurdle models for count data and two-part models for semicontinuous data. Recently, there has been particular interest in the use of these models for the analysis of repeated measures of an outcome variable over time. The aim of this review is to consider motivations for the use of such models in this context and to highlight the central issues that arise with their use. We examine two-part models for semicontinuous and zero-heavy count data, and we also consider models for count data with a two-part random effects distribution.

A corrected formulation for marginal inference derived from two-part mixed models for longitudinal semi-continuous data

For semi-continuous data which are a mixture of true zeros and continuously distributed positive values, the use of two-part mixed models provides a convenient modelling framework. However, deriving population-averaged (marginal) effects from such models is not always straightforward. Su et al. presented a model that provided convenient estimation of marginal effects for the logistic component of the two-part model but the specification of marginal effects for the continuous part of the model presented in that paper was based on an incorrect formulation. We present a corrected formulation and additionally explore the use of the two-part model for inferences on the overall marginal mean, which may be of more practical relevance in our application and more generally.

Segmentation and intensity estimation for microarray images with saturated pixels

Background

Microarray image analysis processes scanned digital images of hybridized arrays to produce the input spot-level data for downstream analysis, so it can have a potentially large impact on those and subsequent analysis. Signal saturation is an optical effect that occurs when some pixel values for highly expressed genes or peptides exceed the upper detection threshold of the scanner software (2¹⁶ - 1 = 65, 535 for 16-bit images). In practice, spots with a sizable number of saturated pixels are often flagged and discarded. Alternatively, the saturated values are used without adjustments for estimating spot intensities. The resulting expression data tend to be biased downwards and can distort high-level analysis that relies on these data. Hence, it is crucial to effectively correct for signal saturation.

Results

We developed a flexible mixture model-based segmentation and spot intensity estimation procedure that accounts for saturated pixels by incorporating a censored component in the mixture model. As demonstrated with biological data and simulation, our method extends the dynamic range of expression data beyond the saturation threshold and is effective in correcting saturation-induced bias when the lost information is not tremendous. We further illustrate the impact of image processing on downstream classification, showing that the proposed method can increase diagnostic accuracy using data from a lymphoma cancer diagnosis study.

Conclusions

The presented method adjusts for signal saturation at the segmentation stage that identifies a pixel as part of the foreground, background or other. The cluster membership of a pixel can be altered versus treating saturated values as truly observed. Thus, the resulting spot intensity estimates may be more accurate than those obtained from existing methods that correct for saturation based on already segmented data. As a model-based segmentation method, our procedure is able to identify inner holes, fuzzy edges and blank spots that are common in microarray images. The approach is independent of microarray platform and applicable to both single- and dual-channel microarrays.

Conditional decomposition diagnostics for regression analysis of zero-inflated and left-censored data

Health and safety studies that entail both incidence and magnitude of effects produce semi-continuous outcomes, in which the response is either zero or a continuous positive value. Zero-inflated left-censored models typically employ latent mixture constructions to allow different covariate processes to impact the incidence versus the magnitude. Assessment of the model, however, requires a focus on the observable characteristics. We employ a conditional decomposition approach, in which the model assessment is partitioned into two observable components: the adequacy of the marginal probability model for the boundary value and the adequacy of the conditional model for values strictly above the boundary. A conditional likelihood decomposition facilitates the statistical assessment. For corresponding residual and graphical analysis, the conditional mean and quantile functions for events above the boundary and the marginal probabilities of boundary events are investigated. Large sample standard errors for these quantities are derived for enhanced graphical assessment, and simulation is conducted to investigate the finite-sample behaviour. The methods are illustrated with data from two health-related safety studies. In each case, the conditional assessments identify the source for lack of fit of the previously considered model and thus lead to an improved model.