MR-Corr2: a two-sample Mendelian randomization method that accounts for correlated horizontal pleiotropy using correlated instrumental variants.

MOTIVATION: Mendelian randomization (MR) is a valuable tool to examine the causal relationships between health risk factors and outcomes from observational studies. Along with the proliferation of genome-wide association studies, a variety of two-sample MR methods for summary data have been developed to account for horizontal pleiotropy (HP), primarily based on the assumption that the effects of variants on exposure (γ) and HP (α) are independent. In practice, this assumption is too strict and can be easily violated because of the correlated HP. RESULTS: To account for this correlated HP, we propose a Bayesian approach, MR-Corr2, that uses the orthogonal projection to reparameterize the bivariate normal distribution for γ and α, and a spike-slab prior to mitigate the impact of correlated HP. We have also developed an efficient algorithm with paralleled Gibbs sampling. To demonstrate the advantages of MR-Corr2 over existing methods, we conducted comprehensive simulation studies to compare for both type-I error control and point estimates in various scenarios. By applying MR-Corr2 to study the relationships between exposure-outcome pairs in complex traits, we did not identify the contradictory causal relationship between HDL-c and CAD. Moreover, the results provide a new perspective of the causal network among complex traits. AVAILABILITY AND IMPLEMENTATION: The developed R package and code to reproduce all the results are available at https://github.com/QingCheng0218/MR.Corr2. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Center-augmented ℓ2 -type regularization for subgroup learning.

The existing methods for subgroup analysis can be roughly divided into two categories: finite mixture models (FMM) and regularization methods with an ℓ1 -type penalty. In this paper, by introducing the group centers and ℓ2 -type penalty in the loss function, we propose a novel center-augmented regularization (CAR) method; this method can be regarded as a unification of the regularization method and FMM and hence exhibits higher efficiency and robustness and simpler computations than the existing methods. In particular, its computational complexity is reduced from the O ( n 2 ) $O(n^2)$ of the conventional pairwise-penalty method to only O ( n K ) $O(nK)$ , where n is the sample size and K is the number of subgroups. The asymptotic normality of CAR is established, and the convergence of the algorithm is proven. CAR is applied to a dataset from a multicenter clinical trial, Buprenorphine in the Treatment of Opiate Dependence; a larger R2 is produced and three additional significant variables are identified compared to those of the existing methods.

Nonparametric regression with right-censored covariate via conditional density function.

Censoring often occurs in data collection. This article, considers nonparametric regression when the covariate is censored under general settings. In contrast to censoring in the response variable in survival analysis, regression with censored covariates is more challenging but less studied in the literature, especially for dependent censoring. We propose to estimate the regression function using conditional hazard rates. The asymptotic normality of our proposed estimator is established. Both theoretical results and simulation studies demonstrate that the proposed method is more efficient than the estimation based on complete observations and other methods, especially when the censoring rate is high. We illustrate the usefulness of the proposed method using a data set from the Framingham heart study and a data set from a randomized placebo-controlled clinical trial of the drug D-penicillamine.

Jackknife approach to the estimation of mutual information.

Quantifying the dependence between two random variables is a fundamental issue in data analysis, and thus many measures have been proposed. Recent studies have focused on the renowned mutual information (MI) [Reshef DN, et al. (2011) Science 334:1518-1524]. However, "Unfortunately, reliably estimating mutual information from finite continuous data remains a significant and unresolved problem" [Kinney JB, Atwal GS (2014) Proc Natl Acad Sci USA 111:3354-3359]. In this paper, we examine the kernel estimation of MI and show that the bandwidths involved should be equalized. We consider a jackknife version of the kernel estimate with equalized bandwidth and allow the bandwidth to vary over an interval. We estimate the MI by the largest value among these kernel estimates and establish the associated theoretical underpinnings.

Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics.

Infectious diseases provide a particularly clear illustration of the spatiotemporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics and, depending on the nature of spatial contagion, may result in traveling waves. Measles epidemics are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatiotemporal variations in population structure and demography. On the basis of a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatiotemporal properties in prevaccination epidemics of measles in England and Wales.

Measles on the edge: coastal heterogeneities and infection dynamics.

Mathematical models can help elucidate the spatio-temporal dynamics of epidemics as well as the impact of control measures. The gravity model for directly transmitted diseases is currently one of the most parsimonious models for spatial epidemic spread. This model uses distance-weighted, population size-dependent coupling to estimate host movement and disease incidence in metapopulations. The model captures overall measles dynamics in terms of underlying human movement in pre-vaccination England and Wales (previously established). In spatial models, edges often present a special challenge. Therefore, to test the model's robustness, we analyzed gravity model incidence predictions for coastal cities in England and Wales. Results show that, although predictions are accurate for inland towns, they significantly underestimate coastal persistence. We examine incidence, outbreak seasonality, and public transportation records, to show that the model's inaccuracies stem from an underestimation of total contacts per individual along the coast. We rescue this predicted 'edge effect' by increasing coastal contacts to approximate the number of per capita inland contacts. These results illustrate the impact of 'edge effects' on epidemic metapopulations in general and illustrate directions for the refinement of spatiotemporal epidemic models.

Cumulative effects of air pollution on public health.

Cumulative effect is an important way through which the pollutants affect public health. However, few existing dynamical models are well enough understood and documented to detect or quantify the cumulative effects and to answer pertinent questions posed by the World Health Organization (WHO): 'Is there a threshold below which no effects of the pollutants on health are expected to occur in all people?' and 'What averaging period (time pattern) is the most relevant from the point of view of health?'. Using a new semi-parametric time series modelling approach, which incorporates non-linearity and latent cumulative variables, we show that the cumulative effects on health due to continual exposure to environmental pollutants can be very serious even at levels below the national ambient air quality standards of America (NAAQS). The situation is especially worrying for chronic sufferers. Our study suggests that different pollutants may require different cumulative periods (on average) to impact on health but they share a similar functional form in respect of their impact. We also suggest some possible revision of the ambient air quality standards.