COBRA Preprint Series

A Bayesian regression tree approach to identify the effect of nanoparticles properties on toxicity profiles

Cecile Low-Kam et al. — Sun, 03 Mar 2013 16:26:21 PST

We introduce a Bayesian multiple regression tree model to characterize relationships between physico-chemical properties of nanoparticles and their in-vitro toxicity over multiple doses and times of exposure. Unlike conventional models that rely on data summaries, our model solves the low sample size issue and avoids arbitrary loss of information by combining all measurements from a general exposure experiment across doses, times of exposure, and replicates. The proposed technique integrates Bayesian trees for modeling threshold effects and interactions, and penalized B-splines for dose and time-response surfaces smoothing. The resulting posterior distribution is sampled via a Markov Chain Monte Carlo algorithm. This method allows for inference on a number of quantities of potential interest to substantive nanotoxicology, such as the importance of physico-chemical properties and their marginal effect on toxicity. We illustrate the application of our method to the analysis of a library of 24 nano metal oxides.

Relating Nanoparticle Properties to Biological Outcomes in Exposure Escalation Experiments

Trina Patel et al. — Wed, 26 Dec 2012 19:11:28 PST

A fundamental goal in nano-toxicology is that of identifying particle physical and chemical properties, which are likely to explain biological hazard. The first line of screening for potentially adverse outcomes often consists of exposure escalation experiments, involving the exposure of micro-organisms or cell lines to a battery of nanomaterials. We discuss a modeling strategy, that relates the outcome of an exposure escalation experiment to nanoparticle properties. Our approach makes use of a hierarchical decision process, where we jointly identify particles that initiate adverse biological outcomes and explain the probability of this event in terms of the particle physico-chemical descriptors. The proposed inferential framework results in summaries that are easily interpretable as simple probability statements. We present the application of the proposed method to a data set on 24 metal oxides nanoparticles, characterized in relation to their electrical, crystal and dissolution properties.

PLS-ROG: Partial least squares with rank order of groups

Hiroyuki Yamamoto — Thu, 01 Nov 2012 09:46:36 PDT

Partial least squares (PLS), which is an unsupervised dimensionality reduction method, has been widely used in metabolomics. PLS can separate score depend on groups in a low dimensional subspace. However, this cannot use the information about rank order of groups. This information is often provided in which concentration of administered drugs to animals is gradually varies. In this study, we proposed partial least squares for rank order of groups (PLS-ROG). PLS-ROG can consider both separation and rank order of groups.

Statistical hypothesis test of factor loading in principal component analysis and its application to metabolite set enrichment analysis

Hiroyuki Yamamoto et al. — Thu, 01 Nov 2012 09:46:33 PDT

Principal component analysis (PCA) has been widely used to visualize high-dimensional metabolomic data in a two- or three-dimensional subspace. In metabolomics, some metabolites (e.g. top 10 metabolites) have been subjectively selected when using factor loading in PCA, and biological inferences for these metabolites are made. However, this approach is possible to lead biased biological inferences because these metabolites are not objectively selected by statistical criterion. We proposed a statistical procedure to pick up metabolites by statistical hypothesis test of factor loading in PCA and make biological inferences by metabolite set enrichment analysis (MSEA) for these significant metabolites. This procedure depends on the fact that the eigenvector in PCA for autoscaled data is proportional to the correlation coefficient between PC score and each metabolite levels. We applied this approach for two metabolomic data of mice liver samples. 136 of 282 metabolites in first case study and 66 of 275 metabolites in second case study were statistically significant. This result suggests that to set the previously-determined number of metabolites is not appropriate because the number of significant metabolites is different in each study when using factor loading in PCA. Moreover, MSEA was performed for these significant metabolites and significant metabolic pathways can be detected. These results are acceptable when compared with previous biological knowledge. It is essential to select metabolites statistically for making unbiased biological inferences from metabolome data, when using factor loading in PCA. We proposed a statistical procedure to pick up metabolites by statistical hypothesis test of factor loading in PCA and make biological inferences by MSEA for these significant metabolites. We developed an R package "mseapca" to perform this approach. The “mseapca” package is publicity available on CRAN website.

Estimating HIV prevalence in the presence of spatial variation

Matthew D. Austin et al. — Mon, 29 Oct 2012 20:21:26 PDT

Data from antenatal clinics in Botswana provide information on age, HIV status, and geographic cluster (clinic) for women in their child-bearing years. To make use of these data, it is necessary to extend spline estimation methods to adjust for correlation that arises due to geographic proximity of clinics and closeness in age among women within clinics. We use a logistic model with mean function specified by natural cubic splines, and a composite likelihood approach to accommodate all possible pairs of geographical clusters. These methods allow us to generate smooth estimates of age-specific HIV prevalence in Botswana. Repeated measures of such estimates will ultimately be useful in evaluating the impact of HIV prevention strategies on HIV incidence in women of child-bearing age.

Quantifying alternative splicing from paired-end RNA-sequencing data

David Rossell et al. — Fri, 12 Oct 2012 14:16:29 PDT

RNA-sequencing has revolutionized biomedical research and, in particular, our ability to study gene alternative splicing. The problem has important implications for human health, as alternative splicing is involved in malfunctions at the cellular level and multiple diseases. However, the high-dimensional nature of the data and the existence of experimental biases pose serious data analysis challenges. We find that the standard data summaries used to study alternative splicing are severely limited, as they ignore a substantial amount of valuable information. Current data analysis methods are based on such summaries and are hence sub-optimal. Further, they have limited flexibility in accounting for technical biases. We propose novel data summaries and a Bayesian modeling framework that overcome these limitations and determine biases in a non-parametric, data-dependent manner. These summaries adapt naturally to the rapid improvements in sequencing technology. We provide efficient point estimates and uncertainty assessments. The approach allows to study alternative splicing patterns for individual samples and can also be the basis for downstream differential expression analysis. We found an over 5 fold improvement in estimation mean square error compared to a popular approach in simulations, and substantially higher correlations between replicates in experimental data. Our findings indicate the need for modifying the routine summarization and analysis of alternative splicing RNA-seq studies. We provide a software implementation in the R package casper.

Robust Estimation of Pure/Natural Direct Effects with Mediator Measurement Error

Eric J. Tchetgen Tchetgen et al. — Mon, 10 Sep 2012 11:16:34 PDT

Recent developments in causal mediation analysis have offered new notions of direct and indirect effects, that formalize more traditional and informal notions of mediation analysis emanating primarily from the social sciences. The pure or natural direct effect of Robins-Greenland-Pearl quantifies the causal effect of an exposure that is not mediated by a variable on the causal pathway to the outcome, and combines with the natural indirect effect to produce the total causal effect of the exposure. Sufficient conditions for identification of natural direct effects were previously given, that assume certain independencies about potential outcomes, and a rich literature on estimation of natural direct effects has since developed. A common situation in epidemiology is that the mediator is subject to measurement error, in which case, existing techniques for estimating natural direct and indirect effects could be biased and the resulting inferences could be incorrect if measurement error were ignored. In this paper, the authors consider classical measurement error of a continuous mediator. The authors propose a three-stage least-squares regression technique for estimating natural direct effects on the additive scale, that is robust to classical measurement error of the mediator under certain assumptions about the structure of confounding. The robustness property implies that no additional data such as a validation sample, nor replicate measurements of the error prone mediator are needed to recover valid mediation inferences. An important appeal of the three-stage approach is that it is easy to implement using standard software. A simulation study is provided illustrating the finite sample performance of the proposed approach as compared to the prevailing mediation technique, and the new methodology is also shown to apply under a specific form of differential additive measurement error, and to extend to multiplicative effects under a log-linear regression framework.

A prior-free framework of coherent inference and its derivation of simple shrinkage estimators

David R. Bickel — Fri, 07 Sep 2012 17:06:13 PDT

The reasoning behind uses of confidence intervals and p-values in scientific practice may be made coherent by modeling the inferring statistician or scientist as an idealized intelligent agent. With other things equal, such an agent regards a hypothesis coinciding with a confidence interval of a higher confidence level as more certain than a hypothesis coinciding with a confidence interval of a lower confidence level. The agent uses different methods of confidence intervals conditional on what information is available. The coherence requirement means all levels of certainty of hypotheses about the parameter agree with the same distribution of certainty over parameter space. The result is a unique and coherent fiducial distribution that encodes the post-data certainty levels of the agent.

While many coherent fiducial distributions coincide with confidence distributions or Bayesian posterior distributions, there is a general class of coherent fiducial distributions that equates the two-sided p-value with the probability that the null hypothesis is true. The use of that class leads to point estimators and interval estimators that can be derived neither from the dominant frequentist theory nor from Bayesian theories that rule out data-dependent priors. These simple estimators shrink toward the parameter value of the null hypothesis without relying on asymptotics or on prior distributions.

Why odds ratio estimates of GWAS are almost always close to 1.0

Yutaka Yasui — Sun, 19 Aug 2012 14:41:21 PDT

“Missing heritability” in genome-wide association studies (GWAS) refers to the seeming inability for GWAS data to capture the great majority of genetic causes of a disease in comparison to the known degree of heritability for the disease, in spite of GWAS’ genome-wide measures of genetic variations. This paper presents a simple mathematical explanation for this phenomenon, assuming that the heritability information exists in GWAS data. Specifically, it focuses on the fact that the great majority of association measures (in the form of odds ratios) from GWAS are consistently close to the value that indicates no association, explains why this occurs, and deduces two specific forms of epistasis/interaction as its cause. The implication is that GWAS may be able to recover “missing heritability” if the two specific forms of epistasis and gene-environmental interaction are fully explored.

On Identification of Natural Direct Effects when a Confounder of the Mediator is Directly Affected by Exposure

Eric J. Tchetgen Tchetgen et al. — Wed, 20 Jun 2012 10:58:00 PDT

Natural direct and indirect effects formalize traditional notions of mediation analysis into a rigorous causal framework and have recently received considerable attention in epidemiology and in the social sciences. Sufficient conditions for identification of natural direct effects were formulated by Judea Pearl under a nonparametric structural equations model, which assumes certain independencies between potential outcomes. A common situation in epidemiology is that a confounder of the mediator is affected by the exposure, in which case, natural direct effects fail to be nonparametrically identified without additional assumptions, even under Pearl's nonparametric structural equations model. In this paper, the authors show that when a single binary confounder of the mediator is affected by the exposure; the natural direct effect is nonparametrically identified under a monotonicity assumption about the effect of the exposure on the confounder. A similar result is shown to hold for a vector of binary confounders of the mediator under a certain independence assumption about the confounders. Finally, the authors show that natural direct effects are more generally identified if there is no-additive mean interaction between the mediator and confounders of the mediator affected by exposure. When correct, this latter assumption is particularly appealing because it does not require monotonicity of effects of the exposure, additionally, it places no restriction on the nature of the confounders of the mediator which can be continuous or polytomous.

On penalized likelihood estimation for a non-proportional hazards regression model

Karthik Devarajan et al. — Wed, 20 Jun 2012 10:57:50 PDT

The fundamental assumption of proportionality of hazards in the Cox
model sometimes does not hold in practice. In this paper, a semi-parametric generalization of the Cox model that permits crossing hazard curves is described. This model allows the interaction between covariates and the baseline hazard, and has been the subject of recent investigation. It includes, for the two sample problem, the case of two Weibull distributions and two extreme value distributions differing in both scale and shape parameters. The partial likelihood approach cannot be applied here to estimate the model parameters, and flexible methods based on splines and sieves for approximating the baseline hazard have been suggested. A theoretical framework for estimation in this generalized model is developed based on penalized likelihood methods. It is shown that the optimal solution to the baseline hazard, baseline cumulative hazard and their ratio are exponential splines with knots at the unique failure times. Its relationship to prior computational approaches for this model is outlined.

Differential Patterns of Interaction and Gaussian Graphical Models

Masanao Yajima et al. — Mon, 18 Jun 2012 11:12:32 PDT

We propose a methodological framework to assess heterogeneous patterns of association amongst components of a random vector expressed as a Gaussian directed acyclic graph. The proposed framework is likely to be useful when primary interest focuses on potential contrasts characterizing the association structure between known subgroups of a given sample. We provide inferential frameworks as well as an efficient computational algorithm to fit such a model and illustrate its validity through a simulation. We apply the model to Reverse Phase Protein Array data on Acute Myeloid Leukemia patients to show the contrast of association structure between refractory patients and relapsed patients.

Hierarchical Rank Aggregation with Applications to Nanotoxicology

Trina Patel et al. — Sat, 31 Mar 2012 13:45:36 PDT

The development of high throughput screening (HTS) assays in the field of nanotoxicology provide new opportunities for the hazard assessment and ranking of engineered nanomaterials (ENM). It is often necessary to rank lists of materials based on multiple risk assessment parameters, often aggregated across several measures of toxicity and possibly spanning an array of experimental platforms. Bayesian models coupled with the optimization of loss functions have been shown to provide an effective framework for conducting inference on ranks. In this article we present various loss function based ranking approaches for comparing ENM within experiments and toxicity parameters. Additionally, we propose a framework for the aggregation of ranks across different sources of evidence while allowing for differential weighting of this evidence based on its reliability and importance in risk ranking. We apply these methods to high throughput toxicity data on 2 human cell lines, exposed to 8 different nanomaterials, and measured in relation to 4 cytotoxicity outcomes.

Robustness of Measures of Interaction to Unmeasured Confounding

Eric J. Tchetgen Tchetgen et al. — Tue, 27 Mar 2012 18:28:18 PDT

In this paper, we study the impact of unmeasured confounding on inference about a two-way interaction in a mean regression model with identity, log or logit link function. Necessary and sufficient conditions are established for a two-way interaction to be nonparametrically identified from the observed data, despite unmeasured confounding for the factors defining the interaction. A lung cancer data application illustrates the results.

Toxicity Profiling of Engineered Nanomaterials via Multivariate Dose Response Surface Modeling

Trina Patel et al. — Fri, 10 Feb 2012 16:56:40 PST

New generation in-vitro high throughput screening (HTS) assays for the assessment of engineered nanomaterials provide an opportunity to learn how these particles interact at the cellular level, particularly in relation to injury pathways. These types of assays are often characterized by small sample sizes, high measurement error and high dimensionality as multiple cytotoxicity outcomes are measured across an array of doses and durations of exposure. In this article we propose a probability model for toxicity profiling of engineered nanomaterials. A hierarchical framework is used to account for the multivariate nature of the data by modeling dependence between outcomes and thereby combining information across cytotoxicity pathways. In this framework we are able to provide a flexible surface-response model that provides inference and generalizations of various classical risk assessment parameters. We discuss applications of this model to data on eight nanoparticles evaluated in relation to four cytotoxicity parameters.

Modeling Protein Expression and Protein Signaling Pathways

Donatello Telesca et al. — Mon, 12 Dec 2011 20:44:14 PST

High-throughput functional proteomic technologies provide a way to quantify the expression of proteins of interest. Statistical inference centers on identifying the activation state of proteins and their patterns of molecular interaction formalized as dependence structure. Inference on dependence structure is particularly important when proteins are selected because they are part of a common molecular pathway. In that case inference on dependence structure reveals properties of the underlying pathway. We propose a probability model that represents molecular interactions at the level of hidden binary latent variables that can be interpreted as indicators for active versus inactive states of the proteins. The proposed approach exploits available expert knowledge about the target pathway to define an informative prior on the hidden conditional dependence structure. An important feature of this prior is that it provides an instrument to explicitly anchor the model space to a set of interactions of interest, favoring a local search approach to model determination. We apply our model to reverse phase protein array data from a study on acute myeloid leukemia. Our inference identifies relevant sub-pathways in relation to the unfolding of the biological process under study.

Modeling Criminal Careers as Departures from a Unimodal Population Age-Crime Curve: The Case of Marijuana Use

Donatello Telesca et al. — Sun, 11 Dec 2011 10:49:44 PST

A major aim of longitudinal analyses of life course data is to describe the within- and between-individual variability in a behavioral outcome, such as crime. Statistical analyses of such data typically draw on mixture and mixed-effects growth models. In this work, we present a functional analytic point of view and develop an alternative method that models individual crime trajectories as departures from a population age-crime curve. Drawing on empirical and theoretical claims in criminology, we assume a unimodal population age-crime curve and allow individual expected crime trajectories to differ by their levels of offending and patterns of temporal misalignment. We extend Bayesian hierarchical curve registration methods to accommodate count data and to incorporate influence of baseline covariates on individual behavioral trajectories. Analyzing self-reported counts of yearly marijuana use from the Denver Youth Survey, we examine the influence of race and gender categories on differences in levels and timing of marijuana smoking. We find that our approach offers a flexible and realistic model for longitudinal crime trajectories that fits individual observations well and allows for a rich array of inferences of interest to criminologists and drug abuse researchers.

Components of the indirect effect in vaccine trials: identification of contagion and infectiousness effects

Tyler J. VanderWeele et al. — Thu, 08 Dec 2011 13:06:20 PST

Vaccination of one person may prevent the infection of another either because (i) the vaccine prevents the first from being infected and from infecting the second or because (ii) even if the first person is infected, the vaccine may render the infection less infectious. We might refer to the first of these mechanisms as a contagion effect and the second as an infectiousness effect. In this paper, for the simple setting of a randomized vaccine trial with households of size two, we use counterfactual theory under interference to provide formal definitions of a contagion effect and an infectiousness effect. Using ideas analogous to mediation analysis, we show that the indirect effect (the effect of one individual's vaccine on another's outcome) can be decomposed into a contagion effect and an infectiousness effect on the risk difference, risk ratio, odds ratio and vaccine efficacy scales. We provide identification assumptions for such contagion and infectiousness effects, and describe a simple statistical techniques to estimate these effects when they are identified. We also give a sensitivity analysis techniques to assess how inferences would change under violations of the identification assumptions. The concepts and results of this paper are illustrated with sample vaccine trial data.

On the definition of a confounder

Tyler J. VanderWeele et al. — Thu, 08 Dec 2011 09:23:19 PST

The causal inference literature has provided a clear formal definition of confounding expressed in terms of counterfactual independence. The causal inference literature has not, however, produced a clear formal definition of a confounder, as it has given priority to the concept of confounding over that of a confounder. We consider a number of candidate definitions arising from various more informal statements made in the literature. We consider the properties satisfied by each candidate definition, principally focusing on (i) whether under the candidate definition control for all "confounders" suffices to control for "confounding" and (ii) whether each confounder in some context helps eliminate or reduce confounding bias. Several of the candidate definitions do not have these two properties. Only one candidate definition of those considered satisfies both properties. We propose that a "confounder" be defined as a pre-exposure covariate C for which there exists a set of other covariates X such that effect of the exposure on the outcome is unconfounded conditional on (X,C) but such that for no proper subset of (X,C) is the effect of the exposure on the outcome unconfounded given the subset. A variable that helps reduce bias but not eliminate bias we propose referring to as a "surrogate confounder."

A proof of Bell's inequality in quantum mechanics using causal interactions

James M. Robins et al. — Sat, 24 Sep 2011 13:21:41 PDT

We give a simple proof of Bell's inequality in quantum mechanics which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal interaction and interference between particles.