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An individual malignant tumor is composed of a heterogeneous collection of single cells with distinct molecular and phenotypic features, a phenomenon termed intratumoral heterogeneity. Intratumoral heterogeneity poses challenges for cancer treatment, motivating the need for combination therapies. Single-cell technologies are now available to guide effective drug combinations by accounting for intratumoral heterogeneity through the analysis of the signaling perturbations of an individual tumor sample screened by a drug panel. In particular, Mass Cytometry Time-of-Flight (CyTOF) is a high-throughput single-cell technology that enables the simultaneous measurements of multiple (>40) intracellular and surface markers at the level of single cells for hundreds of thousands of cells in a sample. We developed a computational framework, entitled Drug Nested Effects Models (DRUG-NEM), to analyze CyTOF single-drug perturbation data for the purpose of individualizing drug combinations. DRUG-NEM optimizes drug combinations by choosing the minimum number of drugs that produce the maximal desired intracellular effects based on nested effects modeling. We demonstrate the performance of DRUG-NEM using single-cell drug perturbation data from tumor cell lines and primary leukemia samples.

Inferring time-varying networks is important to understand the development and evolution of interactions over time. However, the vast majority of currently used models assume direct measurements of node states, which are often difficult to obtain, especially in fields like cell biology, where perturbation experiments often only provide indirect information of network structure. Here we propose hidden Markov nested effects models (HM-NEMs) to model the evolving network by a Markov chain on a state space of signalling networks, which are derived from nested effects models (NEMs) of indirect perturbation data. To infer the hidden network evolution and unknown parameter, a Gibbs sampler is developed, in which sampling network structure is facilitated by a novel structural Metropolis–Hastings algorithm. We demonstrate the potential of HM-NEMs by simulations on synthetic time-series perturbation data. We also show the applicability of HM-NEMs in two real biological case studies, in one capturing dynamic crosstalk during the progression of neutrophil polarisation, and in the other inferring an evolving network underlying early differentiation of mouse embryonic stem cells.

Disease-specific quality indicators are used to compare institutions and health care providers in terms of processes or outcomes relevant to treatment of a particular condition. In the context of surgical cancer treatments, the performance variations can be due to hospital and/or surgeon level differences, creating a hierarchical clustering. We consider how the observed variation in care received at patient level can be decomposed into that causally explained by the hospital performance, surgeon performance within hospital, patient case-mix, and unexplained (residual) variation. For this purpose, we derive a four-way variance decomposition, with particular attention to the causal interpretation of the components. For estimation, we use inputs from a mixed-effect model with nested random hospital/surgeon-specific effects, and a multinomial logistic model for the hospital/surgeon-specific patient populations. We investigate the performance of our methods in a simulation study and demonstrate them through analysis of administrative data on kidney cancer care in Ontario.

The case‐cohort design for longitudinal data consists of a subcohort sampled at the beginning of the study that is followed repeatedly over time, and a case sample that is ascertained through the course of the study. Although some members in the subcohort may experience events over the study period, we refer to it as the “control‐cohort.” The case sample is a random sample of subjects not in the control‐cohort, who have experienced at least one event during the study period. Different correlations among repeated observations on the same individual are accommodated by a two‐level random‐effects model. This design allows consistent estimation of all parameters estimable in a cohort design and is a cost‐effective way to study the effects of covariates on repeated observations of relatively rare binary outcomes when exposure assessment is expensive. It is an extension of the case‐cohort design (Prentice, 1986, Biometrika73, 1–11) and the bidirectional case‐crossover design (Navidi, 1998, Biometrics54, 596–605). A simulation study compares the efficiency of the longitudinal case‐cohort design to a full cohort analysis, and we find that in certain situations up to 90% efficiency can be obtained with half the sample size required for a full cohort analysis. A bootstrap method is presented that permits testing for intra‐subject homogeneity in the presence of unidentifiable nuisance parameters in the two‐level random‐effects model. As an illustration we apply the design to data from an ongoing study of childhood asthma.

Background Disentangling the drivers of genetic differentiation is one of the cornerstones in evolution. This is because genetic diversity, and the way in which it is partitioned within and among populations across space, is an important asset for the ability of populations to adapt and persist in changing environments. We tested three major hypotheses accounting for genetic differentiation—isolation-by-distance (IBD), isolation-by-environment (IBE) and isolation-by-resistance (IBR)—in the annual plant Arabidopsis thaliana across the Iberian Peninsula, the region with the largest genomic diversity. To that end, we sampled, genotyped with genome-wide SNPs, and analyzed 1772 individuals from 278 populations distributed across the Iberian Peninsula. Results IBD, and to a lesser extent IBE, were the most important drivers of genetic differentiation in A. thaliana. In other words, dispersal limitation, genetic drift, and to a lesser extent local adaptation to environmental gradients, accounted for the within- and among-population distribution of genetic diversity. Analyses applied to the four Iberian genetic clusters, which represent the joint outcome of the long demographic and adaptive history of the species in the region, showed similar results except for one cluster, in which IBR (a function of landscape heterogeneity) was the most important driver of genetic differentiation. Using spatial hierarchical Bayesian models, we found that precipitation seasonality and topsoil pH chiefly accounted for the geographic distribution of genetic diversity in Iberian A. thaliana. Conclusions Overall, the interplay between the influence of precipitation seasonality on genetic diversity and the effect of restricted dispersal and genetic drift on genetic differentiation emerges as the major forces underlying the evolutionary trajectory of Iberian A. thaliana.

Family studies to identify disease‐related genes often collect families with multiple cases. If environmental exposures or other measured covariates are also important, they should be incorporated into these genetic analyses to control for confounding and increase statistical power. We propose a two‐level mixed effects model that allows us to estimate environmental effects while accounting for varying genetic correlations among family members and adjusting for ascertainment by conditioning on the number of cases in the family. We describe a conditional maximum likelihood analysis based on this model. When genetic effects are negligible, this conditional likelihood reduces to standard conditional logistic regression. We show that the simpler conditional logistic regression typically yields biased estimators of exposure effects, and we describe conditions under which the conditional logistic approach has little or no bias.

Statistical analyses were applied at the Hanford Site, USA, to assess groundwater contamination problems that included (1) determining local backgrounds to ascertain whether a facility is affecting the groundwater quality and (2) determining a 'pre-Hanford' groundwater background to allow formulation of background-based cleanup standards. The primary purpose of this paper is to extend the random effects models for (1) assessing the spatial, temporal, and analytical variability of groundwater background measurements; (2) demonstrating that the usual variance estimate s2, which ignores the variance components, is a biased estimator; (3) providing formulas for calculating the amount of bias; and (4) recommending monitoring strategies to reduce the uncertainty in estimating the average background concentrations. A case study is provided. Results indicate that (1) without considering spatial and temporal variability, there is a high probability of false positives, resulting in unnecessary remediation and/or monitoring expenses; (2) the most effective way to reduce the uncertainty in estimating the average background, and enhance the power of the statistical tests in general, is to increase the number of background wells; and (3) background for a specific constituent should be considered as a statistical distribution, not as a single value or threshold. The methods and the related analysis of variance tables discussed in this paper can be used as diagnostic tools in documenting the extent of inherent spatial and/or temporal variation and to help select an appropriate statistical method for testing purposes.

Taiwan's global budgeting for hospital health care, in comparison to other countries, assigns a regional budget cap for hospitals' medical benefits claimed on the basis of fee-for-service (FFS) payments. This study uses a stays-hospitals-years database comprising acute myocardial infarction inpatients to examine whether the reimbursement policy mitigates the medical benefits claimed to a third-payer party during 2000–2008. The estimated results of a nested random-effects model showed that hospitals attempted to increase their medical benefit claims under the influence of initial implementation of global budgeting. The magnitudes of hospitals' responses to global budgeting were significantly attributed to hospital ownership, accreditation status, and market competitiveness of a region. The results imply that the regional budget cap superimposed on FFS payments provides only blunt incentive to the hospitals to cooperate to contain medical resource utilization, unless a monitoring mechanism attached with the payment system.

This chapter contains sections titled: Linear models Null hypotheses Analysis of variance Variance components Assumptions Pooling denominator terms Unbalanced nested designs Linear mixed effects models Robust alternatives Power and optimisation of resource allocation Nested ANOVA in R Further reading Key for nested ANOVA Worked examples of real biological data sets

Popular frameworks for studying habitat selection include resource‐selection functions (RSFs) and step‐selection functions (SSFs), estimated using logistic and conditional logistic regression, respectively. Both frameworks compare environmental covariates associated with locations animals visit with environmental covariates at a set of locations assumed available to the animals. Conceptually, slopes that vary by individual, that is, random coefficient models, could be used to accommodate inter‐individual heterogeneity with either approach. While fitting such models for RSFs is possible with standard software for generalized linear mixed‐effects models (GLMMs), straightforward and efficient one‐step procedures for fitting SSFs with random coefficients are currently lacking. To close this gap, we take advantage of the fact that the conditional logistic regression model (i.e. the SSF) is likelihood‐equivalent to a Poisson model with stratum‐specific fixed intercepts. By interpreting the intercepts as a random effect with a large (fixed) variance, inference for random‐slope models becomes feasible with standard Bayesian techniques, or with frequentist methods that allow one to fix the variance of a random effect. We compare this approach to other commonly applied alternatives, including models without random slopes and mixed conditional regression models fit using a two‐step algorithm. Using data from mountain goats (Oreamnos americanus) and Eurasian otters (Lutra lutra), we illustrate that our models lead to valid and feasible inference. In addition, we conduct a simulation study to compare different estimation approaches for SSFs and to demonstrate the importance of including individual‐specific slopes when estimating individual‐ and population‐level habitat‐selection parameters. By providing coded examples using integrated nested Laplace approximations (INLA) and Template Model Builder (TMB) for Bayesian and frequentist analysis via the R packages R‐INLA and glmmTMB, we hope to make efficient estimation of RSFs and SSFs with random effects accessible to anyone in the field. SSFs with individual‐specific coefficients are particularly attractive since they can provide insights into movement and habitat‐selection processes at fine‐spatial and temporal scales, but these models had previously been very challenging to fit. The authors provide a coherent framework for fitting resource‐selection functions (RSFs) and step‐selection functions (SSFs) with random effects. To allow fitting of SSFs, the authors reformulate the conditional logistic regression model as a (likelihood‐equivalent) Poisson model, where stratum‐specific intercepts are included as a random effect with a fixed large prior variance.