Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf.

Quantile-Quantile (Q-Q) plots are often difficult to interpret because it is unclear how large the deviation from the theoretical distribution must be to indicate a lack of fit. Most Q-Q plots could benefit from the addition of meaningful global testing bands, but the use of such bands unfortunately remains rare because of the drawbacks of current approaches and packages. These drawbacks include incorrect global Type I error rate, lack of power to detect deviations in the tails of the distribution, relatively slow computation for large data sets, and limited applicability. To solve these problems, we apply the equal local levels global testing method, which we have implemented in the R Package qqconf, a versatile tool to create Q-Q plots and probability-probability (P-P) plots in a wide variety of settings, with simultaneous testing bands rapidly created using recently-developed algorithms. qqconf can easily be used to add global testing bands to Q-Q plots made by other packages. In addition to being quick to compute, these bands have a variety of desirable properties, including accurate global levels, equal sensitivity to deviations in all parts of the null distribution (including the tails), and applicability to a range of null distributions. We illustrate the use of qqconf in several applications: assessing normality of residuals from regression, assessing accuracy of p values, and use of Q-Q plots in genome-wide association studies.

Accelerated dimensionality reduction of single-cell RNA sequencing data with fastglmpca.

Motivated by theoretical and practical issues that arise when applying Principal Components Analysis (PCA) to count data, Townes et al introduced "Poisson GLM-PCA", a variation of PCA adapted to count data, as a tool for dimensionality reduction of single-cell RNA sequencing (RNA-seq) data. However, fitting GLM-PCA is computationally challenging. Here we study this problem, and show that a simple algorithm, which we call "Alternating Poisson Regression" (APR), produces better quality fits, and in less time, than existing algorithms. APR is also memory-efficient, and lends itself to parallel implementation on multi-core processors, both of which are helpful for handling large single-cell RNA-seq data sets. We illustrate the benefits of this approach in two published single-cell RNA-seq data sets. The new algorithms are implemented in an R package, fastglmpca.

Tradeoffs in Modeling Context Dependency in Complex Trait Genetics.

Genetic effects on complex traits may depend on context, such as age, sex, environmental exposures or social settings. However, it is often unclear if the extent of context dependency, or Gene-by-Environment interaction (GxE), merits more involved models than the additive model typically used to analyze data from genome-wide association studies (GWAS). Here, we suggest considering the utility of GxE models in GWAS as a tradeoff between bias and variance parameters. In particular, We derive a decision rule for choosing between competing models for the estimation of allelic effects. The rule weighs the increased estimation noise when context is considered against the potential bias when context dependency is ignored. In the empirical example of GxSex in human physiology, the increased noise of context-specific estimation often outweighs the bias reduction, rendering GxE models less useful when variants are considered independently. However, we argue that for complex traits, the joint consideration of context dependency across many variants mitigates both noise and bias. As a result, polygenic GxE models can improve both estimation and trait prediction. Finally, we exemplify (using GxDiet effects on longevity in fruit flies) how analyses based on independently ascertained "top hits" alone can be misleading, and that considering polygenic patterns of GxE can improve interpretation.