Identifying Differentially Expressed Genes of Zero Inflated Single Cell RNA Sequencing Data Using Mixed Model Score Tests

Single cell RNA sequencing (scRNA-seq) allows quantitative measurement and comparison of gene expression at the resolution of single cells. Ignoring the batch effects and zero inflation of scRNA-seq data, many proposed differentially expressed (DE) methods might generate bias. We propose a method, single cell mixed model score tests (scMMSTs), to efficiently identify DE genes of scRNA-seq data with batch effects using the generalized linear mixed model (GLMM). scMMSTs treat the batch effect as a random effect. For zero inflation, scMMSTs use a weighting strategy to calculate observational weights for counts independently under zero-inflated and zero-truncated distributions. Counts data with calculated weights were subsequently analyzed using weighted GLMMs. The theoretical null distributions of the score statistics were constructed by mixed Chi-square distributions. Intensive simulations and two real datasets were used to compare edgeR-zinbwave, DESeq2-zinbwave, and scMMSTs. Our study demonstrates that scMMSTs, as supplement to standard methods, are advantageous to define DE genes of zero-inflated scRNA-seq data with batch effects.

Approximations of the power functions for Wald, likelihood ratio, and score tests and their applications to linear and logistic regressions

Traditionally, asymptotic tests are studied and applied under local alternative. There exists a widespread opinion that the Wald, likelihood ratio, and score tests are asymptotically equivalent. We dispel this myth by showing that These tests have different statistical power in the presence of nuisance parameters. The local properties of the tests are described in terms of the first and second derivative evaluated at the null hypothesis. The comparison of the tests are illustrated with two popular regression models: linear regression with random predictor and logistic regression with binary covariate. We study the aberrant behavior of the tests when the distance between the null and alternative does not vanish with the sample size. We demonstrate that these tests have different asymptotic power. In particular, the score test is generally asymptotically biased but slightly superior for linear regression in a close neighborhood of the null. The power approximations are confirmed through simulations.

A robust score test of homogeneity for zero-inflated count data

In many applications of zero-inflated models, score tests are often used to evaluate whether the population heterogeneity as implied by these models is consistent with the data. The most frequently cited justification for using score tests is that they only require estimation under the null hypothesis. Because this estimation involves specifying a plausible model consistent with the null hypothesis, the testing procedure could lead to unreliable inferences under model misspecification. In this paper, we propose a score test of homogeneity for zero-inflated models that is robust against certain model misspecifications. Due to the true model being unknown in practical settings, our proposal is developed under a general framework of mixture models for which a layer of randomness is imposed on the model to account for uncertainty in the model specification. We exemplify this approach on the class of zero-inflated Poisson models, where a random term is imposed on the Poisson mean to adjust for relevant covariates missing from the mean model or a misspecified functional form. For this example, we show through simulations that the resulting score test of zero inflation maintains its empirical size at all levels, albeit a loss of power for the well-specified non-random mean model under the null. Frequencies of health promotion activities among young Girl Scouts and dental caries indices among inner-city children are used to illustrate the robustness of the proposed testing procedure.