Power Analyses for Negative Binomial Models with Application to Multiple Sclerosis Clinical Trials

Power analysis for RNA-Seq differential expression studies using generalized linear mixed effects models

Background

Power analysis becomes an inevitable step in experimental design of current biomedical research. Complex designs allowing diverse correlation structures are commonly used in RNA-Seq experiments. However, the field currently lacks statistical methods to calculate sample size and estimate power for RNA-Seq differential expression studies using such designs. To fill the gap, simulation based methods have a great advantage by providing numerical solutions, since theoretical distributions of test statistics are typically unavailable for such designs.

Results

In this paper, we propose a novel simulation based procedure for power estimation of differential expression with the employment of generalized linear mixed effects models for correlated expression data. We also propose a new procedure for power estimation of differential expression with the use of a bivariate negative binomial distribution for paired designs. We compare the performance of both the likelihood ratio test and Wald test under a variety of simulation scenarios with the proposed procedures. The simulated distribution was used to estimate the null distribution of test statistics in order to achieve the desired false positive control and was compared to the asymptotic Chi-square distribution. In addition, we applied the procedure for paired designs to the TCGA breast cancer data set.

Conclusions

In summary, we provide a framework for power estimation of RNA-Seq differential expression under complex experimental designs. Simulation results demonstrate that both the proposed procedures properly control the false positive rate at the nominal level.

Sample size calculations for comparing two groups of count data

A sample size formula for comparing two groups of count data is derived using the method of moments by matching the first and second moments of the distribution of the count data, and it does not need any further distributional assumption. Compared to sample size formulas derived using a likelihood-based approach or using simulations, the proposed sample size formula applies to count data following any distribution in addition to the negative binomial distribution. The proposed sample size formula can be used even when the study is analyzed with a likelihood-based approach. Because asymptotically, the method of moments is no more efficient than likelihood-based approaches, the proposed sample size formula can be viewed as an upper bound of the required sample size by likelihood-based approaches to start the study. Applications of the sample size formula are illustrated using an asthma study design.

Power analysis for RNA-Seq differential expression studies

BACKGROUND

Sample size calculation and power estimation are essential components of experimental designs in biomedical research. It is very challenging to estimate power for RNA-Seq differential expression under complex experimental designs. Moreover, the dependency among genes should be taken into account in order to obtain accurate results.

RESULTS

In this paper, we propose a simulation based procedure for power estimation using the negative binomial distribution and assuming a generalized linear model (at the gene level) that considers the dependence between gene expression level and its variance (dispersion) and also allows equal or unequal dispersion across conditions. We compared the performance of both Wald test and likelihood ratio test under different scenarios. The null distribution of the test statistics was simulated for the desired false positive control to avoid excess false positives with the usage of an asymptotic chi-square distribution. We applied this method to the TCGA breast cancer data set.

CONCLUSIONS

We provide a framework for power estimation of RNA-Seq data. The proposed procedure is able to properly control the false positive error rate at the nominal level.

Sample size calculation for comparing two negative binomial rates

Negative binomial model has been increasingly used to model the count data in recent clinical trials. It is frequently chosen over Poisson model in cases of overdispersed count data that are commonly seen in clinical trials. One of the challenges of applying negative binomial model in clinical trial design is the sample size estimation. In practice, simulation methods have been frequently used for sample size estimation. In this paper, an explicit formula is developed to calculate sample size based on the negative binomial model. Depending on different approaches to estimate the variance under null hypothesis, three variations of the sample size formula are proposed and discussed. Important characteristics of the formula include its accuracy and its ability to explicitly incorporate dispersion parameter and exposure time. The performance of the formula with each variation is assessed using simulations.