A comparative study of tests for the difference of two Poisson means

Wald tests for variance-adjusted equivalence assessment with normal endpoints

Equivalence tests may be tested with mean difference against a margin adjusted for variance. The justification of using variance adjusted non-inferiority or equivalence margin is for the consideration that a larger margin should be used with large measurement variability. However, under the null hypothesis, the test statistic does not follow a t-distribution or any well-known distribution even when the measurement is normally distributed. In this study, we investigate asymptotic tests for testing the equivalence hypothesis. We apply the Wald test statistic and construct three Wald tests that differ in their estimates of variances. These estimates of variances include the maximum likelihood estimate (MLE), the uniformly minimum variance unbiased estimate (UMVUE), and the constrained maximum likelihood estimate (CMLE). We evaluate the performance of these three tests in terms of type I error rate control and power using simulations under a variety of settings. Our empirical results show that the asymptotic normalized tests are conservative in most settings, while the Wald tests based on ML- and UMVU-method could produce inflated significance levels when group sizes are unequal. However, the Wald test based on CML-method provides an improvement in power over the other two Wald tests for medium and small sample size studies.

Calculating the net activity uncertainty if the background includes a nonstationary component

Knowing the uncertainty of the net signal activity is essential in order to calculate the concentration uncertainty of an analyte in a sample or to decide whether the analyte activity is sufficient for detection. The net signal activity is usually calculated as a difference between the gross signal activity and the blank activity obtained from a material that is added to the sample during the analysis (e.g., acid to dilute the sample or gas to transport it as an aerosol). It is often assumed a priori that the analyte concentration in the blank is the same for any blank measurement, and the dispersion in the blank activities obtained from the individual measurements is related to the intrinsic imprecision of the measurement process only. This case can be called stationary; the relevant uncertainty calculation methods are widely known and used. However, in real applications where only some of the blank activity sources are well characterized, the blank stationarity needs to be demonstrated. The nonstationarity of the blank has serious consequences: (1) for a "well-known background", the net signal uncertainty increases, since it includes the variance of the nonstationary background component; (2) for paired measurements, the net signal uncertainty does not change but cannot be estimated from one single blank analysis, thus compromising the utility of the paired measurement approach. Presenting the lower and upper uncertainty limits is appropriate for the evaluation of the uncertainty of a net signal if the assumption of a stationary blank is questionable.

Statistical methods on detecting differentially expressed genes for RNA-seq data

BACKGROUND

For RNA-seq data, the aggregated counts of the short reads from the same gene is used to approximate the gene expression level. The count data can be modelled as samples from Poisson distributions with possible different parameters. To detect differentially expressed genes under two situations, statistical methods for detecting the difference of two Poisson means are used. When the expression level of a gene is low, i.e., the number of count is small, it is usually more difficult to detect the mean differences, and therefore statistical methods which are more powerful for low expression level are particularly desirable. In statistical literature, several methods have been proposed to compare two Poisson means (rates). In this paper, we compare these methods by using simulated and real RNA-seq data.

RESULTS

Through simulation study and real data analysis, we find that the Wald test with the data being log-transformed is more powerful than other methods, including the likelihood ratio test, which has similar power as the variance stabilizing transformation test; both are more powerful than the conditional exact test and Fisher exact test.

CONCLUSIONS

When the count data in RNA-seq can be reasonably modelled as Poisson distribution, the Wald-Log test is more powerful and should be used to detect the differentially expressed genes.

Sample size for post-marketing safety studies based on historical controls

PURPOSE

As part of a drug's entire life cycle, post-marketing studies are an important part in the identification of rare, serious adverse events. Recently, the US Food and Drug Administration (FDA) has begun to implement new post-marketing safety mandates as a consequence of increased emphasis on safety. The purpose of this research is to provide exact sample size formula for the proposed hybrid design, based on a two-group cohort study with incorporation of historical external data.

METHODS

Exact sample size formula based on the Poisson distribution is developed, because the detection of rare events is our outcome of interest. Performance of exact method is compared to its approximate large-sample theory counterpart.

RESULTS

The proposed hybrid design requires a smaller sample size compared to the standard, two-group prospective study design. In addition, the exact method reduces the number of subjects required in the treatment group by up to 30% compared to the approximate method for the study scenarios examined.

CONCLUSIONS

The proposed hybrid design satisfies the advantages and rationale of the two-group design with smaller sample sizes generally required.