Testing the equality of two Poisson means using the rate ratio

Ng, Hon Keung Tony; Tang, Man‐Lai

doi:10.1002/sim.1949

Cited by 55 publications

(77 citation statements)

References 10 publications

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“…Assuming a cardiovascular event rate of 1260 events per 100 000 person-years (all ages) in the control arm, 6 and a 10% lower event rate in the intervention arm (rate ratio of intervention to control of 0.9), a total sample of about 70 000 patients followed up for 2 years gives 80% power for a test at level 5% (twosided) allowing for 15% withdrawal. 7 This calculation was based on all-age event rates as it was not possible to find an event rate specifically for the over 50s at the time the trial was designed. The intervention was applied to the over 50s population and the outcome was measured in this age group only.…”

Section: Outcomes and Sample Sizementioning

confidence: 99%

Automated electronic reminders to facilitate primary cardiovascular disease prevention: randomised controlled trial

Holt¹,

Thorogood²,

Griffiths³

et al. 2010

Br J Gen Pract

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Primary care databases contain cardiovascular disease risk factor data, but practical tools are required to improve identification of at-risk patients. AimTo test the effects of a system of electronic reminders (the 'e-Nudge') on cardiovascular events and the adequacy of data for cardiovascular risk estimation. Design of studyRandomised controlled trial. SettingNineteen general practices in the West Midlands, UK. MethodThe e-Nudge identifies four groups of patients aged over 50 years on the basis of estimated cardiovascular risk and adequacy of risk factor data in general practice computers. Screen messages highlight individuals at raised risk and prompt users to complete risk profiles where necessary. The proportion of the study population in the four groups was measured, as well as the rate of cardiovascular events in each arm after 2 years. ResultsOver 38 000 patients' electronic records were randomised. The intervention led to an increase in the proportion of patients with sufficient data who were identifiably at risk, with a difference of 1.94% compared to the control group (95% confidence interval [CI] = 1.38 to 2.50, P<0.001). A corresponding reduction occurred in the proportion potentially at risk but requiring further data for a risk estimation (difference = -3.68%, 95% CI = -4.53 to -2.84, P<0.001). No significant difference was observed in the incidence of cardiovascular events (rate ratio = 0.96, 95% CI = 0.85 to 1.10, P = 0.59). ConclusionAutomated electronic reminders using routinely collected primary care data can improve the adequacy of cardiovascular risk factor information during everyday practice and increase the visibility of the atrisk population.

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Section: Outcomes and Sample Sizementioning

confidence: 99%

Automated electronic reminders to facilitate primary cardiovascular disease prevention: randomised controlled trial

Holt¹,

Thorogood²,

Griffiths³

et al. 2010

Br J Gen Pract

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“…Following procedures from the studies [24][25][26] for comparing two independent Poisson rates with unequal sample frames, we derived the Wald's inference procedures using the properties of ˆi γ and φ estimated from MLE and ˆi γ and φ from CMLE with a negative binomial distribution in two conditions ( )…”

Section: Wald Statistical Test and Log-transformed Wald Statistical Testmentioning

confidence: 99%

“…The logarithmic transformation is usually adopted for skewness correction and variance stabilization as suggested by these studies [16,24]. The statistical inference on the quantity is ( )…”

Section: Wald Statistical Test and Log-transformed Wald Statistical Testmentioning

confidence: 99%

Inference and Sample Size Calculations Based on Statistical Tests in a Negative Binomial Distribution for Differential Gene Expression in RNAseq Data

Li¹,

Cooper²,

Shyr³

et al. 2017

J Biom Biostat

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The high throughput RNA sequencing (RNA-seq) technology has become the popular method of choice for transcriptomics and the detection of differentially expressed genes. Sample size calculations for RNA-seq experimental design are an important consideration in biological research and clinical trials. Currently, the sample size formulas derived from the Wald and the likelihood ratio statistical tests with a Poisson distribution to model RNA-seq data have been developed. However, since the mean read counts in the real RNA-seq data are not equal to the variance, an extended method to calculate sample sizes based on a negative binomial distribution using an exact test statistic was proposed by . In this study, we alternatively derive five sample size calculation methods based on the negative binomial distribution using the Wald test, the log-transformed Wald test and the log-likelihood ratio test statistics. A comparison of our five methods and an existing method was performed by calculating the sample sizes and the simulated power in different scenarios. We first calculated the sample sizes for testing a single gene using the six methods given a nominal significance level α at 0.05 and 80% power. Then, we calculated the sample sizes for testing multiple genes given a false discovery rate (FDR) at 0.05 and 0.10. The empirical power and true prognostic genes for differential gene expression analysis corresponding to the estimated sample sizes from the six methods are also estimated via the simulation studies. Using the sample size formulas derived from log-transformed and Wald-based tests, we observed smaller sample properties while maintaining the nominal power close to or higher than 80% in all the settings compared to other methods. Moreover, the Wald test based sample size calculation method is easier to compute and faster in an RNA-seq experimental design. Later, several sample size calculation methods that were derived from the score statistic and the log-likelihood ratio test (LRT) statistic using the Poisson distribution were proposed [16]. However, the assumption of a Poisson distribution that the expected mean and variance are equal usually does not hold for RNA-seq studies, where the variance is typically greater than the mean of the read counts [17]. Therefore, a negative binomial distribution with a dispersion parameter is used to model RNA-seq data by the existing software packages such as DESeq [17] and edgeR [18], in which an exact test is used to test DEGs between conditions. Subsequently, a sample size calculation method based on an exact test statistic with the aid of the edgeR package [18] was proposed [19]. However, sample size methods derived from other test statistics such as the Wald test, the LRT and an extension of Wald test via log-transformation using negative binomial distribution to model the RNA-seq data have not yet been explored.

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“…The sampling we discuss here includes the now popular rate sampling, cf. Thode (1997) and Ng and Tang (2005) for Poisson distribution and Moser et al (1989), and Sprott and Farewell (1993) for the normal distribution, among others.…”

Section: Introductionmentioning

confidence: 99%

“…While in Gaussian case, we have Sichel (1973), Thode (1997), Krishnamoorthy and Thomsons (2004), and Ng and Tang (2005). Rate sampling in the normal case with homogenous variance is known as the regression through the origin case.…”

Section: Introductionmentioning

confidence: 99%

Inference for Noisy Samples

Ahmad

Herawati

2012

Pak.j.stat.oper.res.

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In the current work, some well-known inference procedures including testing and estimation are adjusted to accommodate noisy data that lead to nonidentically distributed sample. The main two cases addressed are the Poisson and the normal distributions. Both one and two sample cases are addressed. Other cases including the exponential and the Pareto distributions are briefly mentioned. In the Poisson case, the situation when the sample size is random is mentioned.

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Testing the equality of two Poisson means using the rate ratio

Cited by 55 publications

References 10 publications

Automated electronic reminders to facilitate primary cardiovascular disease prevention: randomised controlled trial

Automated electronic reminders to facilitate primary cardiovascular disease prevention: randomised controlled trial

Inference and Sample Size Calculations Based on Statistical Tests in a Negative Binomial Distribution for Differential Gene Expression in RNAseq Data

Inference for Noisy Samples

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