Influence of group sample size on statistical power of tests for quantitative data with an imbalanced design / 南方医科大学学报

OBJECTIVE@#To explore the relationship between sample size in the groups and statistical power of ANOVA and Kruskal-Wallis test with an imbalanced design.@*METHODS@#The sample sizes of the two tests were estimated by SAS program with given parameter settings, and Monte Carlo simulation was used to examine the changes in power when the total sample size varied or remained fixed.@*RESULTS@#In ANOVA, when the total sample size was fixed, increasing the sample size in the group with a larger mean square error improved the statistical power, but an excessively large difference in the sample sizes between groups led to reduced power. When the total sample size was not fixed, a larger mean square error in the group with increased sample size was associated with a greater increase of the statistical power. In Kruskal-wallis test, when the total sample size was fixed, increasing the sample size in groups with large mean square errors increased the statistical power irrespective of the sample size difference between the groups; when total sample size was not fixed, a larger mean square error in the group with increased sample size resulted in an increased statistical power, and the increment was similar to that for a fixed total sample size.@*CONCLUSIONS@#The relationship between statistical power and sample size in groups is affected by the mean square error, and increasing the sample size in a group with a large mean square error increases the statistical power. In Kruskal-Wallis test, increasing the sample size in a group with a large mean square error is more cost- effective than increasing the total sample size to improve the statistical power.

Power and sample size for health researchers: uma ferramenta para cálculo de tamanho amostral e poder do teste voltado a pesquisadores da área da saúde / Power and sample size for health researchers: a tool for calculating sample size and statistical power designed for health researchers

Nas próximas edições da seção de Bioestatística da revistaClinical & Biomedical Researchuma nova série de artigos será publicada abordando um assunto de grande importância ao planejar uma pesquisa: o tamanho de amostra mínimo necessário para atingir os objetivos do estudo. Nessa série será apresentado como calcular o tamanho de uma amostra usando a ferramenta PSSHealth(Power and Sample Size for Health Researchers), construído em linguagem R por meio do pacote Shiny, para diferentes tipos e objetivos de estudo, direcionado à pesquisadores da área da saúde, utilizando termos e conceitos comumente utilizados nesta área. Além disso, o pacote fornece uma sugestão de texto com as informações consideradas no cálculo, e como devem ser descritas, com a finalidade de minimizar problemas de interpretação por parte dos pesquisadores. Neste primeiro artigo será apresentada essa ferramenta desenvolvida pela Unidade de Bioestatística do Grupo de Pesquisa e Pós-Graduação do Hospital de Clínicas de Porto Alegre, que permite calcular não apenas o tamanho de amostra, mas também o poder de um teste de hipóteses. (AU)

In the next issues ofClinical and Biomedical Research, the Biostatistics section will introduce a new series of articles addressing a very important subject for research planning: the minimum sample size to achieve the aim of a study. This series will show how to calculate sample size using PSS Health (Power and Sample Size for Health Researchers). This tool was built using R language through the Shiny package. It can be used for different types of study and is designed for health researchers by using terms and concepts commonly used in this area. PSS Health also suggests a text with information considered in the calculation to minimize problems of interpretation by the researchers. In this first article, a general overview of PSS Health will be presented. This tool, which was developed by the Research and Graduate Group Biostatistics Unit of the Hospital de Clínicas de Porto Alegre, is useful not only to calculate sample size but also to determine power of a hypothesis test. (AU)

Role of Statistics in Multidisciplinary Research – With Reference to Psychological Research.

Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. It deals with all aspects of data. It is usually noticed that some routine words are given technical meanings in statistical parlance (e.g. “mean,” “normal,” “significance,” “effect,” and “power”). It is essential to resist the temptation of conflating their technical meanings. A failure to do so may have a lot to do with the ready acceptance of the “effect size” and “power” arguments in recent years. As, statistics is used (i) to describe data in terms of the shape, central tendency, and dispersion of their simple frequency distribution, and (ii) to make decisions about the properties of the statistical populations on the basis of sample statistics. Statistical decisions are made with reference to a body of theoretical distributions: the distributions of various test statistics that are in turn derived from the appropriate sample statistics. In every case, the calculated test statistic is compared to the theoretical distribution, which is made up of an infinite number of tokens of the test statistic in question. Hence, the “in the long run” caution should be made explicit in every probabilistic statement based on inferential statistics (e.g. “the result is significant at the 0.05 level in the long run”).Despite the recent movement to discourage psychologists from conducting significance tests, significance tests can be defended by (i) clarifying some concepts, (ii) examining the role of statistics in empirical research, and (iii) showing that the sampling distribution of the test statistic is both the bridge between descriptive and inferential statistics and the probability foundation of significance tests. The present paper discusses the critical issues of statistics in psychological research.

Revelation of shrunken or stretched binomial dispersion and public perception of situations which might spread AIDS or HIV.

Background: In 1985, the center for disease control coined the name: “Acquired Immune Deficiency Syndrome (AIDS)” to refer a deadly illness. The World Health Organization (WHO) estimated that about 33.4 million people were suffering with AIDS and two million people (including 330,000 children) died in 2009 alone in many parts of the world. A scary fact is that the public worry about situations which might spread AIDS according to reported survey result in Meulders et al. (2001). This article develops and illustrates an appropriate statistical methodology to understand the meanings of the data. Methods: While the binomial model is a suitable underlying model for their responses, the data mean and dispersion violates the model’s required functional balance between them. This violation is called over-under dispersion. This article creates an innovative approach to assess whether the functional imbalance is too strong to reject the binomial model for the data. In a case of rejecting the model, what is a correct way of warning the public about the spreads of AIDS in a specified situation? This question is answered. Results: In the survey data about how AIDS/HIV might spread according to fifty respondents in thirteen nations, the functional balance exists only in three cases: “needle”, “blood” and “sex” justifying using the usual binomial model (1). In all other seven cases: “glass”, “eating”, “object”, “toilet”, “hands”, “kissing”, and “care” of an AIDS or HIV patient, there is a significant imbalance between the dispersion and its functional equivalence in terms of the mean suggesting that the new binomial called imbalanced binomial distribution (6) of this article should be used. The statistical power of this methodology is indeed excellent and hence the practitioners should make use of it. Conclusion: The new model called imbalanced binomial distribution (6) of this article is versatile enough to be useful in other research topics in the disciplines such as medicine, drug assessment, clinical trial outcomes, business, marketing, finance, economics, engineering and public health.

An assessment of nurses' sufficient immunity when treating infectious patients using bumped-up binomial model.

Background: In times of an outbreak of a contagious deadly epidemic1-4 such as severe acute respiratory syndrome (SARS), the patients are quarantined and rushed to an emergency department of a hospital for treatment. Paradoxically, the nurses who treat them to become healthy get infected in spite of the nurses’ precautionary defensive alertness. This is so unfortunate because the nurses might not have been in close contact with the virus otherwise in their life. The nurses’ sufficient immunity level is a key factor to avert hospital site infection. Is it possible to quantify informatics about the nurses’ immunity from the virus? Methods: The above question is answered with a development of an appropriate new model and methodology. This new frequency trend is named Bumped-up Binomial Distribution (BBD). Several useful properties of the BBD are derived, applied, and explained using SARS data5 in the literature. Though SARS data are considered in the illustration, the contents of the article are versatile enough to analyze and interpret data from other contagious diseases. Results: With the help of BBD (3) and the Toronto data in Table 1, we have identified the informatics about the attending nurses’ sufficient immunity level. There were 32 nurses providing 16 patient care services. Though the nurses were precautionary to avoid infection, not all of them were immune to infection in those activities. Using the new methodology of this article, their sufficient immunity level is estimated to be only 0.25 in a scale of zero to one with a p-value of 0.001. It suggests that the nurses’ sufficient immunity level is statistically significant. The power of accepting the true alternative hypothesis of 0.50 immunity level, if it occurs, is calculated to be 0.948 in a scale of zero to one. It suggests that the methodology is powerful. Conclusions: The estimate of nurse’s sufficient immunity level is a helpful factor for the hospital administrators in the time of making work schedules and assignments of the nurses to highly contagious patients who come in to the emergency or regular wings of the hospital for treatment. When the approach and methodology of this article are applied, it would reduce if not a total elimination of the hospital site infections among the nurses and physicians.

Does smoking delay pregnancy? Data analysis by a tweaked geometric distribution answers.

Background: Smoking is generally known to be carcinogenic and health hazardous. What is not clear is whether the smoking impacts on the woman’s reproductive process. There have been medical debates on whether a woman in the child bearing age may delay her pregnancy due to smoking. A definitive conclusion on this issue has not been reached perhaps due to a lack of appropriate data evidence. The missing link to answer the question might be exercising a suitable model to extract the pertinent data information on the number of missed menstrual cycles by smoking women versus non-smoking women. This article develops and demonstrates a statistical methodology to answer the question. Methods: To construct such a needed methodology, a new statistical distribution is introduced as an underlying model for the data on the number of missed menstrual cycles by women who smoke. This new distribution is named Tweaked Geometric Distribution (TGD). Several useful properties of the TGD are derived and explained using a historical data in the literature. Results: In the data of 100 smokers and 486 non-smokers, on the average, smoking women missed 3.22 menstrual cycles and non-smoking women missed only 1.96 menstrual cycles before becoming pregnant. The smoking women exhibited more variation than the non-smoking women and it suggests that the non-smoking women are more homogeneous while the smoking women are more heterogeneous. Furthermore, the impairment level to pregnancy due to smoking among the 486 women is estimated to be 5% in a possible scale of zero to one. The 5% impairment level appears like a small amount, but its impact can be felt once it is cast in terms of fecundity. What is fecundity? The terminology fecundity refers the chance for a woman to become pregnant. The fecundity is 0.24 for smoking woman while it is 0.34 for non-smoking woman. The fecundity of a non-smoking woman is more than twice the fecundity of a smoking woman. Conclusion: The smoking is really disadvantageous to any one in general and particularly to a woman who wants to become pregnant.

Sample Size and Statistical Power Calculation in Genetic Association Studies

A sample size with sufficient statistical power is critical to the success of genetic association studies to detect causal genes of human complex diseases. Genome-wide association studies require much larger sample sizes to achieve an adequate statistical power. We estimated the statistical power with increasing numbers of markers analyzed and compared the sample sizes that were required in case-control studies and case-parent studies. We computed the effective sample size and statistical power using Genetic Power Calculator. An analysis using a larger number of markers requires a larger sample size. Testing a single-nucleotide polymorphism (SNP) marker requires 248 cases, while testing 500,000 SNPs and 1 million markers requires 1,206 cases and 1,255 cases, respectively, under the assumption of an odds ratio of 2, 5% disease prevalence, 5% minor allele frequency, complete linkage disequilibrium (LD), 1:1 case/control ratio, and a 5% error rate in an allelic test. Under a dominant model, a smaller sample size is required to achieve 80% power than other genetic models. We found that a much lower sample size was required with a strong effect size, common SNP, and increased LD. In addition, studying a common disease in a case-control study of a 1:4 case-control ratio is one way to achieve higher statistical power. We also found that case-parent studies require more samples than case-control studies. Although we have not covered all plausible cases in study design, the estimates of sample size and statistical power computed under various assumptions in this study may be useful to determine the sample size in designing a population-based genetic association study.

The Effect of Increasing Control-to-case Ratio on Statistical Power in a Simulated Case-control SNP Association Study

Generally, larger sample size leads to a greater statistical power to detect a significant difference. We may increase the sample size for both case and control in order to obtain greater power. However, it is often the case that increasing sample size for case is not feasible for a variety of reasons. In order to look at change in power as the ratio of control to case varies (1:1 to 4:1), we conduct association tests with simulated data generated by PLINK. The simulated data consist of 50 disease SNPs and 300 non-disease SNPs and we compute powers for disease SNPs. Genetic Power Calculator was used for computing powers with varying the ratio of control to case (1:1, 2:1, 3:1, 4:1). In this study, we show that gains in statistical power resulting from increasing the ratio of control to case are substantial for the simulated data. Similar results might be expected for real data.

Baseline adjustment for statistical efficiency on clinical controlled trial

In a clinical controlled trial involving repeated measures of continuous outcomes such as quality of life, distress, pain, activity level at baseline and after treatment, the possibilities of analyzing these outcomes can be numerous with quite varied findings. This paper examined four methods of statistical analysis using data from an outcome study of a clinical controlled trial to contrast the statistical power on those with baseline adjustment. In this study, data from a CCT with women with breast cancer were utilized. The experiment (n=67) and control (n=74) were about equal ratio. Four method of analysis were utilized, two using ANOVA for repeated measures and two using ANCOVA. The multivariate between subjects of the combined dependents variables and the univariate between subjects test were examined to make a judgement of the statistical power of each method. The results showed that ANCOVA has the highest statistical power. ANOVA using raw data is the least power and is the worst method with no evidence of an intervention effect even when the treatment by time interaction is statistically significant. In conclusion, ANOVA using raw data is the worst method with the least power whilst ANCOVA using baseline as covariate has the highest statistical power to detect a treatment effect other than method. The second best method as shown in this study was in using change scores of the repeated measures.