Epidemiological Studies Concerning The Risk Difference Of A Number Of Issues To Study

Statistical inference of some problems about epidcmiological study are analysized and discussed from the perspective of contingency table in this article.Disease prevalence study is an important topic in epidemiological study, and the study is based on data that is obtained by classifying subjects on whether a disease has been contracted. Classification can be done by high-cost gold standard tests or low-cost screening tests, but the latter are subject to misclassification of subjects. As a compromise between the two, double sampling method is frequently applied to obtain data. When the sample size is not large or samll, based on a 2×2 contingency table and a bernoulli trial, (ⅰ) test procedures for disease prevalence under a double-sampling scheme are considered, the Wald-type test statistic with sample variance, the Wald-type test statistic using the constrained maximum likelihood estimators of parameters for the variance estimation, score and likelihood ratio test statistics are proposed to test this hypothesis testing; performance of the asymptotic and the approximate unconditional test produres based on the above test statistics are compared via empirical type I error rates and actual powers, reliable test procedures are proposed under the small sample design; (ⅱ) confidence intervals for the disease prevalence are considered, the asymptotic, approximate unconditional and the bootstrap methods for the confidence interval construction are proposed, performance of the proposed confidence intervals is evaluated via the coverage probability, expected width, ratio of the mesial non-coverage to non-coverage probability; (ⅲ) we propose two kinds of approximate sample size formulas, the first is derived to guarantee a pre-specified power of a hypothesis test at certain significance level while the second is developed to bound the width of a confidence interval with specified confidence level, and the numerical algorithms for sample size calculation are proposed when we can not obtain the explicit expression. The accuracy of the various formulas derived to control their powers is evaluated via empirical powers and sizes, the accuracy of the formulas derived to control their interval widths is evaluated via empirical coverage probabilities and expected widths. At last, a data about the aplastic anaemia patients is used to demonstrate the methodologies proposed in this article. Empirical results show that (ⅰ)the approximate unconditional method usually pro-duces a more satisfactory empirical typeⅠerror rate and power than its asymptotic coun-terpart. The results also suggest that two of the test statistics - the score test and the Wald test with the variance of the estimates of disease prevalence estimated using the null hypothesis (for simplity, it is denoted as Wald-2) - outperform the others; (ⅱ) the asymp-totic and approximate unconditional score-based confidence intervals and Wald-2-based confidence intervals outperform the others in the sense that their coverage probabilities are close to the nominal confidence level, and their ratios of the mesial non-coverage to non-coverage probabilities lie in [0.4,0.6];(ⅲ) the sample size formulas based on the Wald-2 and score test statistics outperform the others, are hence recommended.In stratified matched-pair studies, the risk difference between two proportions is one of the most frequently used indices in comparing efficiency of two treatments or diagnostic tests. It is of interest to test whether the risk differences for different strata are significantly different from each'other, and which group leads to a significant difference. To address all the above questions with a simple method in a simple step, based on multiple 2×2 contingency tables, we consider the simultaneous confidence intervals of risk differences in stratified paired-designs. we present five simultaneous confidence intervals based on the 'Wald','Wilson-Score' and 'Agresti-coull' simultaneous confidence intervals and two Bootstrap simultaneous confidence intervals for risk differences. Performance of the proposed intervals is evaluated via the empirical coverage probability, expected width and the ratio of the mesial non-coverage to non-coverage probability. At last, a real example from the abnormal parathyroid tissue study is used to illustrate the proposed methodologies.Empirical results show that (ⅰ) the hybrid simultaneous confidence intervals outper-form the non-hybrid simultaneous confidence intervals;(ⅱ) the hybrid simultaneous confi-dence intervals based on median estimator outperform those based on maximum likelihood estimator; (ⅲ) the hybrid simultaneous confidence intervals with'Wilson score' interval and 'Agresti coull' interval, and the bootstrap t-percentile simultaneous interval based on the median unbiased estimators behave satisfactorily for small to large sample sizes in the sense that their empirical coverage probabilities are close to the pre-specified nominal confidence level, and their ratios of the mesial non-coverage to non-coverage probabilities lie in [0.4,0.6], are hence recommended.In otolaryngologic (or ophthalmologic) studies, it is of interest to know whether reti-nal features (e.g. exudates) are associated with successful surgical retinal reattachment, or whether antibiotics for the treatment of otitis media with effusion (OME) have differ-ent cure rates. Accounting for small sample design, sparse data structure and intrclass correlation, we consider the noninferiority or equivalence testing for success rates of two surgerys or cure rates of two antibiotics under the bilateral design, and propose six test statistics based on a 3 x 2 contingency table, i.e., the score statistic, the likelihood ratio statistic, two Wald statistics based on independence model, two Wald statistics based on dependence model. Sample size formulas are derived to achieve a pre-specified power of a statistical test at a pre-chosen significance level, and sample size formulas are derived to controlling a pre-specified width of a confidence interval at pre-chosen a confidence level base on the above test statistics. The accuracy of the power-based formulas is evaluated via the empirical powers and sizes, and the accuracy of the interval-width-based formulas is evaluated via empirical coverage probabilities and widths. A otitis media with effusion (OME) data is used to to demonstrate the methodologies.Empirical results show that (ⅰ)the sample size formulas that derived from the in-dependent model (e.g., Wald test under independent model) are not recommended for applications, because its actual power is not satisfactorily close to the desired power level and the actual size will increase with the correlation coefficient; (ⅱ) for the sample size formulas that derived from the dependent model (e.g., Wald test under dependent model and score test),their actual sizes are satisfactorily close to the nominal level; (ⅲ)the sam-ple size formula for Wald statistic (Rosner statistic) based on the dependence assumption is highly recommended in the sense that its actual power or confidence interval width is satisfactorily close to the desired power level or interval width.In some clinical trial studies, it is of interest to know whether the successful surgical retinal reattachment, or the successful treatment of the antibiotics is associated with the ages of subjects or the levels of surgeons. To address the above question, we regard ages as strataficaiton variables to consider the equivalence testing based on the differences of two proportions under multiple 3×2 contingency tables:(ⅰ)the adjusted score test statistic based on Tarone homogeneity score and WLS test statistic for testing homogeneity of dif-ferences of two proportions, score-based and summary confidence intervals of the common difference of two proportions in a stratified bilateral-sample design are derived; (ⅱ)under the homogeneity hypothesis, stratified and non-stratified score statistic and Wald-type statistics are presented to test the equivalence for the differences of two proportions, the asymptotic and the approximate unconditional tests based on the above statistics are discussed and the corresponding power functions and sample size formulas are presented. Performance of the proposed methodologies is evaluated via the simulations same as the precede chapters. A multiple-center otitis media with effusion (OME) data is used to demonstrate the methodologies.Empirical results show that (ⅰ)for the homogeneity test based on the adjusted score test statistic and WLS test statistic, their empirical typeⅠerror rates are close to the pre-chosen nominal level with high powers; (ⅱ) two confidence intervals demonstrate rea-sonably good coverage property and short interval widths; (ⅲ) the stratified statistics outperform the non-stratified statistics in the sense that their empirical typeⅠerror rates are closer to the nominal level with higher powers; (ⅳ) the stratified score statistic and Wald-type statistic based on dependence assumption outperform other statistics in the sense that their empirical typeⅠerror rates are close to the pregiven nominal level; (ⅴ)the sample size formula derived from the Wald-type statistic under dependence assumption is rather accurate in the sense that its empirical power is pretty close to the pregiven power and its actual size is close to the pre-specified nominal level.We focus on some problems of epidemiological study in this article, however, the research results can be used in the statistical inference about contingency tables, and also can be used in pharmaceutical areas etc..