Tables of the critical values for simultaneous and sequential Bonferroni-z-tests

Simultaneous and sequential BONFERRONI -tests (HOLM , 1979) are going to replace the traditional global tests (ANOVA, PEARSON -χ²). To facilitate (sequential) BONFERRONI -evaluation, BONFERRONI -test limits for the normal distribution are tabulated for r = 1(1)100, 100(2)300, 300(5)800, 800(10)1600, 1600(20)3200, 3200(50)10000 tests and for some conventional alphas in one- and two-sided alternatives.     

Discrimination with a Mixture Population

The regions of classification when one of the populations is a mixture of two or more multivariate normal populations are found to be defined by the functions of the linear discriminant functions used for discriminating between the components of the mixture population and the other multivariate normal population.     

Further Study on the Statistical Test to Detect Spatial Pattern

In the study of spatial patterns, the statistic I' = (n — 1)s²/x was commonly used. In this paper, we found that x — s² has an approximated normal distribution with zero mean if the x_i's (i = 1 to n) are independent identically distributed Poisson variables. Based on this conclusion, the hypothesis that a point pattern is completely random can be tested directly. And a method for the test of spatial patterns was proposed which can be sued as an alternative to the Chi-square based dispersion index test.     

Robustness of Sequential Tests for Means

Three sequential tests of the null hypothesis, μ = μ₀, versus an alternative of the form (μ ? μ₀)²= =σ²d² are compared for different forms of violation of the underlying normal assumption. 10000 samples were simulated for d=0.6; 1.0 and 1.6 (σ² = 1), four (α, β)-combinations and seven alternative distributions. The results show that for small d-values one test is robust for α and another for β. For large d all tests can be used.     

The Use of Multiple Outcomes Analysis in Neurotoxicity: An Example from the New Zealand Study of Offspring of Mothers Exposed to Methyl Mercury

Neurotoxicity has become an important area in the study of the risk to children of noncarcinogens. Many of the tests used to evaluate neurotoxic effects in neurotoxic studies are psychometric tests to assess cognitive, motor, and perceptual performance in individuals in order to determine the presence of psychological problems, impaired educational achievement, or neurological abnormalities. The underlying assumption of these procedures are that a test performance deficit is indicative of a neurological disability, and that such disability derives from the prenatal exposure to an offending substance. The usual analytic paradigm for discerning environmental impacts is to analyze the scores of a particular subtest in a battery taken separately as the dependent variable with regression analysis, which adjusts for cultural background, educational level, and socioeconomic status. The impact of this analysis is to determine the correlation of each of the psychometric test results to exposure. We show a statistical method to simultaneously analyze the multiple outcomes of many tests using General Estimating Equations (GEE) to determine if a correlation exists between the global measure of all these tests and exposure adjusted for covariates of interest and the correlation among the dependent psychometric variables. We show the application of this method to the results of children whose mothers were exposed to mercury during pregnancy.     

A New Statistical Goodness-of-Fit Test Based on Graphical Representation

A statistical goodness-of-fit test, based on representing the sample observations by linked vectors, is developed. The direction and the length of the linked vectors are defined as functions of the expected values of the order statistics and sample order statistics, respectively. The underlying method can be used to test distributional assumptions for any location-scale family. A test statistic Q_n is introduced and some of its properties are studied. It is shown that the proposed test can be generalized to test if two or more independent samples come from the same distribution. The test procedure provides a graphical method of identifying the true distribution when the null hypothesis is rejected.     

Bayesian estimation of multivariate normal mixtures with covariate‐dependent mixing weights,with an application in antimicrobial resistance monitoring

Bacteria with a reduced susceptibility against antimicrobials pose a major threat to public health. Therefore, large programs have been set up to collect minimum inhibition concentration (MIC) values. These values can be used to monitor the distribution of the nonsusceptible isolates in the general population. Data are collected within several countries and over a number of years. In addition, the sampled bacterial isolates were not tested for susceptibility against one antimicrobial, but rather against an entire range of substances. Interest is therefore in the analysis of the joint distribution of MIC data on two or more antimicrobials, while accounting for a possible effect of covariates. In this regard, we present a Bayesian semiparametric density estimation routine, based on multivariate Gaussian mixtures. The mixing weights are allowed to depend on certain covariates, thereby allowing the user to detect certain changes over, for example, time. The new approach was applied to data collected in Europe in 2010, 2012, and 2013. We investigated the susceptibility of Escherichia coli isolates against ampicillin and trimethoprim, where we found that there seems to be a significant increase in the proportion of nonsusceptible isolates. In addition, a simulation study was carried out, showing the promising behavior of the proposed method in the field of antimicrobial resistance.     

Testing Equality of Correlated Means in the Presence of Unequal Variances and Missing Values

Several statistics are proposed for testing the hypothesis of equality of the means of bivariate normal distribution with unknown variances and correlation coefficient when observations are missing on both variatea. The null distributions of the statistics are approximated by well-known distributions. The empirical sizes and powers of the statistics are computed and compared with paired t test and some of the known statistics based on available data. The comparisons support the use of two of the statistics proposed in this paper.     

On Comparing Correlated Means in the Presence of Incomplete Data

Two statistics are proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on both variates. One of the statistics reduces to the one proposed by Bhoj (1978, 1984) when the unpaired observations on the variates are equal. The distributions of the statistics are approximated by well known distributions under the null hypothesis. The empirical powers of the tests are computed and compared with those of some known statistics. The comparison supports the use of one of the statistics proposed in this paper.     

Proposal of k Sample Tests for Bivariate Censored Data for Nondecreasing Ordered Alternatives

Tests are introduced which are designed to test for a nondecreasing ordered alternative among the survival functions of k populations consisting of multiple observations on each subject. Some of the observations could be right censored. A simulation study is conducted comparing the proposed tests on the basis of estimated power when the underlying distributions are multivariate normal. Equal sample sizes of 20 with 25% censoring, and 40 with both 25% and 50% censoring are considered for 3 and 4 populations. All of the tests hold their α‐values well. A recommendation is made as to the best overall test for the situations considered.     

Assessment of the efficacy of disinfectants on surfaces

The Literature on testing the efficacy of disinfectants covers a century. Most predominant and standardized are the so called suspension tests that allow for the quantitative estimation of the microbicidal activity (log reduction factors) of disinfectants on test organisms suspended in solutions of these products.Since the outcome of suspension tests might be a poor predictor for the efficacy of a disinfectant under practical circumstances, especially with regard to bacteria attached to surfaces, a variety of test procedures have been designed to mimic those conditions. Within the framework of CEN/TC 216 a quantitative surface test has been developed to assess the activity of disinfectants on bacteria or fungi attached to steenless steel surfaces. Preliminary data suggest that covering a dried inoculum with disinfectant without any further mechanical action to improve contact between organisms and disinfectant, will usually result in lower reduction factors than those obtained with suspension tests. Comparative testing further suggests that by applying mechanical action, with the effect of resuspending cells in the liquid on the surface,—similar to mopping, brushing etc.— will result in higher reduction rates. Although not unexpected these findings emphasize the importance of designing test methods based on practical applications of disinfectants.     

On a restricted occupancy model and its applications

With the multivariate hypergeometric distribution as a background certain occupancy distributions useful in practical applications are derived. More specifically it is assumed that a sample of n individuals is drawn from a population consisting of m types with r individuals in each type, (i) without replacement and (ii) by returning the selected individual in the population and with it another individual of the same type. The distributions of the number Z of distinct types observed in the sample are obtained in both cases in terms of the numbers. Assuming, in addition to the m equiprobable types of individuals, the existence of a control type, say, with s individuals, the joint distribution of the number U of distinct types observed in the sample and the number V of individuals of the control type present in the sample is obtained in terms of the numbers C(n, k, r) and the marginal distribution of U in terms of the Gould-Hopper numbers. Using these distributions minimum variance unbiased estimators of the number m of types are derived. Moreover small sample tests based on the zero frequency are constructed.     

Multiple imputation in the presence of an incomplete binary variable created from an underlying continuous variable

Multiple imputation (MI) is used to handle missing at random (MAR) data. Despite warnings from statisticians, continuous variables are often recoded into binary variables. With MI it is important that the imputation and analysis models are compatible; variables should be imputed in the same form they appear in the analysis model. With an encoded binary variable more accurate imputations may be obtained by imputing the underlying continuous variable. We conducted a simulation study to explore how best to impute a binary variable that was created from an underlying continuous variable. We generated a completely observed continuous outcome associated with an incomplete binary covariate that is a categorized version of an underlying continuous covariate, and an auxiliary variable associated with the underlying continuous covariate. We simulated data with several sample sizes, and set 25% and 50% of data in the covariate to MAR dependent on the outcome and the auxiliary variable. We compared the performance of five different imputation methods: (a) Imputation of the binary variable using logistic regression; (b) imputation of the continuous variable using linear regression, then categorizing into the binary variable; (c, d) imputation of both the continuous and binary variables using fully conditional specification (FCS) and multivariate normal imputation; (e) substantive-model compatible (SMC) FCS. Bias and standard errors were large when the continuous variable only was imputed. The other methods performed adequately. Imputation of both the binary and continuous variables using FCS often encountered mathematical difficulties. We recommend the SMC-FCS method as it performed best in our simulation studies.     

Simultaneous Statistical Inference Concerning the Standardized Mortality Ratios (SMB) of Several Strata in an Epidemiologic Study

In the present paper, simultaneous prediction intervals are constructed for some mortality measures involving real data in a recent retrospective epidemiologic study of a cohort of man-made mineral fiber workers. The object is to compare a test population with a standard population in which the workers are exposed to several levels (say K) of a suspected carcinogen and the number of deaths in the K exposure groups are recorded. The SMR is chosen as a mortality measure for this comparison. If the total number of deaths d. in the entire study is known, the number of deaths in the various strata become dependent random variables. Using univariate statistical procedures to test the significance of the individual SMR's is inappropriate and may give misleading conclusions. The present paper shows how to test the simultaneous statistical significance of the SMR's of the K exposure groups, i.e., to test the simultaneous null hypothesis H_o : E(SMR₁) = E(SMR₂) =…E(SMR_k) = 100. If the null hypothesis H_o is rejected, it is shown how to identify the SMR (or the SMR's) which contributed to the rejection of H_o. The power function of such a test is also constructed for some simple and useful alternative hypotheses.