A Note on Testing Hypotheses about Trimmed Means

A well known result is that skewness can cause problems when testing hypotheses about measures of location, particulary when a one-sided test is of interest. Wilcox (1994) reports both theoretical and simulation results showing that when testing hypotheses about trimmed means, control over Type I error probabilities can be substantially better than methods for means. However, at least in some situations, control over the probability of a Type I error might still be judged to be inadequate. One way of adressing this concern is to combine trimmed means with the bootsrap method advocated by Westfall and Yuong (1993). This note reports simulation results indicating that there are situations where substantial improvements over Type I error probabilities are indeed obtained.     

Three Multiple Comparison Procedures for Trimmed Means

Two common goals when choosing a method for performing all pairwise comparisons of J independent groups are controlling experiment wise Type I error and maximizing power. Typically groups are compared in terms of their means, but it has been known for over 30 years that the power of these methods becomes highly unsatisfactory under slight departures from normality toward heavy-tailed distributions. An approach to this problem, well-known in the statistical literature, is to replace the sample mean with a measure of location having a standard error that is relatively unaffected by heavy tails and outliers. One possibility is to use the trimmed mean. This paper describes three such multiple comparison procedures and compares them to two methods for comparing means.     

Minimum Sample Size Ensuring Validity of Classical Confidence Intervals for Means of Skewed and Platykurtic Distributions

COCHRAN (1953) and BARTCH (1957) gave formulae for the magnitude of the sample size (n) ensuring the validity of the limiting normal distribution of the sample mean x(ⁿ) obtained from a non-normal distribution with marked asymmetry and kurtosis. These formulae have been checked empirically in this paper using (a) simulated data with given asymmetry and kurtosis and (b) real data gathered from a coronary heart disease study. We find that our results are in general agreement with Bartch's formula. However, in a number of cases, the asymptotic normal distribution is attained for smaller sample size than that required by Bartch's formula.     

A Note on Lancaster's Procedure for the Combination of Independent Events

Lancaster (1961) generalized Fisher's (1932) nonparametric procedure for combining independent p-values by transforming P_i from the i-th experiment to a chi-squared random variable with d_i degrees of freedom, with d_i not necessarily equal to 2. We explore the relationship between Lancaster's procedure and a weighted Lipták procedure (Koziol and Tuckwell, 1994) under which P_i is transformed to the standard normal scale. We investigate approximations to the null distribution of Lancaster's test procedure, chi-squared with d degrees of freedom. We find that the Cornish-Fisher (1960) expansions and the Lugannani-Rice (1980) saddlepoint approximations are quite accurate, for non-integral values of d, and for values of d as low as 20.     

Investigations on Some Attributes of the Likelihood Function for MPN Determination

The paper investigates the likelihood function to determine the MPN (Most Probable Number as a measure of concentration in the virology), dependent on several parameters. Taking only ‘probable’ result schemes into the MPN-tables they would become much shorter. There are suggested two conditions for the selection of the result schemes, given and compared by some tables together with a mathematical foundation of the number of the selected schemes. Some tables and a theorem about success probabilities of the result schemes point out their changes under different conditions (number of tubes, number of dilutions, dilution ratio), and make it possible to estimate success probabilities of result schemes not selected by the more restricted condition.     

A Stochastic Process and Generalized Distributions for the Study of Oviposition Evolution of a Parasite

This paper considers a generalized birth process {X^m(t), t > 0} and presents a new stochastic model for the number of eggs laid by a parasite on a host. Also, given an underlying distribution for the number of visits between parasites and a host, this distribution is generalized by the distribution of the number of eggs per visit laid on the host. If a certain number of eggs are already present on the host, a parasite such as a Japanese weevil, may avoid oviposition in subsequent visits (see JANARDAN (1980)) to the same host. A class of generalized distributions are presented to model such situations. The case of a single egg laying parasite and a Poisson distribution for the number of visits of the parasite to the same host yields a distribution of particular interest. In order to develop this model, certain lemmas are derived. Finally a characteristic property of this stochastic model is presented.     

Some Remarks on the Estimation of the Pair-Correlation Function for Point Processes

Doguwa (1990) proposed kernel based pair-correlation function estimators for Point processes. These estimators transport a part of the probability mass into the negative or left, to a hard-core distance. The reflection technique is used to provide an alternative estimator of the pair-correlation function, which drastically reduces the bias inherent in these estimators for the case of random and clustered point patterns. However, the drastic reduction in bias, is at the cost of a much larger variance.     

Unequivocal determination of sire allele origin for multiallelic microsatellites when only the sire and progeny are genotyped

The effect of a segregating economic trait locus (ETL) can be detected with the aid of a linked genetic marker, if specific alleles of each locus are in association among the individuals genotyped for the genetic marker. For dairy cattle this can be achieved by application of the ‘granddaughter design’. If only the sires and their sons are genotyped for the genetic markers, then the allele origin of sons having the same genotypes as their sires cannot be determined. Seven sires and 101 sons were genotyped for five microsatellites. The mean frequency of heterozygous sires was 77%. The mean number of alleles per locus was 8.2. Frequency of informative sons per locus ranged from 60% to 80% with a mean of 72%. With highly polymorphic microsatellites, at least 60% more grandsire families can be included in the analysis, and the number of sons assayed can be reduced by 40%, as compared to diallelic markers.     

An Estimate of the Variance of Estimators for Lead Time and Screening Benefit Time in Randomized Cancer Screening Trials

Variance estimators are derived for estimators of the average lead time and average benefit time due to screening in a randomized screening trial via influence functions. The influence functions demonstrate that these estimators are asymptotically equivalent to the mean difference, between the study and control case groups, in the appropriate survival times. For estimating benefit time, the survival time is measured since start of study; for estimating lead time, the survival time is measured since time of diagnosis. Asymptotic variances of these estimators can be calculated in a straightforward manner from the influence functions, and these variances can be estimated from actual trial data. The performance of the variance estimators is assessed via a simulated screening trial. The situation involving censored data is also discussed.     

Testing the correlation for clustered categorical and censored discrete time-to-event data when covariates are measured without/with errors

In the analysis of clustered categorical data, it is of common interest to test for the correlation within clusters, and the heterogeneity across different clusters. We address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models, for clustered nominal and ordinal categorical responses. We extend the results to accommodate clustered censored discrete time-to-event data. We next consider such tests in the situation where covariates are measured with errors. We propose using the SIMEX method to construct the score tests for the null hypothesis that the variance components are zero. Key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models, and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates. The asymptotic properties of the proposed tests are studied. We illustrate these tests by analyzing two data sets and evaluate their performance with simulations.     

Some Monte Carlo Studies on the Comparison of Several Means Under Heteroscedasticity and Robustness with Respect to Departure from Normality

By using Monte Carlo studies, this paper compares the Welch test, the James test and the Brown-Forsythe test for comparing several means under heteroscedasticity. It appears that all the tests are quite robust with respect to departure from normality. The Brown-Forsythe test is at least as good as the James test and the Welch test; but the differences are so small that the choice is immaterial for practical purposes.     

Commitment to relationships and preferences for femininity and apparent health in faces are strongest on days of the menstrual cycle when progesterone level is high

Previous studies of changes in women's behavior during the menstrual cycle have offered insight into the motivations underpinning women's preferences for social cues associated with possible direct benefits (e.g., investment, low risk of infection) and indirect benefits (e.g., offspring viability). Here we sought to extend this work by testing for systematic variation in women's preferences for male and female faces and in their attitudes to their romantic relationship during the menstrual cycle. In Study 1, we found partnered women's reported commitment to their romantic relationship and preferences for femininity in male and female faces were strongest on days of the menstrual cycle when progesterone levels are increased (and fertility is low). Happiness in relationships did not change across the cycle. In Study 2, we found that the effect of cycle phase on women's preference for feminine faces was independent of increased attraction to apparent health in faces during the luteal phase. Collectively, these findings are further evidence that women's preferences for social cues associated with possible direct benefits and commitment to relationships are strongest during conditions characterized by raised progesterone level, while attraction to men displaying cues associated with possible indirect benefits is strongest when women are most fertile.     

Metastatic SW620 colon cancer cells are primed for death when detached and can be sensitized to anoikis by the BH3-mimetic ABT-737

Anoikis, a Bax-dependent apoptosis triggered by detachment from the extracellular matrix, is often inhibited in metastatic cancer cells. Using a couple of isogenic human colon cancer cell lines derived either from the primary tumor (SW480) or from a lymph node metastasis (SW620), we found that only SW480 cells were sensitive to anoikis. Bim upregulation but not Mcl-1 degradation was determined to be a critical factor of anoikis initiation in SW480 cells. ERK-mediated phosphorylation targets Bim for ubiquitination and proteasomal degradation. A MEK inhibitor (PD0325901) was able to increase Bim expression in SW620 cells and to sensitize these cells to anoikis. Thus, in both cell lines anoikis is under the control of proteins of the Bcl-2 family. Most interestingly, the BH3-mimetic ABT-737 was found not only to increase the level of apoptosis in suspended SW480 cells but also to sensitize SW620 cells to anoikis. Accordingly, both cell lines cultured in suspension were found to be primed for death, as determined by the detection of Bcl-2:Bim and Bcl-xL:Bim complexes. In contrast, adherent SW480 and SW620 cells were resistant to ABT-737. This indicates that, whether or not they undergo anoikis, colon cancer cells that have detached from the extracellular matrix might go through a transient state, where they are sensitive to BH3 mimetics. This would confer to compounds such as Navitoclax or ABT-199 a therapeutic window where they could have anti-metastatic potential.