Algorithmic construction of optimal block designs for two-colour cDNA microarray experiments using the linear mixed effects model

ABSTRACT

In this study, methods for efficient construction of A-, MV-, D- and E-optimal or near-optimal block designs for two-colour cDNA microarray experiments with array as the block effect are considered. Two algorithms, namely the array exchange and treatment exchange algorithms together with the complete enumeration technique are introduced. For large numbers of arrays or treatments or both, the complete enumeration method is highly computer intensive. The treatment exchange algorithm computes the optimal or near-optimal designs faster than the array exchange algorithm. The two methods however produce optimal or near-optimal designs with the same efficiency under the four optimality criteria.     

The Variable Sampling Interval (VSI) in an Analysis of Taguchi's On-line Quality Monitoring Procedure for Variables

The procedure of on-line process control for variables proposed by Taguchi consists of inspecting the mth item (a single item) of every m items produced and deciding, at each inspection, whether the mean value is increased or not. If the value of the monitored statistic is outside of the control limits, one decides the process is out-of-control and the production is stopped for adjustment; otherwise, it continues. In this article, a variable sampling interval (with a longer L and a shorter m ≤ L) chart with two set of limits is used. These limits are the warning (±W) and the control (±C), where W ≤ C. The process is stopped for adjustment when an observation falls outside of the control limits or a sequence of h observations falls between the warning limits and the control limits. The longer sample interval is used after an adjustment or when an observation falls inside the warning limits; otherwise, the short sampling interval is used. The properties of an ergodic Markov chain are used to evaluate the time (in units) that the process remains in-control and out-of-control, with the aim of building an economic–statistical model. The parameters (the sampling intervals m and L, the control limits W and C and the length of run h) are optimized by minimizing the cost function with constraints on the average run lengths (ARLs) and the conformity fraction. The performance of the current proposal is more economical than the decision taken based on a sequence of length h = 1, L = m, and W = C, which is the model employed in earlier studies. A numerical example illustrates the proposed procedure.     

Race and Place: Exploring the Intersection of Inequity and Volunteerism Among Older Black and White Adults

Although the historical impact of racial segregation and ongoing health and economic inequities between older Black and White adults is well documented, little is known about the relationships among race, individual- and neighborhood-resources, and formal volunteering in later life. This study explores this intersection. Individual-level data from 268 respondents aged 55+ were collected in the St. Louis metropolitan area through paper-based mail surveys. Objective neighborhood data were obtained at the zip code level from secondary sources and matched with respondents. Using exploratory factor analysis, we constructed a 14-item environmental scale with 3 neighborhood dimensions (economic, social, and built environment). Older Black adults had lower levels of education; had fewer financial assets; lived in neighborhoods with less economic resources and lower built environment scores; and fewer formally volunteered when compared to older White adults. Individual resources (financial assets, health) and neighborhood resources (social and built environment) were positively associated with formal volunteering among older Black adults. Only individual resources (age, marital status, financial assets, health) were associated with formal volunteering among older White adults. A coherent set of policies that bolsters individual and environmental capacities may increase the rate of volunteerism among older black adults.     

Internationally adopted children's general and adoption‐specific stressors,coping strategies and psychological adjustment

We examined stress, coping and psychological adjustment of 68 children, aged 8–12, who were internationally adopted to Spain. Using the Kidcope, all children were asked about the most stressful general and adoption‐related problem they experienced and the use and effectiveness of various coping strategies when dealing with the problem. For all reported problems, the nature of the problem (personal, interpersonal, regarding others), the content, the degree of stress it created and its perceived controllability were analysed. Emotional and behavioural functionings were assessed with the Behaviour Assessment System for Children. About half of the children mentioned specific problems concerning the adoption, with inracial adoptees reporting less adoption‐related problems than transracial adoptees. For general and adoption‐related problems, interpersonal problems were mentioned most often. With regard to the content, ‘relationships’ and ‘victimization’ were mentioned most often for general and adoption‐related problems, respectively. Adoption‐related problems were appraised as less controllable. No differences emerged in terms of coping with general or adoption‐related problems except for ‘self‐criticism’. Overall, the children used many coping strategies and were generally well‐adjusted. Identifying the problems and coping strategies of adoptees is important in order to help these children and their families tackle these stressors.     

Indifference-zone ranking and selection: confidence intervals for true achieved P(CD)

In this paper we present procedures which attempt to allow experimenters to take at least partial advantage of more-favorable configurations of the population parameters (without, in the process, sacrificing precise probability statements about the inferences made) by obtaining confidence intervals for the true probability of a correct decision, regarded as a function of the true unknown underlying parameter values.     

Alternative moment approximations for berkson's minimum logit chi-squared estimator

Expressions are derived for the bias to order J^-1 , the variance to order J^-2 and the mean squared error to order J^-2 of Berkson's minimum logit chi-squared estimator where J is the number of distinct design points. These moment approximations are numerically compared to Monte Carlo estimates of the true moments and the moment approximations of Amemiya (1980) which are appropriate when the “average” number of observations per design point is large. They are used to compare the mean squared error of the minimum logit chi-squared estimator to that of the maximum likelihood estimator and to investigate the effect of bias on confidence intenrals constructed using the minimum logit chi-squared estimator.     

Estimation of linear models for field experiments

General mixed linear models for experiments conducted over a series of sltes and/or years are described. The ordinary least squares (OLS) estlmator is simple to compute, but is not the best unbiased estimator. Also, the usuaL formula for the varlance of the OLS estimator is not correct and seriously underestimates the true variance. The best linear unbiased estimator is the generalized least squares (GLS) estimator. However, t requires an inversion of the variance-covariance matrix V, whlch is usually of large dimension. Also, in practice, V is unknown.

We presented an estlmator [Vcirc] of the matrix V using the estimators of variance components [for sites, blocks (sites), etc.]. We also presented a simple transformation of the data, such that an ordinary least squares regression of the transformed data gives the estimated generalized least squares (EGLS) estimator. The standard errors obtained from the transformed regression serve as asymptotic standard errors of the EGLS estimators. We also established that the EGLS estlmator is unbiased.

An example of fitting a linear model to data for 18 sites (environments) located in Brazil is given. One of the site variables (soil test phosphorus) was measured by plot rather than by site and this established the need for a covariance model such as the one used rather than the usual analysis of variance model. It is for this variable that the resulting parameter estimates did not correspond well between the OLS and EGLS estimators. Regression statistics and the analysis of variance for the example are presented and summarized.     

Optimal fractional factorial designs for estimating interactions of one factor with all others: 3m Series

In some experimental situations, only one factor is expected to interact with other factors. Designs which permit estimation of all main effects and the interactions of one factor ‘With All Others’, are termed WAO designs. This paper discusses the existence and construction of s^m WAO designs. A series of WAO designs are presented for the 3^m factorial, for m = 6, 7, ... , 14. The p non-negligible effects are estimable in 9f^? runs, where f^? is the smallest integer such that 9f^? ≥p. These designs are determinant optimal within the class of parallel flats fractions and, except for the case f^? = 9, are new. They are ideally suited for sequential experiments.     

Institutions and Economic Outcomes: A Dominance-Based Analysis

An important issue in both welfare and development economics is the interaction between institutions and economic outcomes. While welfarists are typically concerned with how these variables contribute to overall wellbeing, empirical assessments of their joint contribution are limited. Development economists, on the other hand, have focused extensively on whether institutions cause or are caused by growth yet the relevant literature is still rife with debate. In this article, we use a notion of distributional dominance to tackle both the measurement of multivariate welfare and the evaluation of inter-temporal dependence without hindrance from the mix of discrete (political) and continuous (economic) variables in our data set. On the causality front, our results support the view that institutions promote growth more than growth promotes institutions. On the welfare front, we find that economic growth had a positive impact from 1960 to 2000 but declines in institutional quality over the earlier part of this period were sufficient to produce a decline in overall wellbeing until the mid-1970s. Subsequent improvements in institutions then reversed the trend and, ultimately, wellbeing in 2000 was higher than that in 1960.     

Hazards of stigma: the sexual and physical abuse of gay, lesbian, and bisexual adolescents in the United States and Canada

Some studies suggest lesbian, gay, and bisexual (LGB) teens are at higher risk than peers for violence at home, in school, and in the community. That can bring them into the child welfare system or services for runaway and homeless teens. This study compared self-reported experiences of sexual and physical abuse based on sexual orientation and gender in seven population-based surveys of youth. The authors used c2 and age-adjusted odds of abuse to compare bisexual to heterosexual, mostly heterosexual, and gay and lesbian students. They also provide case studies to illustrate the experiences of such youth.