Exact Multiple Comparisons of Three or More Regression Lines: Pairwise Comparisons and Comparisons with a Control

The problem of finding exact simultaneous confidence bounds for differences in regression models for k groups via the union‐intersection method is considered. The error terms are taken to be iid normal random variables. Under an assumption slightly more general than having identical design matrices for each of the k groups, it is shown that an existing probability point for the multivariate studentized range can be used to find the necessary probability point for pairwise comparisons of regression models. The resulting methods can be used with simple or multiple regression. Under a weaker assumption on the k design matrices that allows more observations to be taken from the control group than from the k‐1 treatment groups, a method is developed for computing exact probability points for comparing the simple linear regression models of the k‐1 groups to that of the control. Within a class of designs, the optimal design for comparisons with a control takes the square root of (k‐1) times as many observations from the control than from each treatment group. The simultaneous confidence bounds for all pairwise differences and for comparisons with a control are much narrower than Spurrier's intervals for all contrasts of k regression lines.     

Pairwise Comparisons in Each of Several Groups with Heterogenous Group Variances

Pairwise comparison procedures are frequently applied to analyze experimental results. In particular, practitioners in the area of medical researches often encounter situations which require these statistical techniques to compare various treatments. In this article, we focus on pairwise comparison procedures in a two‐factor design, where comparisons of one factor are made simultaneously for each level of another factor. For example, several new drugs to treat a certain cancer are being compared for both male and female patients. Previous research efforts were mainly devoted to models with homogeneous variances. The current paper is to address more common scenario where group variances are heterogeneous.     

Discriminating glacial races of burbot (Lota lota) by means of PCR‐RF‐SSCP (PRS) analysis of the mitochondrial control region

We used closely related haplotypes of the mitochondrial control region of burbot (Lota lota) (Teleostei; Gadidae) with known sequences to assess the sensitivity of a standardized PRS (PCR‐RF‐SSCP) approach. In total, 537 pairwise comparisons between PRS patterns were evaluated. Only seven mutations did not result in a detectable change that resulted in 11 pairwise comparisons (2%) with indistinguishable haplotypes. The haplotypes that could not be discriminated were always characteristic for a certain assemblage (glacial race). As such, this method provides a reliable alternative to direct sequencing for phylogeographic studies in case intrapopulation diversity is limited.     

Consistency of genome-wide associations across major ancestral groups

It is not well known whether genetic markers identified through genome-wide association studies (GWAS) confer similar or different risks across people of different ancestry. We screened a regularly updated catalog of all published GWAS curated at the NHGRI website for GWAS-identified associations that had reached genome-wide significance (p ≤ 5 × 10(-8)) in at least one major ancestry group (European, Asian, African) and for which replication data were available for comparison in at least two different major ancestry groups. These groups were compared for the correlation between and differences in risk allele frequencies and genetic effects' estimates. Data on 108 eligible GWAS-identified associations with a total of 900 datasets (European, n = 624; Asian, n = 217; African, n = 60) were analyzed. Risk-allele frequencies were modestly correlated between ancestry groups, with >10% absolute differences in 75-89% of the three pairwise comparisons of ancestry groups. Genetic effect (odds ratio) point estimates between ancestry groups correlated modestly (pairwise comparisons' correlation coefficients: 0.20-0.33) and point estimates of risks were opposite in direction or differed more than twofold in 57%, 79%, and 89% of the European versus Asian, European versus African, and Asian versus African comparisons, respectively. The modest correlations, differing risk estimates, and considerable between-association heterogeneity suggest that differential ancestral effects can be anticipated and genomic risk markers may need separate further evaluation in different ancestry groups.     

Mitochondrial genetic analyses suggest selection against maternal lineages in bipolar affective disorder.

Previous reports of preferential transmission of bipolar affective disorder (BP) from the maternal versus the paternal lines in families suggested that this disorder may be caused by mitochondrial DNA mutations. We have sequenced the mitochondrial genome in 25 BP patients with family histories of psychiatric disorder that suggest matrilineal inheritance. No polymorphism identified more than once in this sequencing showed any significant association with BP in association studies using 94 cases and 94 controls. To determine whether our BP sample showed evidence of selection against the maternal lineage, we determined genetic distances between all possible pairwise comparisons within the BP and control groups, based on multilocus mitochondrial polymorphism haplotypes. These analyses revealed fewer closely related haplotypes in the BP group than in the matched control group, suggesting selection against maternal lineages in this disease. Such selection is compatible with recurrent mitochondrial mutations, which are associated with slightly decreased fitness. Although such mismatch distribution comparisons have been used previously for analyses of population histories, this is, as far as we are aware, the first report of this method being used to study disease.     

Controlled group designs in biofeedback research: Ask, “what does the control group control for?”

The extant literature on the specific role of biofeedback in promoting skeletal muscular relaxation is reviewed and found deficient with respect to the use of properly controlled group outcome research. The review emphasizes the failure of commonly used control procedures to adequately control a number of potentially confounding variables. Strengths and weaknesses of three types of controlled group design (attention placebo, pseudofeedback, and altered contingency) are discussed with respect to their relative usefulness in controlling certain nonspecific or placebo effects in biofeedback research. Many published biofeedback studies failed to measure the credibility of control procedures or the subject's ability to discriminate different feedback contingencies. The studies reviewed suggest that the various control procedures used are not inert and are not equivalent with respect to their effects on control group behavior. The suggestion is made that the controlled group outcome design be accepted as the minimum requirement for testing the specific effects of biofeedback, and possible methods for improving control procedures are discussed.     

Multiple comparisons in the randomization analysis of designed experiments with growth curve responses

A randomization approach to multiple comparisons is developed for comparing several growth curves in randomized experiments. The exact Type I probability error rate for these comparisons may be prespecified, and a Type I error probability for each component test can be evaluated. These procedures are free of many of the standard assumptions for analyzing growth curves and for making multiple comparisons. An application of the procedure gives all pairwise comparisons among the mean growth curves associated with four treatments in an animal experiment using a Youden square design, where growth curves are obtained on monitoring hormone levels over time.     

Is the concept of “control group” valid? A quantitative comparison of behavior of caged baboon groups

Behavioral comparisons between six caged baboon groups indicate that the groups have consistent and similar behavioral attributes. At the same time it is possible to distinguish between classes of animals in each group such as males versus females and high status versus low status rank. Comparable results are obtained in both ANOVA and Kruskal-Wallis one-way analysis of variance by ranks. This investigation supports the assumption that baboon groups exhibit behaviors that are both consistent and predictable where environment and group composition are controlled. Thus there appears to be a strong species-appropriate set of behaviors. Behavioral plasticity and group variability might be due largely to a combination of environmental stimuli and the particular history of that group. Differential individual histories or idiosyncracies do not invalidate experimental designs which rely on randomization to structure control groups.     

Females drive primate social evolution

Within and across species of primates, the number of males in primate groups is correlated with the number of females. This correlation may arise owing to ecological forces operating on females, with subsequent competition among males for access to groups of females. The temporal relationship between changes in male and female group membership remains unexplored in primates and other mammalian groups. We used a phylogenetic comparative method for detecting evolutionary lag to test whether evolutionary change in the number of males lags behind change in the number of females. We found that change in male membership in primate groups is positively correlated with divergence time in pairwise comparisons. This result is consistent with male numbers adjusting to female group size and highlights the importance of focusing on females when studying primate social evolution.     

Nonlinear Analysis of Stride Interval Time Series in Gait Maturation Using Distribution Entropy

ObjectivesThis study aimed to investigate whether DistEn was capable of identifying complexity or irregularity for gait data and whether having low parameter-dependency sensitivity by comparing with the Approximate Entropy (ApEn) and Sample Entropy (SampEn).Material and methodsThe data were divided into three groups according to gait maturation. Firstly, the mean amplitude histogram, standard deviation (SD), and the power spectrum were calculated for each group. Secondly, ApEn, SampEn, and DistEn algorithms were calculated. Statistical analyses were then performed to compare groups.ResultsFor m=3 with M= 256 and M=512 parameters, DistEn showed a statistically significant difference between in pairwise comparisons between all groups (P_a, P_b, and P_c < 0.05). DistEn consistently decreased from Group1, to Group2, and to Group 3. For m=2 with r=0.30 values, SampEn showed a statistically significant difference only in pairwise comparisons between Group1 and Group3 (P_b < 0.05). For with m=3 and r=0.30 parameters, SampEn also showed a statistically significant difference in pairwise comparisons between Group1 and Group3 (P_c < 0.05) as well as Group2 and Group3 (P_c < 0.05) SampEn increased from Group1 to Group3 and from Group2 to Group3. There was not any statistically significant difference in pairwise comparisons of groups for ApEn. Furthermore, DistEn showed less parameter consistency than ApEn and SampEn.ConclusionDistEn showed the best performance in capture the complexity changes in gain patterns with growth.     

Simultaneous One-Sided Pairwise Comparisons in a Two-Way Design

Cheung and Chan (1996) provided a procedure for simultaneous two-sided pairwise comparisons of treatment means in a two-way design. Expanding on this earlier work, we develop a procedure where all such comparisons are instead one-sided. The new procedure is appropriate in situations where the treatment means are a priori ordered. The overall type I error rate for the simultaneous inferences is controlled at a designated level. Tables of upper percentage points of the test statistic are given to facilitate the implementation of our method. The application of the testing procedure is illustrated with an example from a medical study.     

Risk Sensitivity and the Paradox of Colonial Web-Building in Spiders

Group foraging is rare in spiders, occurring only where preyavailability is high. If colonial web-building increases individualprey capture rates as shown, why does group foraging not occurmore often where prey are scarce? Risk sensitivity may explainthis paradox, as variance in prey capture is reduced in groups;risk-averse spiders should join groups only when prey exceeda threshold level. Field studies show that group foraging variesas predicted between species, between populations of a singlespecies, and between sites within a population. However, recentmodels suggest the necessity of examining variance within individualsover time rather than between individuals within populations.Additionally, mechanisms responsible for variance reductionin colonial webs may be less effective than previously assumed.New field data suggest that while prey variance over time maybe somewhat less for individual spiders in groups than for solitaries,the relationship between colonial web-building and variancein prey capture is far more complex than originally thought.The influence of risk sensitivity on reproductive success andthe evolution of colonial web-building is discussed.     

Application of principal components analyses with constant character number in a study of the Bulbostylis/Fimbristylis (Cyperaceae) complex in Nigeria

Interrelationships between OTUs (operational taxonomic units) were assessed through comparisons based on a constant character number, using principal components analysis. This approach results in a uniform treatment of OTUs, despite variations in the number of definite entries for character states that could validly be made. In addition, the risk of distortion of the ordination scatter as a result of a bimodal frequency distribution of the number of characters available for comparisons is minimized. Appropriately applied, the approach also provides indications of the consistency of the features of the ordinations and reveals where more caution in interpretation is advisable.
The main analysis divided the OTUs into two unequal-sized groups, with a few intermediates; these were concluded to be more closely allied to the large than the small group. The significance of these groupings, in terms of their species contents, is discussed in relation to the method and to recent taxonomic treatments of the Bulbostylis/Fimbristylis complex. Some taxonomic conclusions must be tentative because of the limitations of the sample.     

Use of oral buprenorphine ('buprenorphine jello') for postoperative analgesia in rats--a clinical trial

Buprenorphine (0.1, 0.2, 0.3 or 0.4 mg/kg) in a flavoured gelatin base was administered preoperatively to rats undergoing a flank laparotomy. A control group of animals underwent surgery and received only flavoured gelatin. Body weight loss was significantly greater in the group which received no analgesia than in any of the analgesic-treated groups (P < 0.01). Food consumption was reduced significantly in all groups except in those animals which received 0.3 mg/kg buprenorphine. Water consumption was significantly reduced in the control (no analgesia) group (P < 0.001), but was not significantly depressed in the analgesic-treated groups (P > 0.05). Between-group comparisons did not show any significant difference between the different dose rates of analgesia used on either the change in body weight or the reduction in food or water consumption. The results of this study support the use of buprenorphine jelly for post-surgical analgesia in rats. This route of delivery is easy to use, and causes a minimum of stress to the rats.     

Genetic characterization of Escherichia coli populations from host sources of fecal pollution by using DNA fingerprinting

Escherichia coli isolates were obtained from common host sources of fecal pollution and characterized by using repetitive extragenic palindromic (REP) PCR fingerprinting. The genetic relationship of strains within each host group was assessed as was the relationship of strains among different host groups. Multiple isolates from a single host animal (gull, human, or dog) were found to be identical; however, in some of the animals, additional strains occurred at a lower frequency. REP PCR fingerprint patterns of isolates from sewage (n = 180), gulls (n = 133), and dairy cattle (n = 121) were diverse; within a host group, pairwise comparison similarity indices ranged from 98% to as low as 15%. A composite dendrogram of E. coli fingerprint patterns did not cluster the isolates into distinct host groups but rather produced numerous subclusters (approximately >80% similarity scores calculated with the cosine coefficient) that were nearly exclusive for a host group. Approximately 65% of the isolates analyzed were arranged into host-specific groups. Comparable results were obtained by using enterobacterial repetitive intergenic consensus PCR and pulsed-field gel electrophoresis (PFGE), where PFGE gave a higher differentiation of closely related strains than both PCR techniques. These results demonstrate that environmental studies with genetic comparisons to detect sources of E. coli contamination will require extensive isolation of strains to encompass E. coli strain diversity found in host sources of contamination. These findings will assist in the development of approaches to determine sources of fecal pollution, an effort important for protecting water resources and public health.     

Progressive multiple alignment using sequence triplet optimizations and three-residue exchange costs

In this paper we demonstrate a practical approach to construct progressive multiple alignments using sequence triplet optimizations rather than a conventional pairwise approach. Using the sequence triplet alignments progressively provides a scope for the synthesis of a three-residue exchange amino acid substitution matrix. We develop such a 20 x 20 x 20 matrix for the first time and demonstrate how its use in optimal sequence triplet alignments increases the sensitivity of building multiple alignments. Various comparisons were made between alignments generated using the progressive triplet methods and the conventional progressive pairwise procedure. The assessment of these data reveal that, in general, the triplet based approaches generate more accurate sequence alignments than the traditional pairwise based procedures, especially between more divergent sets of sequences.     

On the Numerical Availability of Multiple Comparison Procedures

In the past many multiple comparison procedure were difficult to perform. Usually, such procedures can be traced back to studentized multiple contrast tests. Numerical difficulties restricted the use of the exact procedures to simple, commonly balanced, designs. Conservative approximations or simulation based approaches have been used in the general cases. However, new efforts and results in the past few years have led to fast and efficient computations of the underlying multidimensional integrals. Inferences for any finite set of linear functions of normal means are now numerically feasible. These include all‐pairwise comparisons, comparisons with a control (including dose‐response contrasts), multiple comparison with the best, etc. The article applies the numerical progress on multiple comparisons procedures for common balanced and unbalanced designs within the general linear model.     

Estimating the proportion of identifiable individuals and group sizes in photographic identification studies

Simple Bayesian statistical models are introduced to estimate the proportion of identifiable individuals and group sizes in photographic identification, or photo‐ID, studies of animals that are found in groups. The models require a simple random photographic sampling of animals, where the photographic captures are treated as sampling with replacement within each group. The total number of images, including those that cannot be identified, and the number of images that contain identifiable individuals are used to make inference about the proportion of identifiable individuals within each group and as the population when a number of groups are sampled. The numbers of images for individuals within each group are used to make inference about the group size. Based on analyses of simulated and real data, the models perform well with respect to accuracy and precision of posterior distributions of the parameters. Widths of posterior intervals were affected by the number of groups sampled, sampling duration, and the proportion of identifiable individuals in each group that was sampled. The structure of the models can accommodate covariates, which may affect photographic efficiency, defined in this study as the probability of photographically capturing individuals.     

Mixed-phenotype grouping: the interaction between oddity and crypsis

Aggregations of different-looking animals are frequently seen in nature, despite well-documented selection pressures on individuals to maintain phenotypically homogenous groups. Two well-known theories, the ‘confusion effect’ (reduced ability of a predator to accurately target an individual in a group) and the ‘oddity effect’ (preferential targeting of phenotypically distinct, ‘odd’, individuals) act together to predict the evolution of behaviours in prey that lead to groups of animals that are homogeneous in appearance. In contrast, a recently proposed mechanism suggests that mixed groups could be maintained if one species in a mixed group is more conspicuous against the habitat than the other, as confusion effects generated by the conspicuous species impede predator targeting of the cryptic species; thus, cryptic species benefit from association with conspicuous ones. We test these contrasting predictions from the perspective of both predators and prey, and show that cryptic individual Daphnia are at reduced risk of predation from three-spine sticklebacks Gasterosteus aculeatus when in mixed-phenotype groups, a risk that is reduced further as the number of conspicuous individuals increases, supporting the hypothesis for the evolution of mixed groups. In contrast, while the preference for associating with colour-matched conspecifics by mollies (Poecilia sphenops) was reduced when they were cryptic, we found no evidence for active association with conspicuous conspecifics. We conclude that prey animals must balance the relative risks of oddity and conspicuousness in their social decisions, and that this could potentially lead to the evolution of mixed-phenotype grouping as a response to predation risk alone.     

Natural skip oviposition of the mosquito Aedes aegypti indicated by codominant genetic markers

This study examines the use of codominant restriction fragment length polymorphism (RFLP) markers to estimate the number of sibling families found within and among oviposition sites used by the mosquito Aedes aegypti (L) (Diptera: Culicidae). Estimates were made using pairwise relatedness (rxy) calculations based on alleles shared between individuals. Genotypes for eight laboratory mosquito families were determined at six RFLP loci and the observed allele frequencies were used to generate simulated distributions of rxy from full-sibling and unrelated pairs of individuals. The midpoint (mp) between the means of the pairwise rxy distributions was used to discriminate full-sibling families from unrelated families. Clusters of individuals with rxy values higher than the mp value were grouped as putative sibling families. This method was tested by calculating actual rxy for all pairwise comparisons of the known laboratory full-sibling and paternal half-sibling families, followed by upgma cluster analysis to group sibling families. The technique was then used for sibling estimations on wild caught mosquitoes collected at three locations in Trinidad, West Indies. From field populations, 35 families were estimated among 122 individuals tested with an average of 6.2 families per container. Members of 19 predicted families clustered as groups across multiple containers, providing molecular evidence for skip-oviposition behaviour in Ae. aegypti females, whereby individual females oviposit in more than one container.