Selection of the Better of Two Treatments when They May Not be Equivalent

A procedure for selecting the better of two treatments which allows for the possibility of non-selection when the treatments appear to be equivalent (that is, similar) is presented. The proposed procedure is a modification of the indifference zone approach. It is assumed that the treatments are compared with respect to a continuous response variable, which has a normal or a two-parameter exponential distribution. For the normal distribution, each of the parameters is considered as the ranking parameter. For the two-parameter exponential distribution, the guarantee time (location parameter) is the ranking parameter. The values of the estimates of the ranking parameters and the observed distance between these estimates are used in this selection procedure.     

Subset Selection Procedures for Randomized Designs

Starting from the principle that there exists a randomization procedure that assigns treatments to experimental units, four subset selection rules for the problem of selecting the best treatment from a set of different treatments are proposed. Two of these are extensions of already existing subset selection procedures, which were defined for unbalanced designs, and need a separate selection constant for each individual treatment. The other two rules proposed are new and need only one selection constant for all treatments. The various procedures are compared, and illustrated by application to a plant breeding variety trial.     

A Selection and Testing Procedure for Comparing Several Experimental Treatments with a Control

We consider a selection and testing procedure for comparing k experimental treatments with a control treatment where the treatments are assumed to be normally distributed with unknown means and a common, unknown variance. Stein‐type sampling is used in the selection phase to screen for an experimental treatment that exhibits evidence of being better than the control treatment and each of the other experimental treatments, where better is defined in terms of the largest mean. In the testing phase, the best experimental treatment is compared to the control using a hypothesis test. If no experimental treatment indicates that it is an improvement over the control during the selection phase, our procedure allows for early termination. We provide definitions of level and power appropriate for our hybrid procedure and compute procedure parameters required to implement our procedure.     

An Integrated Formulation for Comparing Treatments with Binary Response with a Control

The problem of comparing k(≧2) bernoulli rates of success with a control is considered. An one-stage decision procedure is proposed for either (1) choosing the best among several experimental treatments and the control treatment when the best is significantly superior or (2) selecting a random size subset that contains the best experimental treatment if it is better than the control when the difference between the best and the remaining treatments is not significant. We integrate two traditional formulations, namely, the indifference (IZ) approach and the subset selection (SS) approach, by seperating the parameter space into two disjoint sets, the preference zone (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the best experimental treatment for a correct selection (CS₁) but in the IZ we define any selected subset to be correct (CS₂) if it contains the best experimental treatment which is also better than the control. We propose a procedure R to guarantee lower bounds P₁* for P(CS₁≧PZ) and P₂* for P(CS₂≧IZ) simultaneously. A brief table on the common sample size and the procedure parameters is presented to illustrate the procedure R.     

Quantifying the magnitude of baseline covariate imbalances resulting from selection bias in randomized clinical trials

Selection bias is most common in observational studies, when patients select their own treatments or treatments are assigned based on patient characteristics, such as disease severity. This first-order selection bias, as we call it, is eliminated by randomization, but there is residual selection bias that may occur even in randomized trials which occurs when, subconsciously or otherwise, an investigator uses advance knowledge of upcoming treatment allocations as the basis for deciding whom to enroll. For example, patients more likely to respond may be preferentially enrolled when the active treatment is due to be allocated, and patients less likely to respond may be enrolled when the control group is due to be allocated. If the upcoming allocations can be observed in their entirety, then we will call the resulting selection bias second-order selection bias. Allocation concealment minimizes the ability to observe upcoming allocations, yet upcoming allocations may still be predicted (imperfectly), or even determined with certainty, if at least some of the previous allocations are known, and if restrictions (such as randomized blocks) were placed on the randomization. This mechanism, based on prediction but not observation of upcoming allocations, is the third-order selection bias that is controlled by perfectly successful masking, but without perfect masking is not controlled even by the combination of advance randomization and allocation concealment. Our purpose is to quantify the magnitude of baseline imbalance that can result from third-order selection bias when the randomized block procedure is used. The smaller the block sizes, the more accurately one can predict future treatment assignments in the same block as known previous assignments, so this magnitude will depend on the block size, as well as on the level of certainty about upcoming allocations required to bias the patient selection. We find that a binary covariate can, on average, be up to 50% unbalanced by third-order selection bias.     

Selection of odorants for memory tests on the basis of familiarity,perceived complexity,pleasantness, similarity and identification

In a procedure for the selection of two equivalent sets of familiar and two equivalent sets of unfamiliar odours for use in odour memory studies, 24 na?ve subjects were first asked to rate the familiarity, perceived complexity and pleasantness of 54 a priori unfamiliar odours and 57 a priori familiar odours and to identify the latter. After selection of the 40 most familiar and the 40 least familiar odours, the subjects sorted each of these two sets into groups of similar odours. Their results were analysed by multidimensional scaling and cluster analysis and each set was divided into two recognition sets that had the same degree of similarity between target and distractor odours and that had similar values of familiarity, pleasantness, perceived complexity (familiar and unfamiliar sets) and identifiability (familiar sets). Finally, recognition tasks were performed in order to check the equivalence in memory performance of both the two familiar and the two unfamiliar recognition sets.     

The significance for breeding of linear regression analysis of genotype-environment interactions.

Methods of regression analysis of genotype-environment interaction are considered in relation to existing theory dealing with the relative efficiencies of selection for general or specific adaptation to the environment, and the choice of environments for assessment. The two alternative models is involving regression on to environmental effects (model 2) or genotypic effects (model 3) are equivalent when regression lines are concurrent, but are shown to be mutually exclusive when concurrence is absent...     

A rapid method of protein structure alignment

A reduction in the time required to compare two protein structures has been achieved for a previously developed structure alignment method, by reducing the number of residue pair comparisons which must be performed between the two structures. Subsets of residue pairs are selected by an iterative procedure. Initially, selection is based on similarities in solvent accessible surface areas or torsional angles or a combination of both properties, giving subsets containing approximately 2% of the total number of residue pairs. Using these subsets, a rough comparison of the two structures is generated by the structural alignment program. The information returned from this can be used to identify more accurately topologically equivalent residues in the two proteins, thus enabling a new and much smaller subset (less than 0.2% of the total number of residue pairs) to be selected. The process of iterative refinement of the residue pair subsets is repeated once more, when in 95% of the structure comparisons tested, the correct alignment of the proteins was obtained. Times required to compare the structures using the refined subsets are insignificant compared to the initial comparison, so that considerable increases in speed are possible. The method was tested on two groups of proteins, a set of remotely related alpha/beta nucleotide proteins and the variable and constant domains of the immunoglobulins. Increases in speed ranging from 50-fold to greater than 150-fold were obtained depending on the degree of similarity of the two structures. In some comparisons the alignment was improved due to the reduction in noise obtained by comparing mainly equivalent residues.     

Personalized treatment plans with multivariate outcomes

In this work, we propose a novel method for individualized treatment selection when the treatment response is multivariate. Our method covers any number of treatments and it can be applied for a broad set of models. The proposed method uses a Mahalanobis-type distance measure to establish an ordering of treatments based on treatment performance measures. Our investigation in this work deals with means of responses conditional on lower dimensional composite scores based on covariates where these scores are built using single index models to approximate mean responses against patient covariates. Smoothed estimates of such conditional means are combined to construct an estimate of the aforementioned distance measure, which is then used to estimate the optimal treatment. An empirical study demonstrates the performance of the proposed method in finite samples. We also present a data analysis using an HIV clinical trial data to show the applicability of the proposed procedure for real data.     

A computer program for testing average partial association in three-way contingency tables (PARCAT).

PARCAT is a computer program which implements alternative tests for average partial association in three-way contingency tables within the framework of the product multiple hypergeometric probability model. Primary attention is directed at the relationship between two of the variables, controlling for the effects of a covariable. This approach is essentially a multivariate extension of the Cochran/Mantel-Haenszel test to sets of (s x r) tables. A set of scores such as uniform, ridits, or probits can be assigned to categories which are ordinally scaled. In particular, if ridit scores with midranks assigned for ties are utilized, this procedure is equivalent to a partial Kruskal-Wallis test when one variable is ordinally scaled, and is equivalent to a partial Spearman rank correlation test when both variables are ordinally scaled.     

Two-Stage Procedures for Comparing Treatments with a Control: Elimination at the First Stage and Estimation at the Second Stage

We consider the problem of comparing a set of p₁ test treatments with a control treatment. This is to be accomplished in two stages as follows: In the first stage, N₁ observations are allocated among the p₁ treatments and the control, and the subset selection procedure of Gupta and Sobel (1958) is employed to eliminate “inferior” treatments. In the second stage, N₂ observations are allocated among the (randomly) selected subset of p₂(≤p₁) treatments and the control, and joint confidence interval estimates of the treatment versus control differences are calculated using Dunnett's (1955) procedure. Here both N₁ and N₂ are assumed to be fixed in advance, and the so-called square root rule is used to allocate observations among the treatments and the control in each stage. Dunnett's procedure is applied using two different types of estimates of the treatment versus control mean differences: The unpooled estimates are based on only the data obtained in the second stage, while the pooled estimates are based on the data obtained in both stages. The procedure based on unpooled estimates uses the critical point from a p₂-variate Student t-distribution, while that based on pooled estimates uses the critical point from a p₁-variate Student t-distribution. The two procedures and a composite of the two are compared via Monte Carlo simulation. It is shown that the expected value of p₂ determines which procedure yields shorter confidence intervals on the average. Extensions of the procedures to the case of unequal sample sizes are given. Applicability of the proposed two-stage procedures to a drug screening problem is discussed.     

Multiple testing to establish superiority/equivalence of a new treatment compared with k standard treatments for unbalanced designs

In clinical studies, multiple superiority/equivalence testing procedures can be applied to classify a new treatment as superior, equivalent (same therapeutic effect), or inferior to each set of standard treatments. Previous stepwise approaches (Dunnett and Tamhane, 1997, Statistics in Medicine16, 2489-2506; Kwong, 2001, Journal of Statistical Planning and Inference 97, 359-366) are only appropriate for balanced designs. Unfortunately, the construction of similar tests for unbalanced designs is far more complex, with two major difficulties: (i) the ordering of test statistics for superiority may not be the same as the ordering of test statistics for equivalence; and (ii) the correlation structure of the test statistics is not equi-correlated but product-correlated. In this article, we seek to develop a two-stage testing procedure for unbalanced designs, which are very popular in clinical experiments. This procedure is a combination of step-up and single-step testing procedures, while the familywise error rate is proved to be controlled at a designated level. Furthermore, a simulation study is conducted to compare the average powers of the proposed procedure to those of the single-step procedure. In addition, a clinical example is provided to illustrate the application of the new procedure.     

Combining One‐sided and Two‐sided Confidence Interval Procedures for Successive Comparisons of Ordered Treatment Effects

Lee and Spurrier (1995) present one‐sided and two‐sided confidence interval procedures for making successive comparisons between ordered treatments. Their procedures have important applications for problems where the treatments can be assumed to satisfy a simple ordering, such as for a sequence of increasing dose‐levels of a drug. The two‐sided procedure provides both upper and lower bounds on the differences between successive treatments, whereas the one‐sided procedure only provides lower bounds on these differences. However, the one‐sided procedure allows sharper inferences regarding which treatments can be declared to be better than their previous ones. In this paper we apply the results obtained in Hayter , Miwa , and Liu (2000) to develop a new procedure which combines the good aspects of both the one‐sided and the two‐sided procedures. This new procedure maintains the inferential sensitivity of the one‐sided procedure while also providing both upper and lower bounds on the differences between successive treatments. Some new critical points are needed which are tabulated for the balanced case where the sample sizes are all equal. The application of the new procedure is illustrated with an example.     

A unified treatment of the probability of fixation when population size and the strength of selection change over time

The fixation probability is determined when population size and selection change over time and differs from Kimura's result, with long-term implications for a population. It is found that changes in population size are not equivalent to the corresponding changes in selection and can result in less drift than anticipated.     

Who is in the neighborhood? Conspecific and heterospecific responses to perceived density for breeding habitat selection

Theoretical models of habitat selection often incorporate negative density dependence. Despite strong negative density‐dependent effects on habitat selection, more recent studies indicate that animals settle near members of their own (conspecific) and other species (heterospecific) when selecting habitat with social cues. Social cue use for habitat selection is particularly common among songbirds, but few studies have investigated if songbirds use social cues to assess conspecific or heterospecific density (as opposed to just presence/absence) when making settlement decisions. We conducted a playback experiment to evaluate if yellow warblers (Setophaga petechia) and willow flycatchers (Empidonax traillii), two potential competitors for breeding habitat, use social cues to assess density (conspecific for warblers and heterospecific for flycatchers) when selecting breeding locations at two spatial scales. We simulated yellow warbler density to be high or low at multiple treatment plots (3.14 ha) with song playback and then evaluated settlement decisions by comparing yellow warbler and willow flycatcher abundances across plots (broad‐scale habitat selection) and individual space use within plots (fine‐scale territory establishment). Yellow warbler density treatments did not affect habitat selection by yellow warblers at the broad scale, but caused individuals to cluster territories at high‐density treatments. Willow flycatchers were most abundant at high‐density treatment plots, but yellow warbler density treatments did not affect territory locations. The results indicate that perceived density affects the habitat selection process for both conspecifics and heterospecifics.     

In vitro selection and extended culture of antigen-specific T lymphocytes. II. Mechanisms of selection.

Functional selection of antigen-specific T lymphocytes can be achieved by culturing thymus-dependent (T) lymphocytes from immunized guinea pigs on "monolayers" of antigen-pulsed adherent peritoneal exudate cells (PEC) from nonimmune syngeneic donors. Several aspects of the in vitro selection of T lymphocyte-rich peritoneal exudate lymphocytes (PEL) were studied. It was shown that irradiated adherent PEC were equivalent to nonirradiated adherent PEC in supporting selection cultures, indicating that the lymphocytes harvested at the end of the selection culture derive from the immune donors of the PEL and not from the nonimmune donor of the adherent PEC. The relative importance of specific adherence and specific proliferation for achieving selection was determined by comparing the degree of selection obtained when nonadherent cells were discarded at 24 hr with that noted when the discard step was omitted. It was found that omitting the discard step markedly diminished the degree of selection. On the other hand, blocking proliferation with specific alloantisera after the discard step did not diminish the degree of selection, although it did diminish the cell yield. Thus, specific adherence to antigen-pulsed PEC appeared to be critical in the selection culture procedure. An estimate of the degree of enrichment obtained by the selection culture procedure was obtained by culturing selected cells in an excess of nonprimed PEL, so that auxiliary cells would not be limiting. Under these conditions, it appeared that selected cells were enrichied from 4- to 10-fold in antigen-responsive cells with respect to the initial cell population.     

Elevated temperature changes female costs and benefits of reproduction

Despite obvious benefits, reproduction also imposes severe costs on females. Such costs and benefits are highly sensitive to environmental factors. Rapidly changing conditions may thus disturb a finely poised balance between the two and pose a challenge to natural populations. A more complete understanding of reproduction and population fitness across different environments is, hence, crucial. In particular, sexual selection could either be beneficial or detrimental when conditions change abruptly. Here Tribolium castaneum females were subjected to mating treatments with or without sexual selection (virginity, monogamy, polyandry) replicated at standard versus elevated temperatures. We found a substantial survival cost of reproduction at the standard, but not at the elevated temperature. Reproductive success was similar across mating treatments at the standard temperature, but at elevated temperature we detected a significant benefit of polyandry compared to monogamy. These findings indicate that environmental heterogeneity can strongly influence the balance between costs and benefits when sexual selection is allowed to act. Furthermore, reproduction may be critically affected by changes in temperature with potentially profound consequences for population fitness.     

Exact significance testing to establish treatment equivalence with ordered categorical data

This communication concerns the problem of establishing the therapeutic equivalence of two treatments that are being compared on the basis of ordered categorical data. The problem is formulated as a significance test in which the null hypothesis specifies a treatment difference. An efficient numerical algorithm for computing the exact significance level is provided, along with a simple method for obtaining the asymptotic significance level. Both methods are applied to a clinical trial of a new agent versus an active control. Guidelines for when to use the exact procedure and when to rely on asymptotic theory are provided.     

A Two-stage Design for Comparing Clinical Trials

A two-stage design is proposed to choose among several experimental treatments and a standard treatment in clinical trials. The first stage employs a selection procedure to select the best treatment, provided it is better than the standard. The second stage tests the hypothesis between the best treatment selected at the first stage (if any) and the standard treatment. All the treatments are assumed to follow normal distributions and the best treatment is the one with the largest population mean. The level and the power are defined and they are used to set up equations to solve unknown first stage sample size, second stage sample size, and procedure parameters. The optimal design is the one that gives the smallest average sample size. Numerical results are presented to illustrate the improvement of one design as compared to existing one stage design.     

Adaptive plasticity and genetic divergence in feeding efficiency during parallel adaptive radiation of whitefish (Coregonus spp.)

Parallel phenotypic divergence in replicated adaptive radiations could either result from parallel genetic divergence in response to similar divergent selection regimes or from equivalent phenotypically plastic response to the repeated occurrence of contrasting environments. In post‐glacial fish, replicated divergence in phenotypes along the benthic‐limnetic habitat axis is commonly observed. Here, we use two benthic‐limnetic species pairs of whitefish from two Swiss lakes, raised in a common garden design, with reciprocal food treatments in one species pair, to experimentally measure whether feeding efficiency on benthic prey has a genetic basis or whether it underlies phenotypic plasticity (or both). To do so, we offered experimental fish mosquito larvae, partially burried in sand, and measured multiple feeding efficiency variables. Our results reveal both, genetic divergence as well as phenotypically plastic divergence in feeding efficiency, with the phenotypically benthic species raised on benthic food being the most efficient forager on benthic prey. This indicates that both, divergent natural selection on genetically heritable traits and adaptive phenotypic plasticity, are likely important mechanisms driving phenotypic divergence in adaptive radiation.