Powerful Exact Unconditional Tests for Agreement between Two Raters with Binary Endpoints

Asymptotic and exact conditional approaches have often been used for testing agreement between two raters with binary outcomes. The exact conditional approach is guaranteed to respect the test size as compared to the traditionally used asymptotic approach based on the standardized Cohen''s kappa coefficient. An alternative to the conditional approach is an unconditional strategy which relaxes the restriction of fixed marginal totals as in the conditional approach. Three exact unconditional hypothesis testing procedures are considered in this article: an approach based on maximization, an approach based on the conditional p-value and maximization, and an approach based on estimation and maximization. We compared these testing procedures based on the commonly used Cohen''s kappa with regards to test size and power. We recommend the following two exact approaches for use in practice due to power advantages: the approach based on conditional p-value and maximization and the approach based on estimation and maximization.     

The 2 x 2 matched-pairs trial: exact unconditional design and analysis

An exact unconditional method for the design and analysis of the 2 x 2 matched-pairs trial is presented. Unlike the exact conditional method, which is based on only the number of discordant pairs, the exact unconditional method uses the total number N of sampled pairs. This unconditional test, based on a simple Z statistic, yields sample sizes that are generally smaller than those produced by the exact conditional test for the cases tabulated herein, namely one-sided alpha = .01, .025, and .05 along with 80% and 90% power. Moreover, it is found to be uniformly more powerful than the latter for all the combinations of parameters considered in this paper, namely alpha = .01, .025, and .05, and N = 10(1)200. The method is illustrated by assessing various design options of an in vitro study of the effectiveness of antimicrobial agents. Some numerical examples of matching efficiency are also given.     

Unconditional and conditional QTL analysis of kernel weight related traits in wheat (Triticum aestivum L.) in multiple genetic backgrounds

Wheat thousand kernel weight (TKW) is a complex trait, and is largely controlled by several kernel traits, including kernel length (KL) and kernel width (KW). In order to reveal the genetic relationship between TKW and these kernel traits (KW and KL) as accurate as possible, we applied both unconditional and conditional mapping analyses to three distinct genetic populations, one DH population and two RIL populations. This report describes the identifications of 36 unconditional and conditional additive QTLs and 30 pairs of unconditional and conditional epistatic QTLs, all of which are closely associated with TKW. While the conditional additive locus Qtkw1B, detected in the RIL2 population, exhibited the largest contribution, explaining 14.12 % of TKW variance, the unconditional epistatic QTLs Qtkw3A-2/Qtkw5B.1, detected in the DH population, accounted for 11.95 % of phenotypic variance. This study also showed that, compared with unconditional mapping, conditional mapping resulted in very different numbers and different extent of effects of additive and epistatic QTLs that were associated with TKW when TKW was conditioned on kernel traits (KW and KL). These data strongly suggest that KW and KL indeed play a significant role in determining TKW. Furthermore, we demonstrated that the effects of the 25 additive QTLs for TKW were either entirely or largely determined by KW, while the effects of the other 25 additive QTLs for TKW were either entirely or largely affected by KL. We conclude that the conditional mapping can be useful for a better understanding of the interrelationship between the yield contributing traits at the QTL level.     

Tonic and phasic stimulus control of blood pressure responses using opposing unconditional stimuli

The transswitching paradigm was used in the present study to investigate the effects of tonic (long duration) environmental stimuli paired with opposing unconditional stimuli on human blood pressure. Sixty volunteers participated for two sessions, one week apart. Subjects were presented with a pseudorandom sequence of four trials of red lights (five minutes each) and four trials of blue lights (five minutes each) within each session. All subjects received the cold pressor test during the red lights. During the blue lights, half the subjects received warm water and the other half received a neutral temperature water. Subjects received the presentations of the water in one of three methods: as determined by the experimenter, preceded by a warning signal, or self-administered. The results indicated that conditional and unconditional responses during the red lights were progressive increases in blood pressure. During the blue lights associated with warm water, conditional and unconditional responses were often progressive decreases in blood pressure. The method of administration of the water affected the magnitude of the unconditional responses. Evidence for phasic stimulus control was not as unequivocal as tonic stimulus control. The present results indicated that it is possible to modify blood pressure in two directions (increases and decreases) when two high contrast, opposing unconditional stimuli are presented.     

Improved exact confidence intervals for the odds ratio in two independent binomial samples

For two independent binomial samples, the usual exact confidence interval for the odds ratio based on the conditional approach can be very conservative. Recently, Agresti and Min (2002) showed that the unconditional intervals are preferable to conditional intervals with small sample sizes. We use the unconditional approach to obtain a modified interval, which has shorter length, and its coverage probability is closer to and at least the nominal confidence coefficient.     

Explained variation and degrees of necessity and of sufficiency for competing risks survival data

In this contribution, the Schemper–Henderson measure of explained variation for survival outcomes is extended to accommodate competing events (CEs) in addition to events of interest. The extension is achieved by moving from the unconditional and conditional survival functions of the original measure to unconditional and conditional cumulative incidence functions, the latter obtained, for example, from Fine and Gray models. In the absence of CEs, the original measure is obtained as a special case. We define explained variation on the population level and provide two different types of estimates. Recently, the authors have achieved a multiplicative decomposition of explained variation into degrees of necessity and degrees of sufficiency. These measures are also extended to the case of competing risks survival data. A SAS macro and an R function are provided to facilitate application. Interesting empirical properties of the measures are explored on the population level and by an extensive simulation study. Advantages of the approach are exemplified by an Austrian study of breast cancer with a high proportion of CEs.     

A Comparison of the Three Conditional Exact Tests in Two‐way Contingency Tables Using the Unconditional Exact Power

The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact test, the exact chi‐squared test and the exact likelihood ratio test are popular and can be implemented in software StatXact. In this paper we investigate which test is the best in small samples in terms of the unconditional exact power. In equal sample cases it is proved that the three tests produce the same unconditional exact power. A symmetry of the unconditional exact power is also found. In unequal sample cases the unconditional exact powers of the three tests are computed and compared. In most cases the Fisher's exact test turns out to be best, but we characterize some cases in which the exact likelihood ratio test has the highest unconditional exact power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

QTL mapping of inbreeding-related cold sensitivity and conditional lethality in Drosophila melanogaster

Inbreeding depression is a central theme within genetics, and is of specific interest for researchers within evolutionary and conservation genetics and animal and plant breeding. Inbreeding effects are thought to be caused by the joint expression of conditional and unconditional deleterious alleles. Whenever the expression of deleterious alleles is conditional, this can result in extreme environmental sensitivity in certain inbred lineages. Analysis of conditional lethal effects can reveal some of the loci that are sensitive to inbreeding. We performed a QTL (quantitative trait locus) mapping study of inbreeding-related and conditionally expressed lethality in Drosophila melanogaster. The lethal effect was triggered by exposure to a cold shock. We used a North Carolina crossing Design 3 to establish the mapping population, as well as to estimate the average dominance ratio and heritability. We found two QTL on the major autosomes carrying recessive lethals that caused male mortality, one of which also affected female mortality. More detailed study of these loci will provide information on the mechanistic basis and environmental sensitivity of inbreeding depression.     

Application of logistic regression to case-control association studies involving two causative loci

Models in which two susceptibility loci jointly influence the risk of developing disease can be explored using logistic regression analysis. Comparison of likelihoods of models incorporating different sets of disease model parameters allows inferences to be drawn regarding the nature of the joint effect of the loci. We have simulated case-control samples generated assuming different two-locus models and then analysed them using logistic regression. We show that this method is practicable and that, for the models we have used, it can be expected to allow useful inferences to be drawn from sample sizes consisting of hundreds of subjects. Interactions between loci can be explored, but interactive effects do not exactly correspond with classical definitions of epistasis. We have particularly examined the issue of the extent to which it is helpful to utilise information from a previously identified locus when investigating a second, unknown locus. We show that for some models conditional analysis can have substantially greater power while for others unconditional analysis can be more powerful. Hence we conclude that in general both conditional and unconditional analyses should be performed when searching for additional loci.     

QTL detected for grain-filling rate in maize using a RIL population

The grain-filling rate plays an important role in determining grain yield. To elucidate the genetic basis of the grain-filling rate, a set of 203 recombinant inbred lines was evaluated at two locations over 2 years. Quantitative trait loci (QTL) for grain-filling rate were detected using conditional and unconditional QTL analysis of genetic linkage maps comprising 217 SSR markers. The results showed that the grain-filling rate increased between 15 and 35 days after pollination, then decreased at the last two sampling times. Hybrids with high grain-filling rates determined the grain yield in those areas with a short growth season for maize. A total of 23 unconditional QTL for grain-filling rate were detected using the 100-kernel weight as the input data at different sampling stages. They were distributed on 10 chromosomes (except chromosome 9), and some QTL were detected at different sampling stages. In addition, nine conditional QTL were identified using the average increase in 100-kernel weight of per day between two sampling times, and six conditional QTL were detected simultaneously using the unconditional QTL mapping strategy. The QTL mapping results demonstrated that the grain-filling rate is controlled by a complex genetic mechanism, and the QTL detected at different sampling stages might be important contributors to grain yield in maize.     

Interim Treatment Selection in Drug Development

We consider hypothesis testing in a clinical trial with an interim treatment selection. Recently, unconditional and conditional procedures for selecting one treatment as the winner have been proposed when the mean responses are approximately normal. In this paper, we generalize both procedures to multi-winner cases. The distributions of the test statistics are obtained and step-down approaches are proposed. We prove that both unconditional and conditional procedures strongly control the family-wise error rate. We give a brief discussion on power comparisons.     

A cautionary note on exact unconditional inference for a difference between two independent binomial proportions

Fisher's exact test for comparing response proportions in a randomized experiment can be overly conservative when the group sizes are small or when the response proportions are close to zero or one. This is primarily because the null distribution of the test statistic becomes too discrete, a partial consequence of the inference being conditional on the total number of responders. Accordingly, exact unconditional procedures have gained in popularity, on the premise that power will increase because the null distribution of the test statistic will presumably be less discrete. However, we caution researchers that a poor choice of test statistic for exact unconditional inference can actually result in a substantially less powerful analysis than Fisher's conditional test. To illustrate, we study a real example and provide exact test size and power results for several competing tests, for both balanced and unbalanced designs. Our results reveal that Fisher's test generally outperforms exact unconditional tests based on using as the test statistic either the observed difference in proportions, or the observed difference divided by its estimated standard error under the alternative hypothesis, the latter for unbalanced designs only. On the other hand, the exact unconditional test based on the observed difference divided by its estimated standard error under the null hypothesis (score statistic) outperforms Fisher's test, and is recommended. Boschloo's test, in which the p-value from Fisher's test is used as the test statistic in an exact unconditional test, is uniformly more powerful than Fisher's test, and is also recommended.     

Unifying sources and sinks in ecology and Earth sciences

The paired source and sink concepts are used increasingly in ecology and Earth sciences, but they have evolved in divergent directions, hampering communication across disciplines. We propose a conceptual framework that unifies existing definitions, and review their most significant consequences for the various disciplines. A general definition of the source and sink concepts that transcends disciplines is based on net flows between the components of a system: a source is a subsystem that is a net exporter of some living or non‐living entities of interest, and a sink is a net importer of these entities. Sources and sinks can further be classified as conditional and unconditional, depending on the intrinsic propensity of subsystems to either produce (source) or absorb (sink) a surplus of these entities under some (conditional) or all (unconditional) conditions. The distinction between conditional and unconditional sources and sinks, however, is strongly context dependent. Sources can turn into sinks, and vice versa, when the context is changed, when systems are subject to temporal fluctuations or evolution, or when they are considered at different spatial and temporal scales. The conservation of ecosystem services requires careful consideration of the source?sink dynamics of multiple ecosystem components. Our synthesis shows that source?sink dynamics has profound consequences for our ability to understand, predict, and manage species and ecosystems in heterogeneous landscapes.     

Unconditional inferences on the difference of two proportions in cross-sectional studies

In order to analyse a 2 x 2 table it is usual to perform inferences (hypothesis test or interval of confidence) on the difference d = p2 - p1 between two independent proportions. To this end it has been customary to adopt the Fisher conditional method, but nowadays the unconditional method of Barnard is increasingly adopted. However, all the present unconditional inferences are based on a double-binomial model. This article performs these inferences - exact and asymptotic - under a multinomial model, which is the appropriate one when the data proceed from a cross-sectional survey. At http://www.ugr.es/-bioest/SG_ASO.EXE there is a program for performing the said unconditional tests that may be copied.     

Dynamic QTL Analysis of Rice Protein Content and Protein Index Using Recombinant Inbred Lines

Protein content (PC) and protein index (PI) play important roles in determining nutritional quality in rice (Oryza sativa L.). We used 71 lines derived from “Asominori/IR24” to analyze the developmental behavior of PC and PI through unconditional and conditional QTL mapping methods. In all, 10 unconditional QTLs and 6 conditional QTLs for PC, and 11 unconditional QTLs and 9 conditional QTLs for PI, were identified at four stages of grain filling. More were identified in the first three stages than at the final stage. Temporal patterns of gene expression for PC and PI differed over time, with several QTLs being expressed across two or three stages but many being expressed at only one stage. Some of these QTLs were closely linked with maturity QTLs reported previously. Many QTLs for PC and PI were co-localized, supporting the significant correlation found between PC and PI. Our results suggest that dynamic QTL mapping might be a valid means for revealing more genetic information about protein accumulations during seed development.     

Conditional QTL mapping of protein content in wheat with respect to grain yield and its components

Grain protein content in wheat (Triticum aestivum L.) is generally considered a highly heritable character that is negatively correlated with grain yield and yield-related traits. Quantitative trait loci (QTL) for protein content was mapped using data on protein content and protein content conditioned on the putatively interrelated traits to evaluate possible genetic interrelationships between protein content and yield, as well as yield-related traits. Phenotypic data were evaluated in a recombinant inbred line population with 302 lines derived from a cross between the Chinese cultivar Weimai 8 and Luohan 2. Inclusive composite interval mapping using IciMapping 3.0 was employed for mapping unconditional and conditional QTL with additives. A strong genetic relationship was found between protein content and grain yield, and yield-related traits. Unconditional QTL mapping analysis detected seven additive QTL for protein content, with additive effects ranging in absolute size from 0.1898% to 0.3407% protein content, jointly accounting for 43.45% of the trait variance. Conditional QTL mapping analysis indicated two QTL independent from yield, which can be used in marker-assisted selection for increasing yield without affecting grain protein content. Three additional QTL with minor effects were identified in the conditional mapping. Of the three QTLs, two were identified when protein content was conditioned on yield, which had pleiotropic effects on those two traits. Conditional QTL mapping can be used to dissect the genetic interrelationship between two traits at the individual QTL level for closely correlated traits. Further, conditional QTL mapping can reveal additional QTL with minor effects that are undetectable in unconditional mapping.     

Genetic dissection of interactions between wheat flour starch and its components in two populations using two QTL mapping methods

Starch content and its components are important for determining wheat end-use quality and yield. However, little information is available about their interactions at the QTL/gene level in more than one population using different QTL mapping methods. Therefore, to dissect these interactions, two mapping populations from two locations over 2 years were used. The QTLs for the populations were analyzed by unconditional and conditional QTL mapping by two different analysis methods. In the two populations, there were a total of 24 unconditional additive QTLs detected for flour amylose (FAMS), flour amylopectin (FAMP), flour total starch (FTSC), and the ratio of FAMS to FAMP using ICIMapping4.1 methods, but 26 unconditional QTLs were found using QTLNetwork2.0 methods. Of these QTLs, 10 stable major additive QTLs were identified in more than one environment, mainly distributed on chromosomes 3B, 4A, 5A, and 7D. The maximum percentage of phenotypic variance explained (PVE) reached 54.31%. Two new unconditional major additive QTLs on chromosome 3B (Qftsc3B and Qfamp3B) were found. A total of 23 and 19 conditional additive QTLs were identified in the two populations using two different methods, respectively. Of which, eight and six stable major conditional QTLs were detected on chromosomes 3B, 4A, and 7D, respectively. New repressed QTLs were identified, such as Qftsc/fams5B-1 and Qftsc/fams5B-2. There were 20 epistatic unconditional and 15 conditional QTLs detected. In all, important QTLs on chromosomes 3B, 4A, and 7A were found in both populations. However, the number of important QTLs in the special recombinant inbred line (RIL) population was higher than that in the double haploid (DH) population, especially on chromosomes 7D and 5B. Moreover, the QTLs on chromosomes 4A, 7A, and 7D were close to the Wx-1 loci in the RIL population. These indicated better results can be obtained by a special population to target traits than by a common population. The important QTLs on key chromosomes can always be detected no matter what kinds of populations are used, such as the QTLs on chromosome 4A. In addition, QTL clusters were found on chromosomes 4A, 3B, 7A, 7D, and 5A in the two populations, indicating these chromosome regions were very important for starch biosynthesis.     

Reinforcement Learning Explains Conditional Cooperation and Its Moody Cousin

Direct reciprocity, or repeated interaction, is a main mechanism to sustain cooperation under social dilemmas involving two individuals. For larger groups and networks, which are probably more relevant to understanding and engineering our society, experiments employing repeated multiplayer social dilemma games have suggested that humans often show conditional cooperation behavior and its moody variant. Mechanisms underlying these behaviors largely remain unclear. Here we provide a proximate account for this behavior by showing that individuals adopting a type of reinforcement learning, called aspiration learning, phenomenologically behave as conditional cooperator. By definition, individuals are satisfied if and only if the obtained payoff is larger than a fixed aspiration level. They reinforce actions that have resulted in satisfactory outcomes and anti-reinforce those yielding unsatisfactory outcomes. The results obtained in the present study are general in that they explain extant experimental results obtained for both so-called moody and non-moody conditional cooperation, prisoner’s dilemma and public goods games, and well-mixed groups and networks. Different from the previous theory, individuals are assumed to have no access to information about what other individuals are doing such that they cannot explicitly use conditional cooperation rules. In this sense, myopic aspiration learning in which the unconditional propensity of cooperation is modulated in every discrete time step explains conditional behavior of humans. Aspiration learners showing (moody) conditional cooperation obeyed a noisy GRIM-like strategy. This is different from the Pavlov, a reinforcement learning strategy promoting mutual cooperation in two-player situations.     

Quantitative demonstration of the reciprocity of ligand effects in the ternary complex of chicken heart lactate dehydrogenase with nicotinamide adenine dinucleotide oxalate.

The reciprocity of effects of two ligands simultaneously bound to a protein as a ternary complex may be proven by measurements of four standard free energies of binding. Two of these are for the binding of each ligand in the absence of the other, and the other two for the binding of each ligand in the presence of saturating amounts of the other (conditional free energies). These four quantities have been measured for the complexes of oxalate and nicotinamide adenine dinucleotide with chick heart lactate dehydrogenase. The differences between conditional and unconditional free energies are: oxalate, -1.1 +/- 0.3 kcal; NADH,-1.3 +/- 0.2 kcal, thus proving the reciprocity within experimental error.     

THE JOINT EVOLUTION OF DISPERSAL AND DORMANCY IN A METAPOPULATION WITH LOCAL EXTINCTIONS AND KIN COMPETITION

Dispersal and dormancy are two strategies that allow recolonization of empty patches and escape from kin competition. Because they presumably respond to similar evolutionary forces, it is tempting to consider that these strategies may substitute for each other. Yet in order to predict the outcome of the evolution of dispersal and dormancy, and to characterize the emerging covariation between both traits, it is necessary to consider models where dispersal and dormancy evolve jointly. Here, we analyze the evolution of dispersal and dormancy as a function of direct fitness costs, environmental variation, and competition among relatives. We consider two scenarios depending on whether the rates of dormancy for philopatric and dispersed individuals are constrained to be the same (unconditional dormancy) or allowed to be different (conditional dormancy). We show that only philopatric individuals should enter dormancy, at a rate increasing with increasing rates of local extinction and decreasing population sizes. When dormancy and dispersal evolve jointly, we observe a wide range of evolutionary outcomes. In particular, we find that the pattern of covariation between the evolutionarily stable rates of dispersal and dormancy is molded by the rate of extinction and the local population size.