Comparison of FST outlier tests for SNP loci under selection

When the discussion about algorithmic fairness first started to receive academic attention, much of the debate was about criteria that use aggregate statistics of observed data to determine whether a predictive model is fair. At the center of the debate were the two criteria equalized odds and predictive parity. Equalized odds requires that false positive and false negative error rates be equal for different protected groups (e.g., men and women) in order for a predictive model to be considered fair. Predictive parity, on the other hand, stipulates that a model must have equal predictive values for different protected groups. At first glance, both criteria seem like reasonable and intuitive conditions for algorithmic fairness. As it turned out, however, the two criteria are (under realistic circumstances) mutually incompatible.1 This means, it is in most cases impossible to satisfy both—when one is satisfied, the other must be violated. This was a frustrating result since both conditions have some intuitive appeal. At the same time, these impossibility results inadvertently provided a justification for companies, governments, and other organizations to use predictive models which violate one of the fairness criteria: they could simply argue that the model cannot but violate the criterion since it satisfies the other. To illustrate the impossibility of satisfying both equalized odds and predictive parity in a practical setting, consider a predictive model that estimates a person's risk of defaulting on a loan. Let us say this model is used by a bank to renegotiate the loan terms. To retrospectively compare the model's performance for two different demographic groups, we could examine how many people in each group who defaulted on their loan were predicted to do so. Equalized odds requires that this proportion be the same for both groups. Alternatively, we could check how many people in each group who were predicted to default actually did default. Predictive parity requires that this proportion be the same for both groups. However, if one group has a lower default rate than the other, it is impossible to satisfy both equalized odds and predictive parity simultaneously. If equalized odds is satisfied, the proportion of those who do in fact default among those predicted to default will differ between the two groups, violating predictive parity. Conversely, if predictive parity is satisfied, equalized odds will be violated. The bank could exploit this fact to justify the use of a discriminatory predictive model. Various approaches have been proposed to address the issue of the impossibility theorem. Some authors have suggested abandoning one of the fairness criteria,2 while others have proposed that the choice of criterion should depend on the context.3 Still, others have argued for the abandonment of both equalized odds and predictive parity in favor of an alternative criterion.4 However, given the intuitive appeal of these two criteria, it is hard to accept any of these options. As a result, there remains a lack of consensus on how best to deal with the impossibility theorem. In this article, I will argue that both criteria can be modified in a way that retains their intuitive appeal and renders them universally compatible. Instead of requiring that error rates or predictive values be equal across protected groups, the modified equalized odds and predictive parity criteria require that the protected characteristic does not cause discrepancies in these metrics across groups. To formalize these modified versions of equalized odds and predictive parity, I will use a method called matching, which is typically used for causal inference in observational studies. The remainder of this article is organized as follows. In Section II, I introduce the two statistical fairness criteria, equalized odds and predictive parity, and present the Kleinberg-Chouldechova impossibility theorem that involves them. I then present criticisms of the two criteria. In Section III, I turn away from fairness for a moment to introduce the method of matching. In Section IV, I utilize this method to define versions of equalized odds and predictive parity that better capture their intended interpretation. As will be shown, the two modified criteria are universally compatible. Section V concludes the article. Let us begin by providing more precise definitions of the two statistical fairness criteria equalized odds and predictive parity.5 We will here focus on binary predictions (or classifications) and take the predictive model to be a function from a set of input variables to the prediction. We will denote the variable representing the protected characteristic with A (which will also be assumed to be binary), the prediction with Y ̂ , and the target variable that is to be predicted with Y. Let P be a joint probability distribution function of A, Y ̂ , and Y, such that (i) P(E) ≥ 0 for all events E in the event space defined on the sample space; (ii) P(Ω) = 1, where Ω is the sample space, which is the set of all possible outcomes; and (ii) P(E1∪E2) = P(E1) + P(E2) for all events E1 and E2 that are mutually exclusive in the event space, meaning they cannot both occur simultaneously. The event space is a collection of subsets of the sample space that represent different possible events. We will also denote conditional probability (i.e., the probability of an event occurring given another event) by P E 1 E 2 , which is defined as P E 1 | E 2 = P E 1 ∩ E 2 P E 2 . The probability of a variable V taking on the value v is denoted as P(V = v), abbreviated as P(v) when there is no ambiguity. The probability of two events occurring simultaneously, V = v and U = u, will be abbreviated as P(v, u). We can now formally define the two criteria as follows: Definition 1.(Equalized odds). A predictive model satisfies equalized odds (relative to protected characteristics a1, a2∈DA) if and only if for all y ̂ ∈ D Y ̂ and y∈DY, P y ̂ a 1 y = P y ̂ a 2 y . Definition 2.(Predictive parity). A predictive model satisfies predictive parity (relative to protected characteristics a1, a2∈DA) if and only if for all y ̂ ∈ D Y ̂ and y∈DY, P y a 1 y ̂ = P y a 2 y ̂ . In most contexts, equalized odds and predictive parity cannot be satisfied simultaneously. This follows from a theorem of which two versions were simultaneously and independently proved by Chouldechova6 and Kleinberg.7 More precisely, the theorem states that whenever the prevalence, that is, the relative frequency of an occurrence of the event represented by the target variable, is different for different protected groups, a predictive model which satisfies equalized odds must violate predictive parity, and vice versa.8 For example, a predictive model intended to predict whether a defendant will reoffend (i.e., commit a future crime) cannot at the same time produce equal error rates and have equal predictive values for different ethnic groups, if the prevalence of reoffence (i.e., the relative frequency of defendants committing another crime in the future) differs across these groups. To state this more concisely, the theorem can be formulated as follows: Theorem 1.(The Kleinberg-Chouldechova impossibility). If the prevalence differs across protected groups, no (imperfect) predictive model can satisfy both equalized odds and predictive parity. If both equalized odds and predictive parity were deemed universally necessary conditions for predictive fairness, this impossibility theorem would suggest that truly fair predictive models are an unattainable goal. There is, however, another possible interpretation of this impossibility: namely that it highlights a flaw in our formalization of what constitutes fair predictive models. The impossibility result can then be seen as an indicator that we have to rethink the definitions of the two fairness criteria and reevaluate whether they actually formalize the more intuitive ideas they are intended to formalize. The argument pursued here is along those lines. I will argue that while the intuitive appeal of both fairness criteria is undeniable, they impose stronger requirements than what is necessary in order to avoid certain types of unfairness in predictive models. Before we examine both criteria, let us first consider how we can cash out the broader idea of fairness for predictive models. Algorithmic fairness is, in the context of such models, generally taken to mean the absence of discrimination. Discrimination, in turn, can be understood as the wrongful disadvantageous treatment of an individual on the basis of a sensitive characteristic like ethnicity, gender, or religion.9 There is disagreement on what constitutes wrongful disadvantageous treatment in this context. However, the most widely accepted definitions are based on the ideas that the sensitive characteristic is irrelevant in most situations10 and that a person should be treated as an individual.11 Wrongfulness then arises from basing disadvantageous treatment on an irrelevant sensitive characteristic, or from treating someone disadvantageously based on presumed statistical patterns that associate their sensitive characteristic with some other trait in a way that disregards their individuality. Predictive models, by definition, are mathematical models used to predict the value of a specific variable. The output of such a model can be seen as representing a belief-like propositional attitude. If the possession of a certain sensitive characteristic leads to disadvantageous predictions, such as in terms of accuracy or their impact on the decision for which the model is used, this process can be considered discriminatory. We can consequently understand equalized odds and predictive parity as criteria that prevent discriminatory outcomes in predictive models. Equalized odds can be interpreted as a criterion that prevents discriminatory outcomes by preventing systematic cognitive bias with regard to a sensitive characteristic. By systematic cognitive bias, we here mean misjudging how informative a certain trait is in predicting another trait.12 Assume, for example, that in making predictions about whether someone will get lung cancer, we overestimate how informative it is that the person smokes. More precisely, if someone is a smoker, we predict that they will get lung cancer, and if not, we predict that they will not get lung cancer. We are clearly biased with regard to smoking in predicting lung cancer: not everyone who smokes gets lung cancer, and some people get it without ever having touched a cigarette. It is easy to see that this will result in different error rates for the group of smokers and the group of non-smokers. The smokers will have a false negative rate of 0 (simply for the fact that no smoker was predicted to not get lung cancer) but a false positive error rate above 0 (some smokers do not get lung cancer). Vice versa, the non-smokers will have a false negative rate above 0 (there are some who get lung cancer, but we never predict a non-smoker to get lung cancer) but a false positive rate of 0 (because no non-smoker is predicted to get lung cancer). One could say that this model is systematically biased with regard to smoking in predicting lung cancer. If, however, instead of using the predictive model just described we used a predictive model which guarantees that the error rates across smokers and non-smokers are equal, then we could be sure that the predictor contains no such bias. While being a smoker is typically not considered a sensitive characteristic, overestimating the informativeness of a sensitive characteristic like gender could lead to disadvantageous predictions on the basis of an irrelevant (or less relevant than warranted) sensitive characteristic.13 Yet, it is important to note that a violation of equalized odds across protected groups is an indicator and not a definition of systematic cognitive bias. To see this, note that the statement relating error rates to bias is a conditional: if there is bias with regard to trait A, there will be disparities in error rates between those with trait A and those without. By simple logic, this implies that whenever there are no disparities in error rates, there is no bias. Yet, it does not imply that whenever we observe disparities in error rates between those with trait A and those without, we can conclude that the predictor is biased with regard to A. In other words, equalized odds relative to A is a sufficient condition for the absence of bias with regard to A, but not a necessary one. Hence, trying to deduce that a predictor is biased from the observation that error rates among groups differ amounts to committing the well-known fallacy of affirming the consequent. At best, observing disparities in error rates allows one to make an inference to the best explanation: when disparities in error rates between two groups are observed, and there is no other plausible explanation, then one is justified in suspecting that this is due to bias with regard to the trait that distinguishes the groups. While this inference may seem plausible in many cases, it is important to note that it is a fallible inference, and that is what matters for our purposes (Figure 1). To illustrate this with an example, imagine a health insurance company that tries to predict the healthcare costs an individual incurs in a given year in order to decide how to set their customers' premiums. To simplify things, imagine the company is trying to predict only whether an individual's annual costs are above a certain threshold. This allows us to represent the target variable and the prediction as binary variables. Now imagine that in country C, citizens of religion R1 are, on average, younger than citizens of religion R2 (we can imagine that this is due to the fact that many people of religion R1 in C have recently immigrated, and that people generally tend to immigrate when they are somewhat younger). Suppose that, upon examination, the predictions turn out to have a higher false positive rate for people of religion R1 than for people of religion R2. Can we conclude that the predictive model the insurance company used has a discriminatory bias against people of religion R1? The observation of different error rates does not conclusively establish this. Different explanations for this discrepancy are conceivable. Imagine first a scenario in which the insurance company uses a predictive model which solely takes the individual's age into account. Now imagine further that the predictor is biased with regard to age, in that it overestimates how informative young age is of risky behavior, and hence of increased health costs. This, as we have shown above, will obviously lead to higher false positive rates for predictions of high health costs among young people. Because, on average, people of religion R1 are younger, and the predictive model is biased with regard to age, it will produce predictions with a higher false positive rate for people of religion R1. However, it can be argued that the outcomes of this predictive model do not discriminate against people of religion R1. To see this, consider the following. Imagine that instead of C, the health insurance company operated in a different country D, where citizens of religion R2 are, on average, younger than citizens of religion R1. Again, we can assume that this is because in this context people of religion R2 are mostly recent immigrants to D. It is easy to see that here, the predictive model would produce predictions with a higher false positive rate for people of religion R2. Remember that this model is exactly the same as the one above and that the higher false positive rate for R2 would not occur in C, where the reverse was the case. If we define bias as disparities in observed error rates, we would come to the somewhat contradictory conclusion that the predictive model is biased against people of religion R1, but that, had the insurance company applied the exact same predictive model in a different country, the model would be biased against people of religion R2. We can see that which religion a person has does not, in any sense, influence the predictions (or, for that matter, the error rates). It only happens to be the case that, in the given context, the predictive model works on average less well for one religious group than for another. While this might be worrisome in its own right, it can hardly be considered discrimination on the basis of religion, as there is no explanatory relation between a customer's religion and the predicted health costs. Compare this with a second scenario, depicted in 1(b), in which the insurance's predictor takes a person's religion into account in order to make a healthcare cost prediction. From an observational point of view, the two predictors' performances might be indistinguishable, as they could both produce the same discrepancies in error rates between different religious groups. Yet, on a narrow understanding of systematic cognitive bias, only the latter can be said to be biased against people of religion R1. This is of course not to say that disparities in error rates among different protected groups are of no moral concern by themselves. Disparities in error rates can, if tied to decision-making, lead to unjust distributions of resources and burdens. Yet, we are here following Eidelson14 in claiming that (direct and structural) discrimination is conceptually distinct from matters of distributive justice, and trying to subsume one under the other will get in the way of a clear analysis of each. Especially in the context of algorithmic decision-making, it seems that distinguishing between discriminatory predictions and unjust decisions is necessary in order to determine an appropriate method of mitigating the unfairness without introducing other unanticipated biases into the decision-making process.15 We are here solely concerned with fairness criteria for predictions. A discussion of distributive justice arising from algorithmic decision-making, although important, is beyond the scope of this article. Let us now turn to predictive parity. Predictive parity is often interpreted as a criterion that prohibits the meaning of a prediction from depending on a person's sensitive characteristic, as doing so could incentivize discriminatory behavior.16 Here, a similar observation can be made. Imagine a medical device that tests for a specific disease. Given a person has the disease, there is a 95 percent probability that the test turns out positive. When applied to a person who is healthy, there is a 5 percent probability that the test nonetheless turns out positive. This, we can imagine, can be shown to robustly hold across genders. There is no difference whatsoever in the likelihood of receiving an erroneous result, no matter whether a patient is male or female. Intuitively, it seems, there is no difference in meaning of the prediction for men and for women. But now imagine that the disease happens to occur more frequently in men. More specifically, we can imagine that one in every 10 men has the disease, but only one in every 100 women does. Then the positive predictive value, that is, the probability of actually having the disease given that one receives a positive test result, is different for men and women. For men it is roughly 68 percent, whereas for women it is only about 16 percent.17 This means, in this intuitively fair case, predictive parity is not satisfied. But it seems that this is not due to bias in the testing device, but just to the prevalence of the disease, which differs across genders. In other words, it is not gender which causes the difference in predictive value (since the testing device works, by assumption, equally well for a randomly chosen man as for a randomly chosen woman). So it seems that here, too, we want to distinguish between discrepancies in predictive value which are (causally) explained by gender, and discrepancies in predictive value which are due to external factors, such as differences in the prevalence of a disease. In light of these criticisms, it seems that the definitions of both equalized odds and predictive parity do not adequately explicate the underlying moral intuitions they were designed to capture.18 This, in turn, could mean that the Kleinberg-Chouldechova impossibility result is not so disastrous after all. If neither equalized odds nor predictive parity are, as they are currently defined, necessary conditions for fairness, the impossibility loses its bite. There is a chance that the impossibility theorem is just an artifact of the way the criteria are defined. The remainder of this article will examine this possibility by trying to provide modified definitions of equalized odds and predictive parity that retain all the intuitively plausible aspects of the current definitions but avoid the impossibility. We can use method for causal inference on the basis of observational define modified versions of equalized odds and predictive parity. In this I will the The from the following In many it would be to be to whether and to which a given variable has a causal on some other variable. The for causal is the specific of however, it is impossible or to or the only data is observational for about the health of smoking on It would be to a group of to Yet, there might be observational data on the health of that in a where at one of the smokes. to the of a for observational data as best as to for the of causal in cases like the above, where data is causal by the results of an on one group of randomly treatment to a group who do not receive the This that any observed differences between the groups are due to the and not other For example, in a to test the of an could be randomly to receive the or a and the of the could be by the frequency of in the two groups. A of observational is that they can for that may both who receives the treatment and the being this with a without If the were to to take and the results were to those who did not receive the the results could be by One such is the age of the people are more to from and might hence be more to take At the same time, age obviously also whether and with which frequency someone This that the treatment group may have a higher average frequency of than the which could lead to the conclusion that the is not In a however, the age distributions of the treatment and groups would be roughly equal, for a more of the When we only have observational we can to matching. Instead of randomly to the treatment or observational data can be used to a group that does not systematically differ from the treatment group on any observed or variables other than the treatment (i.e., variable, This is as follows. that the data of on the causal variable, the variable, and a of other in this context, will be called the For each individual in the treatment we the individual from the group values are as similar as possible to the values of the individual from the treatment the We with a treatment and a group that have or similar distributions the and certain that we will get to in a for the conclusion that any difference between the groups with regard to the variable is by the difference in the causal variable. To illustrate this, we can to the of the of the on the of To a we would to in the group with that are as as possible to the of the in the treatment as well as similar of By a group with these we would that the treatment and groups have similar distributions of age and us to conclude that any differences in the of between the groups is due to the treatment than age or that the is we would the frequency of to be lower in the group than in the treatment there may be other that could the but allows us to for observed and provide a more of the Let us now address a namely how to In order for to be as a method for causal as it is that the set of contains all the variables that influence both the causal and the variable (i.e., all This is important because it that there are no differences between the and treatment group conditional on the observed The that this is the case is typically called In our above, is most not there could be other variables that influence both treatment and like for and so we have some by on age and we could get a better of the if we had the data on these other important for is not to any variables that are by the causal variable. This might lead to an of the causal and the let us that there is an of The of the group on the used, whether one uses or the data point is the average of the most similar data and whether is with or without (i.e., whether a data point can be more than The specific choice of however, is of no to the argument Let us now to the to equalized odds and predictive parity to avoid the Kleinberg-Chouldechova impossibility. We will consider both fairness criteria in Let us begin by out the intended interpretation of the fairness criterion which is to equalized We will this criterion equalized equalized odds requires that the protected characteristic has no on the predictor in a way that its error For if a predictor satisfies equalized it that the fact that a defendant is does not the probability of receiving a false positive can we determine if a predictor satisfies equalized We can this as a causal inference by the causal of the protected characteristic on a error This as explained in the can be using matching. We the protected characteristic as the treatment variable and an appropriate set of We then a such that the treatment and group (i.e., the two protected no systematic differences other than in their protected characteristics and the predictions they we compare the error rates of the two groups. If only the error rates are equal, equalized odds is satisfied. Some more are to be said about the choice of The first point is that we can, of only determine whether a predictor satisfies equalized odds if the satisfy the of a fairness hence

Environmental factors are strong drivers of local adaptation in forest tree species. Toona ciliata var. pubescens, an endangered tree species endemic to China, is widely distributed across Eastern and Southwestern China. In this study, we used 8 genomic microsatellite markers and 17 EST-SSR markers across nine populations from the Yunnan–Kweichow Plateau and Eastern China, to explore the adaptive variation and genetic structure of T. ciliata var. pubescens. Patterns of population structure were apparent using a Bayesian clustering program, STRUCTURE, which identified four distinct clusters. We identified four outlier loci that were potentially under selection using the Dirichlet-multinomial and hierarchic simulation models. Through the Mantel test, it was found that geographic and climatic factors have jointly affected the genetic structure of T. ciliata var. pubescens in the study area. Based on redundancy analysis (RDA), it was shown that the correlation between climatic variables associated with variation is stronger than that of geographic variables. It is worth mentioning that the eight alleles from outlier loci have potentially adaptive and are associated with either precipitation or temperature variables. All analyses revealed high genetic diversity and significant genetic differentiation in the populations of T. ciliata var. pubescens. This indicated that the climatic variables including precipitation and temperature are drivers of local adaptation in the populations of T. ciliata var. pubescens.

Whole-genome scans with large number of genetic markers provide the opportunity to investigate local adaptation in natural populations and identify candidate genes under positive selection. In the present study, adaptation genetic differentiation associated with solar radiation was investigated using 695 polymorphic SNP markers in wild emmer wheat originated in a micro-site at Yehudiyya, Israel. The test involved two solar radiation niches: (1) sun, in-between trees; and (2) shade, under tree canopy, separated apart by a distance of 2–4 m. Analysis of molecular variance showed a small (0.53%) but significant portion of overall variation between the sun and shade micro-niches, indicating a non-ignorable genetic differentiation between sun and shade habitats. Fifty SNP markers showed a medium (0.05 ≤ FST ≤ 0.15) or high genetic differentiation (FST > 0.15). A total of 21 outlier loci under positive selection were identified by using four different FST-outlier testing algorithms. The markers and genome locations under positive selection are consistent with the known patterns of selection. These results suggested that genetic differentiation between sun and shade habitats is substantial, radiation-associated, and therefore ecologically determined. Hence, the results of this study reflected effects of natural selection through solar radiation on EST-related SNP genetic diversity, resulting presumably in different adaptive complexes at a micro-scale divergence. The present work highlights the evolutionary theory and application significance of solar radiation-driven natural selection in wheat improvement.

To evaluate the false-negative and false-positive error rates both in a screening and a non-screening population. A total of 4192 prostatic biopsies were reported in a 6-year period by 15 consultant histopathologists, two of whom had an interest in uropathology and were deemed to be specialists (J.O. and C.S.). All biopsies were reviewed prior to the multidisciplinary team (MDT) meeting. The overall false-negative rate was 1.7% (screening 2.1%, non-screening 1.5%). The overall false-positive rate was 0.5% (screening 0.9%, non-screening 0.4%). These error rates varied among pathologists, with the false-negative rate ranging from 0% to 9.3%, and the false-positive rate ranging from 0% to 3.8%. The false-negative rate was three times greater than the false-positive rate, showing that detection of significant pathology is far greater in the negative biopsies. More errors occurred in the screening population than in the non-screening population. The consultants making the most errors were non-specialists, but the specialists also made false-negative errors, suggesting that just using specialist reporting alone would not have eradicated errors.

Validation of the Minimum Data Set in Identifying Hospitalization Events and Payment Source

Understanding the extent of local adaptation in natural populations and the mechanisms that allow individuals to adapt to their native environment is a major avenue in molecular ecology research. Evidence for the frequent occurrence of diverging ecotypes in species that inhabit multiple ecological habitats is accumulating, but experimental approaches to understanding the biological pathways as well as the underlying genetic mechanisms are still rare. Parasites are invoked as one of the major selective forces driving evolution and are themselves dependent on the ecological conditions in a given habitat. Immunological adaptation to local parasite communities is therefore expected to be a key component of local adaptation in natural populations. Here, we use next-generation sequencing technology to compare the transcriptome-wide response of experimentally infected three-spined sticklebacks from a lake and a river population, which are known to evolve under selection by distinct parasite communities. By comparing overall gene expression levels as well as the activation of functional pathways in response to parasite exposure, we identified potential differences between the two stickleback populations at several levels. Our results suggest locally adapted patterns of gene regulation in response to parasite exposure, which may reflect different local optima in the trade-off between the benefits and the disadvantages of mounting an immune response because of quantitative differences of the local parasite communities.

Understanding how the environment shapes genetic variation provides critical insight about the evolution of local adaptation in natural populations. At multiple spatial scales and multiple geographic contexts within a single species, such information could address a number of fundamental questions about the scale of local adaptation and whether or not the same loci are involved at different spatial scales or geographic contexts. We used landscape genomic approaches from three local elevational transects and rangewide sampling to (a) identify genetic variation underlying local adaptation to environmental gradients in the California endemic oak, Quercus lobata; (b) examine whether putatively adaptive SNPs show signatures of selection at multiple spatial scales; and (c) map putatively adaptive variation to assess the scale and pattern of local adaptation. Of over 10k single-nucleotide polymorphisms (SNPs) generated with genotyping-by-sequencing, we found signatures of natural selection by climate or local environment at over 600 SNPs (536 loci), some at multiple spatial scales across multiple analyses. Candidate SNPs identified with gene-environment tests (LFMM) at the rangewide scale also showed elevated associations with climate variables compared to the background at both rangewide and elevational transect scales with gradient forest analysis. Some loci overlap with those detected in other oak species, raising the question of whether the same loci might be involved in local climate adaptation in different congeneric species that inhabit different geographic contexts. Mapping landscape patterns of adaptive versus background genetic variation identified regions of marked local adaptation and suggests nonlinear association of candidate SNPs and environmental variables. Taken together, our results offer robust evidence for novel candidate genes for local climate adaptation at multiple spatial scales.

Tardos has proposed a randomized fingerprinting code that is provably secure against collusion attacks. We revisit his scheme and show that it has significantly better performance than suggested in the original paper. First, we introduce variables in place of Tardos' hard-coded constants and we allow for an independent choice of the desired false positive (FP) and false negative (FN) error rates. Following through Tardos' proofs with these modifications, we show that the code length can be reduced by more than a factor of two in typical content distribution applications where high FN rates can be tolerated. Second, we study the statistical properties of the code. Under some reasonable assumptions, the accusation sums can be regarded as Gaussian-distributed stochastic variables. In this approximation, the desired error rates are achieved by a code length twice shorter than in the first approach. Overall, typical FP and FN error rates may be achieved with a code length approximately five times shorter than in the original construction.

<p>The purpose of this study was to extend Glas and Vos's (1998) Bayesian procedure to the 3PL IRT model by using the MCMC method. In the context of fixed-length mastery tests, the Bayesian decision-theoretic procedure was compared with two conventional procedures (conventional- Proportion Correct and conventional- EAP) across different simulation conditions. Several simulation conditions were investigated, including two loss functions (linear and threshold loss function), three item pools (high discrimination, moderate discrimination and real item pool) and three test lengths (20, 40 and 60). Different loss parameters were manipulated in the Bayesian decision-theoretic procedure to examine the effectiveness of controlling false positive and false negative errors. The degree of decision accuracy for the Bayesian decision-theoretic procedure using both the 3PL and 1PL models was also compared. Four criteria, including the percentages of correct classifications, false positive error rates, false negative error rates, and phi correlations between the true and observed classification status, were used to evaluate the results of this study. According to these criteria, the Bayesian decision-theoretic procedure appeared to effectively control false negative and false positive error rates. The differences in the percentages of correct classifications and phi correlations between true and predicted status for the Bayesian decision-theoretic procedures and conventional procedures were quite small. The results also showed that there was no consistent advantage for either the linear or threshold loss function. In relation to the four criteria used in this study, the values produced by these two loss functions were very similar. One of the purposes of this study was to extend the Bayesian procedure from the 1PL to the 3PL model. The results showed that when the datasets were simulated to fit the 3PL model, using the 1PL model in the Bayesian procedure yielded less accurate results. However, when the datasets were simulated to fit the 1PL model, using the 3PL model in the Bayesian procedure yielded reasonable classification accuracies in most cases. Thus, the use of the Bayesian decision-theoretic procedure with the 3PL model seemed quite promising in the context of fixed-length mastery tests.</p>

The Diagnosis Performance of Ultrasonic Transient Elastography for Noninvasive Assessment of Liver Fibrosis in 1138 Chronic Hepatitis C Patients

The Centers for Medicare and Medicaid Services (CMS) publish a report card for nursing homes with 19 clinical quality measures (QMs). These measures include minimal risk adjustment. To develop QMs with more extensive risk adjustment and to investigate the impact on quality rankings. Retrospective analysis of individual level data reported in the Minimum Data Set (MDS). Random effect logistic models were used to estimate risk adjustment models for 5 outcomes: pressure ulcers for high and low risk patients, physical restraints, and pain for long- and short-stay patients. These models were used to create 5 QMs with extended risk adjustment, enhanced QMs (EQMs). The EQMs were compared with the corresponding QMs. All (17,469) nursing homes that reported MDS data in the period 2001-2005, and their 9.6 million residents. QMs were compared with EQMs for all nursing homes in terms of agreement on outlier identification: Kappa, false positive and false negative error rates. Kappa values ranged from 0.63 to 0.90. False positive and negative error rates ranged from 8% to 37%. Agreement between QMs and EQMs was better on high quality rather than on low quality. More extensive risk adjustment changes quality ranking of nursing homes and should be considered as potential improvement to the current QMs. Other methodological issues related to construction of the QMs should also be investigated to determine if they are important in the context of nursing home care.

False positive errors are a significant component of many ecological data sets, which in combination with false negative errors, can lead to severe biases in conclusions about ecological systems. We present results of a field experiment where observers recorded observations for known combinations of electronically broadcast calling anurans under conditions mimicking field surveys to determine species occurrence. Our objectives were to characterize false positive error probabilities for auditory methods based on a large number of observers, to determine if targeted instruction could be used to reduce false positive error rates, and to establish useful predictors of among-observer and among-species differences in error rates. We recruited 31 observers, ranging in abilities from novice to expert, who recorded detections for 12 species during 180 calling trials (66,960 total observations). All observers made multiple false positive errors, and on average 8.1% of recorded detections in the experiment were false positive errors. Additional instruction had only minor effects on error rates. After instruction, false positive error probabilities decreased by 16% for treatment individuals compared to controls with broad confidence interval overlap of 0 (95% CI:--46 to 30%). This coincided with an increase in false negative errors due to the treatment (26%;--3 to 61%). Differences among observers in false positive and in false negative error rates were best predicted by scores from an online test and a self-assessment of observer ability completed prior to the field experiment. In contrast, years of experience conducting call surveys was a weak predictor of error rates. False positive errors were also more common for species that were played more frequently but were not related to the dominant spectral frequency of the call. Our results corroborate other work that demonstrates false positives are a significant component of species occurrence data collected by auditory methods. Instructing observers to only report detections they are completely certain are correct is not sufficient to eliminate errors. As a result, analytical methods that account for false positive errors will be needed, and independent testing of observer ability is a useful predictor for among-observer variation in observation error rates.

To evaluate three non-invasive assays for the diagnosis of schistosomiasis mansoni in an Egyptian village. Urine was collected for the detection of circulating cathodic antigen (CCA) and cell-free parasite DNA (cfpd) by Point-of-contact (POC)-cassette assay and PCR, respectively. These tests were compared to Kato-Katz (KK) faecal thick smear for detection of Schistosoma mansoni eggs. Disease prevalence by POC-CCA assay was 86%; by PCR it was 39% vs. 27% by KK. Compared to KK, the sensitivity of POC-CCA reached 100%, but its specificity was only 19.2% with 41% accuracy. Sensitivity of the PCR assay for cfpd was 55.56%, and specificity was 67.12% with 64% accuracy. A new end point was calculated for combined analysis of KK, POC-CCA assay and PCR. Sensitivity for the three tests was 52.94%, 90.2% and 76.47%; specificity was 100% for KK and PCR and 18.37% for POC-CCA. The accuracy calculated for the three tests at the end point was 76% for KK, 55% for POC-CCA assay and 88% for PCR. Conventional PCR assay for detection of cfpd provides a potential screening tool for intestinal schistosomiasis with reliable specificity, reasonable accuracy and affordable financial and technical cost.

To compare the clinical utilities of the SITA-based central 24-2 and 30-2 threshold tests. Three hundred sixty-five (365) eyes of 183 glaucoma and glaucoma suspect patients who had undergone both central 30-2 and 24-2 threshold testing using the Swedish interactive threshold algorithm (SITA) standard strategy were retrospectively reviewed. The tests were performed in patients with a minimum visual acuity of LogMAR best-corrected visual acuity (BCVA) 0.3. We compared test time, fixation loss (%), false-positive error rate (%), and false-negative error rate (%), all of which are indices of reliability. We additionally compared the mean deviation (MD), pattern standard deviation (PSD), and visual field index (VFI), all of which are indices of the visual field test. The mean age was 54.67 ± 14.95. MD, VFI, and fixation loss showed no significant difference between the 30-2 and 24-2 tests. As expected, 24-2 was shorter in duration: 5.64 ± 1.09min versus 7.51 ± 1.38min (p < .001), a 24.51 ± 9.45% difference. The false-positive error rate was significantly higher, but the false-negative error rate was lower, with the 24-2 threshold test (p = .009, p < .001). The PSD also was lower with 24-2 than with 30-2 (p < .001). The two tests' VFI and MD are comparable. The 24-2 test may be a more efficient examination for most patients in terms of test time. In the other relevant aspects, the two tests are not identical. Therefore, it would be advisable to tailor visual field testing to the individual patient.

Genotype-environment association (GEA) studies have the potential to identify the genetic basis of local adaptation in natural populations. Specifically, GEA approaches look for a correlation between allele frequencies and putatively selective features of the environment. Genetic markers with extreme evidence of correlation with the environment are presumed to be tagging the location of alleles that contribute to local adaptation. In this study, we propose a new method for GEA studies called the Weighted-Z Analysis (WZA) that combines information from closely linked sites into analysis windows in a way that was inspired by methods for calculating FST . Performing GEA methods in analysis windows has the advantage that it takes advantage of the increased linkage disequilibrium expected surrounding sites subject to local adaptation. We analyse simulations modelling local adaptation to heterogeneous environments to compare the WZA with existing methods. In the majority of cases we tested, the WZA either outperformed single-SNP (single nucleotide polymorphism)-based approaches or performed similarly. In particular, the WZA outperformed individual SNP approaches when a small number of individuals or demes were sampled. Particularly troubling, we found that some GEA methods exhibit very high false positive rates. We applied the WZA to previously published data from lodgepole pine and identified candidate loci that were identified in the original study alongside numerous loci that were not found in the original study.