Erosion of regression effect in a survival study

Lack of persistence, or erosion, of the regression effect is an alternative to proportional hazards of particular interest in many medical applications. Such a departure from proportional hazards is often the most likely direction in which the model may be inadequate. Questions such as, is the effect of treatment only transitory or to what extent does an initially measured prognostic variable maintain its impact, frequently arise. In the context of a simple changepoint model, we propose a test of the null hypothesis of proportional hazards against the specific alternative of erosion of the regression effect. The particular changepoint model used can be viewed as a first approximation to a more complex reality, an approximation that enables us to avoid specifically modeling the functional form that any erosion might take. Practical guidelines for carrying out the test are provided. The approach is illustrated in the context of a study on risk factors for breast cancer survival.     

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.     

Sex chromosomes and male ornaments: a comparative evaluation in ray-finned fishes

Theory predicts that the mechanism of genetic sex determination can substantially influence the evolution of sexually selected traits. For example, female heterogamety (ZZ/ZW) can favour the evolution of extreme male traits under Fisher's runaway model of sexual selection. We empirically test whether the genetic system of sex determination has played a role in the evolution of exaggerated male ornaments in actinopterygiian fishes, a clade in which both female-heterogametic and male-heterogametic systems of sex determination have evolved multiple times. Using comparative methods both uncorrected and corrected for phylogenetic non-independence, we detected no significant correlation between sex-chromosome systems and sexually selected traits in males. Results suggest that sex-determination mechanism is at best a relatively minor factor affecting the outcomes of sexual selection in ray-finned fishes.     

Statistical test for the comparison of samples from mutational spectra

The Monte Carlo estimate of the p value of the hypergeometric test is described and advocated for the testing of the hypothesis that different treatments induce the same mutational spectrum. The hypergeometric test is a generalization of Fisher's "exact" test for tables with more than two rows and two columns. Use of the test is demonstrated by the analysis of data from the characterization of nonsense mutations in the lacI gene of Escherichia coli. Unlike the chi-square test, the hypergeometric test remains valid when applied to sparse cross-classification tables. The hypergeometric test has the most discrimination power of any statistical test that could be employed routinely to compare samples from mutational spectra. Direct application of the hypergeometric test to large cross-classification tables is excessively computation intensive, but estimation of its p value via Monte Carlo techniques is practical.     

Modelling the recovery of resident shorebirds following a fox eradication program using citizen science data

Historically, the land-based threat to shorebird colonies on Phillip Island, Victoria, Australia, was fox predation. As a result, a fox eradication programme consisting of three phases: knock-down (i.e., 2006), clean-up (i.e., 2011), and post-eradication. In 2011 an effective knock-down was declared, signalling the beginning of the clean-up phase. The purpose of this research is to assess the recovery of six resident shorebird species on Phillip Island following fox removal. The statistical methodologies used are novel for assessing bird species population recovery following a successful predator eradication program. We used citizen science data from 2003 to 2017, extracted from the Atlas of Living Australia. The first analysis method used INLA modelling, which relied on a Negative Binomial distribution for bird counts to look for upward trends in shorebird populations during the fox eradication operation. The second method use changepoint analysis techniques to see whether successive phases of the eradication process were associated with changes in bird population numbers. Four of the six shorebird species investigated responded positively to reduced fox populations over the 15-year study, and all changepoint approaches consistently recognised the start of the clean-up phase, with less consistency identifying the start of the knock-down phase. Since 2006, the INLA models indicate a significant increase in the upward trend of shorebird populations for three of the six shorebird species investigated. Agreement across the four changepoint techniques indicates that changes in bird numbers were associated with the date of the eradication program's clean-up phase for all of these shorebird species. These results demonstrate some promise for these methods to monitor native species recovery during eradication programs.     

The spatial distribution of transient alleles in a subdivided population: a simulation study

The spatial distributions of newly introducted alleles in a subdivided population are generated using a computer program to model the processes of selection, gene flow and genetic drift. Advantageous, neutral and deleterious alleles are considered, and certain aspects of the patterns generated by new alleles that are ultimately fixed and ultimately lost are examined. To characterize the spatial pattern of rare alleles, the distribution, P(i), the probability that the new allele is found in exactly i local populations before it is lost, is defined and estimated from the simulations. The shape of the P(i) distribution is surprisingly similar for selected and neutral alleles. For advantageous alleles going to fixation, the "wave of advance" is set up quickly, but stochastic effects reduce the wave speed from Fisher's (1937) value. Gene flow is much more effective in dispersing alleles in a two-dimensional array than in one dimension. Long distance gene flow has a much smaller effect in two dimensions than in one dimension.     

The significance of not finding a gene

As more investigators conduct extensive whole-genome linkage scans for complex traits, interest is growing in meta-analysis as a way of integrating the weak or conflicting evidence from multiple studies. However, there is a bias in the most commonly used meta-analysis linkage technique (i.e., Fisher's [1925] method of combining of P values) when it is applied to many nonparametric (i.e., model free) linkage results. The bias arises in those methods (e.g., variance components, affected sib pair, extremely discordant sib pairs, etc.) that truncate all "negative evidence against linkage" into the single value of LOD = 0. If incorrectly handled, this bias can artificially inflate or deflate the combined meta-analysis linkage results for any given locus. This is an especially troublesome problem in the context of a genome scan, since LOD = 0 is expected to occur over half the unlinked genome. The bias can be overcome (nearly) completely by simply interpreting LOD = 0 as a P value of 1divided by 2ln(2) is approximately equal to .72 in Fisher's formula.     

A novel approach to search for identity by descent in small samples of patients and controls from the same mendelian breeding unit: a pilot study on myopia.

Autosomal dominant high myopia, a genetic disorder already mapped to region 18p11.31, is common in Carloforte (Sardinia, Italy), an isolated village of 8,000 inhabitants descending from a founder group of 300 in the early 1700s. Fifteen myopic propositi and 36 normal controls were selected for not having ancestors in common at least up to the grandparental generation, although still descendants of the original founders. All subjects were genotyped for 14 markers located on autosome 18 at a resolution of about 10 cM. Allelic distributions were found to be similar at all tested loci in propositi and controls, except for the candidate marker D18S63 known to segregate in close linkage association with high myopia. In particular, the frequency of allele 85 among the propositi was almost double that of the controls (Fisher's exact test, p = 0.037). The association is more striking when the frequency of the genotype 85/85 in the two groups is compared (Fisher's exact test, p = 0.005). This conclusion was further evaluated through a bootstrap analysis by computing the overall probability of the observed data under the null hypothesis (i.e. no difference between the two groups in frequency distributions for the chromosome 18 markers). Again, marker D18S63 was found to have a sample probability lower than 0.004, which is significant at the 0.05 level after correcting for simultaneous testing of multiple loci. The study demonstrates the efficiency of our novel strategy to detect identity by descent (IBD) in small numbers of patients and controls when they are both part of well-defined Mendelian breeding units (MBUs). The iterative application of our strategy in separate MBUs is expected to become the method of choice to evaluate the ever-growing number of reported associations between candidate genes and multifactorial traits and diseases.     

Combining probability from independent tests: the weighted Z-method is superior to Fisher's approach

The most commonly used method in evolutionary biology for combining information across multiple tests of the same null hypothesis is Fisher's combined probability test. This note shows that an alternative method called the weighted Z-test has more power and more precision than does Fisher's test. Furthermore, in contrast to some statements in the literature, the weighted Z-method is superior to the unweighted Z-transform approach. The results in this note show that, when combining P-values from multiple tests of the same hypothesis, the weighted Z-method should be preferred.     

Detection of a treatment effect when not all experimental subjects will respond to treatment.

Non-responders attenuate average response an inflate sample variance, reducing the power of standard parametric tests. A new Fisher's type randomization test, which has no parametric analogue, is recommended when not all subjects may be capable of responding to treatment. The new test was evaluated by Monte Carlo means and applied to drug abuse data and to virus titre data. In most trial applications the new test proved to be more sensitive to treatment effects than Student's t.     

Segmented regression in the presence of covariate measurement error in main study/validation study designs

This article considers the problem of segmented regression in the presence of covariate measurement error in main study/validation study designs. First, we derive a closed and interpretable form for the full likelihood. After that, we use the likelihood results to compute the bias of the estimated changepoint in the case when the measurement error is ignored. We find the direction of the bias in the estimated changepoint to be determined by the design distribution of the observed covariates, and the bias can be in either direction. We apply the methodology to data from a nutritional study that investigates the relation between dietary folate and blood serum homocysteine levels and find that the analysis that ignores covariate measurement error would have indicated a much higher minimum daily dietary folate intake requirement than is obtained in the analysis that takes covariate measurement error into account.     

A comparison of eight methods for the dual-endpoint evaluation of efficacy in a proof-of-concept HIV vaccine trial

To support the design of the world's first proof-of-concept (POC) efficacy trial of a cell-mediated immunity-based HIV vaccine, we evaluate eight methods for testing the composite null hypothesis of no-vaccine effect on either the incidence of HIV infection or the viral load set point among those infected, relative to placebo. The first two methods use a single test applied to the actual values or ranks of a burden-of-illness (BOI) outcome that combines the infection and viral load endpoints. The other six methods combine separate tests for the two endpoints using unweighted or weighted versions of the two-part z, Simes', and Fisher's methods. Based on extensive simulations that were used to design the landmark POC trial, the BOI methods are shown to have generally low power for rejecting the composite null hypothesis (and hence advancing the vaccine to a subsequent large-scale efficacy trial). The unweighted Simes' and Fisher's combination methods perform best overall. Importantly, this conclusion holds even after the test for the viral load component is adjusted for bias that can be introduced by conditioning on a postrandomization event (HIV infection). The adjustment is derived using a selection bias model based on the principal stratification framework of causal inference.     

Genotype of an individual single nucleotide polymorphism regulates DNA methylation at the TRPC3 alternative promoter

A fundamental challenge in the post-genomics era is to understand how genetic variants can influence phenotypic variability and disease. Recent observations from a number of studies have highlighted a mechanism by which common genetic polymorphisms can influence DNA methylation, a major epigenetic silencing mechanism. We report that the alternative promoter of the human TRPC3 gene is regulated by allelic DNA methylation, dictated by the genotype of a single base pair polymorphism, rs13121031 located within the promoter CpG island. The common G allele is associated with high levels of methylation, while the less prevalent C allele is unmethylated. This methylation profile is observed in many tissue types, despite the expression of?TRPC3?being restricted to brain and heart.?TRPC3?is prominently expressed in the hindbrain, and a heterozygous brain sample showed modest skewing according to the allelic methylation, with preferential expression from the C allele. The?TRPC3?gene encodes a transient receptor potential channel that has been implicated in cerebellar ataxia and heart hypertrophy. The genotype-frequencies of rs13121031 were determined in cohorts of ataxia patients and in individuals with cardiac hypertrophy. These analyses revealed a statistical trend for the rare unmethylated homozygous C genotype to be present at a higher frequency in idiopathic ataxia patients (Fisher's test p=0.06), but not in those patients with known mutations (Fisher's test p=0.55) or in individuals with heart disease (Fisher's test p=0.807), when compared to a control population. Our results suggest that the?TRPC3?alternative promoter is a methylation quantitative-trait locus that may be involved in modulating the ataxia phenotype.     

Changes in the erythrocyte glutathione concentration in the course of diabetes mellitus

This study aims to evaluate the significance of the changes of erythrocyte reduced glutathione (GSH) in the course of diabetes mellitus including the pre-diabetes stage and cardiovascular disease co-morbidity. A total of 222 participants (female:male, 107:115) were selected and their erythrocyte GSH levels were measured. The participants were divided into four groups: (i) control; (ii) those with blood glucose level > or =5.6 mmol/l but < 6.9 mmol/l as pre-diabetes mellitus with no other pathology; (iii) diabetes without co-morbidity; and (iv) those with diabetes mellitus and cardiovascular disease. Statistical analysis was by ANOVA followed by a Fisher's LSD post hoc test. We observed that GSH concentration was significantly different between groups (P < 0.04). The Fisher's post hoc test indicated significant differences in erythrocyte GSH levels between the pre-diabetes mellitus and diabetes mellitus groups compared to control (P < 0.005 and P < 0.05, respectively). A statistically significant change (P < 0.001) involving an initial fall followed by a rise in erythrocyte GSH levels was observed when diabetes mellitus and diabetes mellitus+cardiovascular disease groups were combined and assessed with respect to period of diabetes. We conclude that oxidative stress is already present in the pre-diabetes stage as determined by the fall in GSH, representing the initial phase of oxidative stress in diabetes mellitus progression. This finding provides evidence that antioxidant markers such as GSH could be a useful tool for pre-diabetes mellitus screening.     

Optimally weighted Z-test is a powerful method for combining probabilities in meta-analysis

The inverse normal and Fisher's methods are two common approaches for combining P-values. Whitlock demonstrated that a weighted version of the inverse normal method, or 'weighted Z-test', is superior to Fisher's method for combining P-values for one-sided T-tests. The problem with Fisher's method is that it does not take advantage of weighting and loses power to the weighted Z-test when studies are differently sized. This issue was recently revisited by Chen, who observed that Lancaster's variation of Fisher's method had higher power than the weighted Z-test. Nevertheless, the weighted Z-test has comparable power to Lancaster's method when its weights are set to square roots of sample sizes. Power can be further improved when additional information is available. Although there is no single approach that is the best in every situation, the weighted Z-test enjoys certain properties that make it an appealing choice as a combination method for meta-analysis.     

Serum levels of soluble CD30 in adult patients affected by atopic dermatitis and its relation to age,duration of disease and Scoring Atopic Dermatitis index

The value of CD30 and the soluble circulating fragment of CD30 (sCD30) for atopic dermatitis (AD) remains unclear. In particular, little is known about the effects of age, duration of disease and Scoring Atopic Dermatitis index (SCORAD) on the levels of serum sCD30 in patients affected by AD. In the present study, we have analysed serum sCD30 levels of adult patients affected by AD. The study's population includes 18 non-smoking outpatients, with a diagnosis of AD. As a control group we studied 18 non-atopic subjects from laboratory staff, matched for sex and age. These subjects had no history of AD, urticaria or seasonal or perennial rhinitis or asthma, and had negative skin prick test to a panel of allergens. The sCD30 serum levels were clearly higher in patients affected by AD (14.2+/-9.0 IU/ml) than in healthy subjects (1.2+/-0.8 IU/ml) (p<0.001). No differences were observed between males and females affected by atopic dermatitis, regarding age, duration of disease and SCORAD. Significant correlations were found between serum levels of sCD30 levels and age (r=-0.55; 95% confidence interval (CI) for r (Fisher's z transformed)=-0.81 to -0.12; p=0.01), duration of the disease (months) (r=-0.64; 95% CI for r (Fisher's z transformed)=-0.85 to -0.24; p=0.004) and SCORAD (r=-0.74; 95% CI for r (Fisher's z transformed)=-0.89 to -0.42; p=0.004). As demonstrated by the close correlation with age, duration of disease and SCORAD, serum levels of sCD30 appear to be an additional marker for the follow-up of AD.     

Handling Stress as a Measurement of Personality in Great Tit Nestlings (Parus major)

Interest in personality is growing in a wide range of disciplines, but only in a few systems it is possible to assess the survival value of personality. Field studies looking at the relationship between personality and survival value early in life are greatly hampered by the fact that personality can at present only be assessed after individuals become independent from their parents. In passerines, for example, this is often after a period of intensive selection for the survival on fledglings. The main aim of this study is therefore to develop a method to measure personality before this period of selection. For this purpose, we developed the handling stress (HS) test. We measured HS in 14-d-old great tit nestlings by counting the number of breast movements (breath rate) in four subsequent 15-s bouts for 1 min; before and after they were socially isolated from their siblings for 15 min. To calculate the repeatability of HS, we repeated the test 6 mo later. To assess the relationship between HS and exploratory behaviour, we correlated the outcome of both tests. We ran tests both on birds of lines selected for extreme personality and on wild birds from a natural population. We found that birds selected for fast exploration reacted more to HS compared with birds selected for slow exploration and that HS was repeatable in different life phases. We confirmed this by finding an increase in the HS with increasing exploratory scores in wild birds. These results show that we can use the HS test as a measurement of personality, making it a potential tool for studying the relationship between personality and survival value early in life.     

Comparative study of gene set enrichment methods

Background  

The analysis of high-throughput gene expression data with respect to sets of genes rather than individual genes has many advantages. A variety of methods have been developed for assessing the enrichment of sets of genes with respect to differential expression. In this paper we provide a comparative study of four of these methods: Fisher's exact test, Gene Set Enrichment Analysis (GSEA), Random-Sets (RS), and Gene List Analysis with Prediction Accuracy (GLAPA). The first three methods use associative statistics, while the fourth uses predictive statistics. We first compare all four methods on simulated data sets to verify that Fisher's exact test is markedly worse than the other three approaches. We then validate the other three methods on seven real data sets with known genetic perturbations and then compare the methods on two cancer data sets where our a priori knowledge is limited.     

A comparison of tests for independence in the FBI RFLP data bases

Several tests of independence of alletic frequencies within and between loci have been compared, and it has been found that Fisher's exact test is the best test to use. When this test is applied to RFLP databases established by the FBI, paying no attention to the single-band problem, there is generally evidence for independence at one locus but not at two loci. When the test is restricted to double-banded entries in the databases; there is overall evidence for independence.     

Evolution by small steps and rugged landscapes in the RNA virus phi6

Fisher's geometric model of adaptive evolution argues that adaptive evolution should generally result from the substitution of many mutations of small effect because advantageous mutations of small effect should be more common than those of large effect. However, evidence for both evolution by small steps and for Fisher's model has been mixed. Here we report supporting results from a new experimental test of the model. We subjected the bacteriophage phi6 to intensified genetic drift in small populations and caused viral fitness to decline through the accumulation of a deleterious mutation. We then propagated the mutated virus at a range of larger population sizes and allowed fitness to recover by natural selection. Although fitness declined in one large step, it was usually recovered in smaller steps. More importantly, step size during recovery was smaller with decreasing size of the recovery population. These results confirm Fisher's main prediction that advantageous mutations of small effect should be more common. We also show that the advantageous mutations of small effect are compensatory mutations whose advantage is conditional (epistatic) on the presence of the deleterious mutation, in which case the adaptive landscape of phi6 is likely to be very rugged.