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.