A KPSS test for stationarity for spatial point processes

Summary .   We propose a formal method to test stationarity for spatial point processes. The proposed test statistic is based on the integrated squared deviations of observed counts of events from their means estimated under stationarity. We show that the resulting test statistic converges in distribution to a functional of a two-dimensional Brownian motion. To conduct the test, we compare the calculated statistic with the upper tail critical values of this functional. Our method requires only a weak dependence condition on the process but does not assume any parametric model for it. As a result, it can be applied to a wide class of spatial point process models. We study the efficacy of the test through both simulations and applications to two real data examples that were previously suspected to be nonstationary based on graphical evidence. Our test formally confirmed the suspected nonstationarity for both data.     

Semiparametric modelling and estimation of covariate-adjusted dependence between bivariate recurrent events

A time-dependent measure, termed the rate ratio, was proposed to assess the local dependence between two types of recurrent event processes in one-sample settings. However, the one-sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received. The focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events. We propose the covariate-adjusted rate ratio, a measure of covariate-adjusted dependence. We propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events: the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure. We develop a pseudo-partial likelihood to estimate the parameters in the proportional rate ratio model. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. We illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local/distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence.     

亲代传递的独立性与传递不平衡的边缘齐性检验

传递不平衡检验其实质是边缘齐性检验,需同时考察家系中两个亲代向受累子代的传递情形．但是,其零假设成立时,同一家系中父亲的传递与母亲的传递并不一定相互独立．本文探讨了父母传递的独立性条件对检验统计量的影响．结果表明,即使父母传递不独立时,边缘齐性检验仍然适合．     

A Modified Chi-Square Test for Testing Equality of Two Multinomial Populations Against an Ordering Restricted Alternative

A modified chi-square test for testing the equality of two multinomial populations against an ordering restricted alternative in one sample and two sample cases is constructed. The relation between a concept of dependence called dependence by chi-square and stochastic ordering is established. A tabulation of the asymptotic distribution of the test statistic under the null hypothesis is given. Simulations are used to compare the power of this test with the power of the likelihood ratio test of stochastic ordering of the two multinomial populations.     

Hydrogen exchange and proteolytic degradation of ribonuclease A. Similarities and distinctions of the kinetic mechanisms

The studies by IR spectroscopy of the temperature dependence of the H-D exchange rate of the RNase A peptide NH atoms permit one to characterize two types of conformation fluctuations, local and global. A comparison with the temperature dependence of the proteolytic degradation rate of RNase A shows that similar in nature fluctuations allow for the H-D exchange of NH atoms and the splitting of peptide bonds of the native protein. In the low temperature region, both processes occur through local fluctuations, by way of the EX2 mechanism, and in the high temperature region, they occur through global fluctuations with the overall denaturation desorganization of the native structure, by way of the EX1 mechanism. The biphasic dependence of the rate of H-D exchange and proteolytic degradation of RNase A on urea concentration is also explained by the combination of local and global fluctuations.     

Adaptive designs with arbitrary dependence structure

Adaptive designs were originally developed for independent and uniformly distributed p‐values. There are trial settings where independence is not satisfied or where it may not be possible to check whether it is satisfied. In these cases, the test statistics and p‐values of each stage may be dependent. Since the probability of a type I error for a fixed adaptive design depends on the true dependence structure between the p‐values of the stages, control of the type I error rate might be endangered if the dependence structure is not taken into account adequately. In this paper, we address the problem of controlling the type I error rate in two‐stage adaptive designs if any dependence structure between the test statistics of the stages is admitted (worst case scenario). For this purpose, we pursue a copula approach to adaptive designs. For two‐stage adaptive designs without futility stop, we derive the probability of a type I error in the worst case, that is for the most adverse dependence structure between the p‐values of the stages. Explicit analytical considerations are performed for the class of inverse normal designs. A comparison with the significance level for independent and uniformly distributed p‐values is performed. For inverse normal designs without futility stop and equally weighted stages, it turns out that correcting for the worst case is too conservative as compared to a simple Bonferroni design.     

A semi-parametric approach for comparing the estimated spectra of two stationary point processes

In this paper, we provide a semi-parametric test for the hypothesis that the spectra of two stationary point processes (SPPs) are the same. The estimates of the second-order spectral density functions of the SPPs are obtained by using two different approaches: (a) by smoothing the modified periodogram statistics using a moving average weighting scheme, (b) by employing the Welch's method on the modified periodogram statistics. The test is based on the likelihood ratio function under two alternative hypotheses. The first alternative hypothesis suggests that the ratio of the spectra is a constant (there is a shift to the power) while the second one adopts a quadratic model for the logarithmic ratio of the spectra. A comparison with a log-linear model indicates coincidence in the results. This is explained by using an illustrative example from the field of neurophysiology. It is shown that the information transferred to the spinal cord by the sensory axons, closely related with the complex physiological system called muscle spindle, under the influence of two different stimuli can be separated in two parts. The first part corresponds to the range of frequencies 0-19 Hz while the second to the range of frequencies 19-100 Hz. However, the dependence on the frequency in both parts is of a quadratic form.     

Rates of diffusion controlled reactions in one, two and three dimensions

The dimensionality of diffusion may markedly affect the rate and economy of diffusion controlled reactions. Moreover, the degree of dependence of the steady state rate of these reactions on the concentration of each of the two reacting species is also dictated by the dimensionality and it ranges from linear dependence in the three dimensional case to a nearly square dependence in the one dimensional case. These theoretical observations emerge from a direct analysis of the steady state diffusion controlled rates which are derived here using a simple straightforward approach. This approach is based on the conjecture that in the steady state the rate of diffusional encounters between the two reaction partners equals to the sum of the encounter rates of two independent processes which are obtained by alternately immobilizing one of the reaction partners while the other partner diffuses freely. Unlike Smoluchowski's classical approach, the presented point of view permits to obtain in a unified fashion reaction rates for all dimensionalities.     

Small Vaccination Experiments with Binary Outcome: The Paradox of Increasing Power with Decreasing Sample Size and/or Increasing Imbalance

In animal vaccination experiments with binary outcome (diseased/non diseased), the comparison of the vaccinated and control group is often based on the Fisher exact test. A tool for the evaluation of different designs is proposed, based on the expected power of the Fisher exact test. The expected power can sometimes unexpectedly increase with decreasing sample size and/or increasing imbalance. The reasons for these peculiar results are explained and compared to the results of two other types of tests: the unconditional test and the randomisation test. In a vaccination experiment with a restricted number of animals it is shown to be important to consider expected power in order to choose the most appropriate design.     

Mechanical characterization of liver capsule through uniaxial quasi-static tensile tests until failure

Accidentology data showed that liver is often injured in car crashes; three types of injuries occur: hematoma, laceration and vessel failure. This paper focuses on surface laceration, which involves liver capsule and hepatic parenchyma. Liver capsule behavior has been studied but its failure properties are still unclear, particularly on a local point of view. In the present study, tensile quasi-static tests are run on parenchyma and capsule samples until failure to characterize capsule failure. Normalized load as well as failure properties—ultimate load per width unit and ultimate strain—are determined. Digital image correlation is used to measure the full local strain field on the capsule. Mean values of failure characteristics for hepatic capsule are 47±29% for the ultimate local strain and 0.3±0.3 N/mm for the ultimate load per width unit. A comparison between human and porcine tissues is conducted based on Mann–Whitney statistical test; it reveals that capsule characteristics are close between these two species; however, freezing preservation significantly affects porcine capsule failure properties. Therefore using porcine instead of human tissue to determine failure characteristics of liver capsule seems satisfactory only on fresh tissues.     

Population dynamics of coral-reef fishes: Controversial concepts and hypotheses

Abstract Knowledge of processes that drive the local population dynamics of coral-reef fishes is important for managing reef fisheries, and for using these species as models for understanding the ecology of demersal marine fishes in general. However, the reef-fish literature is replete with poorly defined concepts and vague hypotheses regarding the issue of population dynamics. Dichotomous arguments, such as whether or not recruitment drives population dynamics, are misdirected because they fail to incorporate several important concepts. First, changes in local population size are driven by four demographic rates (birth, death, immigration and emigration), all of which must be studied to understand population dynamics. Second, all populations that persist do so because at least one of these demographic rates operates in a density-dependent way that is both sufficiently strong and appropriately time-lagged. Therefore, identifying the source(s) of direct density dependence is critical for understanding the limits to variation in population size (i.e. population regulation). Third, regulation does not imply a simple point equilibrium in population size; density dependence in populations of reef fishes is bound to lie within a field of stochastic variation, and thus be difficult to detect. Since its formal origin in 1981, the ‘recruitment limitation’ hypothesis for explaining local population dynamics in reef fishes has undergone ambiguous changes in definition that threaten its usefulness. ‘Recruitment, ‘originally defined as the appearance of newly settled fish on a reef, more recently is often measured months after settlement, thus confounding pre- and post-settlement processes. ‘Limitation, ‘ which originally referred to recruitment being so low as to preclude local populations from reaching densities where resources were limiting, is more recently defined as an absence of any form of density dependence after settlement. The most effective means of testing whether post-settlement mortality is in fact density-independent is to examine patterns of mortality directly, rather than indirectly by interpreting the shape of the relationship between initial recruit density and subsequent adult density within a cohort (the recruit-adult function). Understanding the population dynamics of coral-reef fishes will require a more equitable focus on all four demographic rates, be they density dependent or not, as well as greater attention to identifying sources of density dependence. Such a pluralistic focus necessitates integrated studies of both pre- and post-settlement processes conducted at multiple spatial and temporal scales. For example, recent evidence suggests that density-dependent pre-dation on new recruits that have settled among reefs at different densities may prove to be an important source of local population regulation, especially via the aggregative response of transient piscivores.     

Stochastically driven adult–recruit associations of tree species on Barro Colorado Island

The spatial placement of recruits around adult conspecifics represents the accumulated outcome of several pattern-forming processes and mechanisms such as primary and secondary seed dispersal, habitat associations or Janzen–Connell effects. Studying the adult–recruit relationship should therefore allow the derivation of specific hypotheses on the processes shaping population and community dynamics. We analysed adult–recruit associations for 65 tree species taken from six censuses of the 50 ha neotropical forest plot on Barro Colorado Island (BCI), Panama. We used point pattern analysis to test, at a range of neighbourhood scales, for spatial independence between recruits and adults, to assess the strength and type of departure from independence, and its relationship with species properties. Positive associations expected to prevail due to dispersal limitation occurred only in 16% of all cases; instead a majority of species showed spatial independence (≈73%). Independence described the placement of recruits around conspecific adults in good approximation, although we found weak and noisy signals of species properties related to seed dispersal. We hypothesize that spatial mechanisms with strong stochastic components such as animal seed dispersal overpower the pattern-forming effects of dispersal limitation, density dependence and habitat association, or that some of the pattern-forming processes cancel out each other.     

Penalized survival models for the analysis of alternating recurrent event data

Recurrent event data are widely encountered in clinical and observational studies. Most methods for recurrent events treat the outcome as a point process and, as such, neglect any associated event duration. This generally leads to a less informative and potentially biased analysis. We propose a joint model for the recurrent event rate (of incidence) and duration. The two processes are linked through a bivariate normal frailty. For example, when the event is hospitalization, we can treat the time to admission and length-of-stay as two alternating recurrent events. In our method, the regression parameters are estimated through a penalized partial likelihood, and the variance-covariance matrix of the frailty is estimated through a recursive estimating formula. Moreover, we develop a likelihood ratio test to assess the dependence between the incidence and duration processes. Simulation results demonstrate that our method provides accurate parameter estimation, with a relatively fast computation time. We illustrate the methods through an analysis of hospitalizations among end-stage renal disease patients.     

Analysis of multi-type recurrent events in longitudinal studies; application to a skin cancer prevention trial

We consider the statistical modeling and analysis of replicated multi-type point process data with covariates. Such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types. The underlying processes are modeled as nonhomogeneous mixed Poisson processes with random (subject) and fixed (covariate) effects. The method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients. Score tests and likelihood ratio statistics are used for covariate selection. A graphical test of goodness of fit of the selected model is based on generalized residuals. Measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed. An application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer.     

Nonparametric One‐way Analysis of Variance of Replicated Bivariate Spatial Point Patterns

A common problem in neuropathological studies is to assess the spatial patterning of cells on tissue sections and to compare spatial patterning between disorder groups. For a single cell type, the cell positions constitute a univariate point process and interest focuses on the degree of spatial aggregation. For two different cell types, the cell positions constitute a bivariate point process and the degree of spatial interaction between the cell types is of interest. We discuss the problem of analysing univariate and bivariate spatial point patterns in the one‐way design where cell patterns have been obtained for groups of subjects. A bootstrapping procedure to perform a nonparametric one‐way analysis of variance of the spatial aggregation of a univariate point process has been suggested by Diggle, Lange and Bene? (1991). We extend their replication‐based approach to allow the comparison of the spatial interaction of two cell types between groups, to include planned comparisons (contrasts) and to assess whole groups against complete spatial randomness and spatial independence. We also accommodate several replicate tissue sections per subject. An advantage of our approach is that it can be applied when processes are not stationary, a common problem in brain tissue sections since neurons are arranged in cortical layers. We illustrate our methods by applying them to a neuropathological study to investigate abnormalities in the functional relationship between neurons and astrocytes in HIV associated dementia. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A measure of local variation of inter-spike intervals

It has been revealed in our recent study that cortical neurons are categorized into distinct types, according to a new measure of the local variation of inter-spike intervals, L(V). In this paper, we obtain values of the local variation L(V) and a conventional coefficient of variation C(V) for a variety of model point processes. While the value of C(V) undergoes large changes by rate fluctuation of the point processes, the value of L(V) does not undergo large changes by rate fluctuation, and is principally determined by the form of intrinsic interval distribution of the original model point process.     

On the use of comparison regions in visualizing stochastic uncertainty in some two-parameter estimation problems

When considering simultaneous inference for two parameters, it is very common to visualize stochastic uncertainty by plotting two-dimensional confidence regions. This allows us to test post hoc null hypotheses about a single point in a simple manner. However, in some applications the interest is not in rejecting hypotheses on single points, but in demonstrating evidence for the two parameters to be in a convex subset of the parameter space. The specific convex subset to be considered may vary from one post hoc analysis to another. Then it is of interest to have a visualization allowing to perform corresponding analyses. We suggest comparison regions as a simple tool for this task.     

Local-regional relationships and the geographical distribution of species

Aim Local‐regional (LR) species diversity plots were conceived to assess the contribution of regional and local processes in shaping the patterns of biological diversity, but have been used also to explore the scaling of diversity in terms of its alpha, beta, and gamma components. Here we explore the idea that patterns in the geographical ranges of species over a continent can determine the shape of small region to large region (SRLR) plots, which are equivalent to LR plots when comparing the diversity of sites at two regional scales. Location To test that idea, we analysed the diversity patterns at two regional scales for the mammals of North America, defined as the mainland from Alaska and Canada to Panama. Method We developed a theoretical model relating average range size of species over a large‐scale region with its average regional point species diversity (RPD). Then, we generated a null model of expected SRLR plots based on theoretical predictions. Species diversities at two scales were modelled using linear and saturation functions for Type I and Type II SRLR relationships, respectively. We applied the models to the case of North American mammals by examining the regional diversity and the RPD for 21 large‐scale quadrats (with area equal to 160,000 km²), arranged along a latitudinal gradient. Results Our model showed that continental and large‐scale regional patterns of distribution of species can generate both types of SRLR relationship, and that these patterns can be reflected in LR plots without invoking any kind of local processes. We found that North American nonvolant mammals follow a Type I SRLR relationship, whereas bats follow a Type II pattern. This difference was linked to patterns in which species of the two mammalian groups distribute in geographical space. Conclusion Traditional LR plots and the new SRLR plots are useful tools in exploring the scaling of species diversity and in showing the relationship between distribution and diversity. Their usefulness in comparing the relative role of local and regional processes is, however, very limited.     

The role of chronotype,gender, test anxiety,and conscientiousness in academic achievement of high school students

Previous findings have demonstrated that chronotype (morningness/intermediate/eveningness) is correlated with cognitive functions, that is, people show higher mental performance when they do a test at their preferred time of day. Empirical studies found a relationship between morningness and higher learning achievement at school and university. However, only a few of them controlled for other moderating and mediating variables. In this study, we included chronotype, gender, conscientiousness and test anxiety in a structural equation model (SEM) with grade point average (GPA) as academic achievement outcome. Participants were 158 high school students and results revealed that boys and girls differed in GPA and test anxiety significantly, with girls reporting better grades and higher test anxiety. Moreover, there was a positive correlation between conscientiousness and GPA (r = 0.17) and morningness (r = 0.29), respectively, and a negative correlation between conscientiousness and test anxiety (r = –0.22). The SEM demonstrated that gender was the strongest predictor of academic achievement. Lower test anxiety predicted higher GPA in girls but not in boys. Additionally, chronotype as moderator revealed a significant association between gender and GPA for evening types and intermediate types, while intermediate types showed a significant relationship between test anxiety and GPA. Our results suggest that gender is an essential predictor of academic achievement even stronger than low or absent test anxiety. Future studies are needed to explore how gender and chronotype act together in a longitudinal panel design and how chronotype is mediated by conscientiousness in the prediction of academic achievement.     

Electrostatic effect upon association of reduced nicotinamide adenine dinucleotide and equine liver alcohol dehydrogenase

The rate of association of equine liver alcohol dehydrogenase and its coenzymes exhibits a large pH dependence with slower rates at basic pH and an observed kinetic pKa value of approximately 9-9.5. This pH dependence has been explained by invoking local active site electrostatic effects which result in repulsion of the negatively charged coenzyme and the ionized hydroxyl anion form of the zinc-bound water molecule. We have examined a simpler hypothesis, namely, that the pH dependence results from the electrostatic interaction of the coenzyme and the enzyme which changes from an attractive interaction of the negatively charged coenzyme and the positively charged enzyme to a repulsive interaction between the two negatively charged species at the isoelectric point for the enzyme (pH 8.7). We have tested this proposal by examining the ionic strength dependence of the association rate constant at various pH values. These data have been interpreted by using the Wherland-Gray equation, which we have shown can be applied to the kinetics of enzyme-coenzyme association. Our results indicate that the shielding of the buffer electrolyte changes from a negative to a positive value as the charge on the protein changes at the isoelectric point. This result is exactly that which is predicted for electrostatic effects that depend on the charge of the protein molecule and is not consistent with predictions based upon the local active site effects. At low ionic strength values of 10 mM or less, approximately 75% of the observed pH dependence results from the enzyme electrostatic effects; the remaining pH dependence may result from active site effects.(ABSTRACT TRUNCATED AT 250 WORDS)