Conditional Rejection Probabilities of Student's t‐test and Design Adaptations

For clinical trials with interim analyses conditional rejection probabilities play an important role when stochastic curtailment or design adaptations are performed. The conditional rejection probability gives the conditional probability to finally reject the null hypothesis given the interim data. It is computed either under the null or the alternative hypothesis. We investigate the properties of the conditional rejection probability for the one sided, one sample t‐test and show that it can be non monotone in the interim mean of the data and non monotone in the non‐centrality parameter for the alternative. We give several proposals how to implement design adaptations (that are based on the conditional rejection probability) for the t‐test and give a numerical example. Additionally, the conditional rejection probability given the interim t‐statistic is investigated. It does not depend on the unknown σ and can be used in stochastic curtailment procedures. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the interpretation of the hazard ratio in Cox regression

We argue that the term “relative risk” should not be used as a synonym for “hazard ratio” and encourage to use the probabilistic index as an alternative effect measure for Cox regression. The probabilistic index is the probability that the event time of an exposed or treated subject exceeds the event time of an unexposed or untreated subject conditional on the other covariates. It arises as a well known and simple transformation of the hazard ratio and nicely reveals the interpretational limitations. We demonstrate how the probabilistic index can be obtained using the R-package Publish.     

Testing Equivalence Simultaneously for Location and Dispersion of two Normally Distributed Populations

In clinical trials with an active control usually therapeutical equivalence of a new treatment is investigated by looking at a location parameter of the distributions of the primary efficacy variable. But even if the location parameters are close to each other existing differences in variability may be connected with different risks for under or over treatment in an individual patient. Assuming normally distributed responses a multiple test procedure applying two shifted one-sided t-tests for the mean and accordingly two one-sided F-tests for the variances is proposed. Equivalence in location and variability is established if all four tests lead to a rejection at the (one-sided) level α. A conservative procedure “correcting” the t-tests for heteroscedasticity is derived. The choice of a design in terms of the global level α, the global power, the relevant deviations in the population means and variances, as well as the sample size is outlined. Numerical calculations of the actual level and power for the proposed designs show, that for balanced sample sizes the classical uncorrected one-sided t-tests can be used safely without exaggerating the global type I error probability. Finally an example is given.     

Diminished Confidence Levels in the Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y=β₀ + β₁ x + e (model I of linear regression) in the literature confidence estimators of an unknown position x₀ are given at which either the expectation of y is given (see FIELLER, 1944; FINNEY, 1952), or realizations of y are given (see GRAYBILL, 1961). These confidence regions with level 1—α need not be intervals. The occurrence of interval shape is a random event. Its probability is equal to the power of the t test for the examination of the hypothesis H: β₁ = 0. The papers mentioned above claim to provide confidence intervals with level 1 ? α. But because of the restriction of (1 —α)—confidence regions to intervals the true confidence probability is the conditional probability W_c: W_c = P (the confidence region covers x₀| the region has interval shape). Here this conditional probability is shown to be less than 1 —α. Evidence on the possible deviations from 1 —α has been obtained by simulations.     

Enhancing Confidence in Drinking Water Quality for Improved Risk Decisions

Reliance is often placed on “indirect” indicators to detect changes in water quality in real time. However, there are challenges in using these indirect indicators, as they cannot replace standardized laboratory tests. As an alternative, reliance on three successive test cases is examined, based on “joint and conditional probabilities” of hazard (contaminant level exceeding acceptable level) that could enhance confidence in monitoring results: (i) a simple and quick screening analysis sensor (primary analyzer, having type-1 error, i.e., α = 0.10 and type-2 error, i.e., β = 0.05), (ii) a repeat of the analysis with the same rapid analyzer is feasible, and (iii) further analysis of the sample with a highly reliable capability is feasible (secondary analyzer with α = 0.05 and β = 0.02). This three-level monitoring protocol for obtaining the posterior probability of hazard is examined and a method is proposed for taking improved risk management decisions by accounting for sensitivity and specificity of monitoring instruments. The revised probability of hazard will ensure that a positive harmful detect is proven false or real with much greater certainty and series of action (or no action) is taken at the earliest.     

Continuous and discrete extreme climatic events affecting the dynamics of a high-arctic reindeer population

Climate at northern latitudes are currently changing both with regard to the mean and the temporal variability at any given site, increasing the frequency of extreme events such as cold and warm spells. Here we use a conceptually new modelling approach with two different dynamic terms of the climatic effects on a Svalbard reindeer population (the Brøggerhalvøya population) which underwent an extreme icing event (“locked pastures”) with 80% reduction in population size during one winter (1993/94). One term captures the continuous and linear effect depending upon the Arctic Oscillation and another the discrete (rare) “event” process. The introduction of an “event” parameter describing the discrete extreme winter resulted in a more parsimonious model. Such an approach may be useful in strongly age-structured ungulate populations, with young and very old individuals being particularly prone to mortality factors during adverse conditions (resulting in a population structure that differs before and after extreme climatic events). A simulation study demonstrates that our approach is able to properly detect the ecological effects of such extreme climate events.     

Lack of exposure to natural light in the workspace is associated with physiological,sleep and depressive symptoms

The diurnal light cycle has a crucial influence on all life on earth. Unfortunately, modern society has modified this life-governing cycle by stressing maximum production and by giving insufficient attention to the ecological balance and homeostasis of the human metabolism. The aim of this study is to evaluate the effects of exposure or lack of exposure to natural light in a rest/activity rhythm on cortisol and melatonin levels, as well as on psychological variables in humans under natural conditions. This is a cross-sectional study. The subjects were allocated split into two groups according to their workspace (10 employees in the “with window” group and 10 in the “without window” group). All participants were women and wore anactigraph (Actiwatch 2, Philips Respironics), which measures activity and ambient light exposure, for seven days. Concentrations of melatonin and cortisol were measured from the saliva samples. Participants were instructed to collect saliva during the last day of use of the actigraph at 08:00 am, 4:00 pm and 10:00 pm. The subjects answered the Self-Reporting Questionnaire-20 (SRQ-20) to measure the presence of minor psychiatric disorders; the Montgomery-Asberg (MA) scale was used to measure depression symptoms, and the Pittsburgh Sleep Quality Index questionnaire (PSQI) was used to evaluate the quality of sleep. The Rayleigh analysis indicates that the two groups, “with window” an d “without window”, exhibited similar activities and light acrophases. In relation to light exposure, the mesor was significantly higher (t?=??2.651, p?=?0.023) in t he “with window” group (191.04?±?133.36) than in the “without window” group (73.8?±?42.05). Additionally, the “with window” group presented the highest amplitude of light exposure (298.07?±?222.97). Cortisol levels were significantly different between the groups at 10:00 pm (t?=?3.009, p?=?0.008; “without window” (4.01?±?0.91) “with window” (3.10?±?0.30)). In terms of the melatonin levels, the groups differed at two different times of day: 08:00 am (t?=?2.593, p?=?0.018) and 10:00 pm (t?=??2.939, p?=?0.009). The “with window” group had a lower melatonin level at 08:00 am (3.54?±?0.60) but a higher level at 10:00 pm (24.74?±?4.22) than the “without window” group. Higher cortisol levels were positively correlated with minor psychiatric disorders and depressive symptoms (MA) at 10:00 pm. Lower melatonin levels at 10:00 pm were correlated with depressive symptoms and poor quality of sleep (PSQI). Our study demonstrated that not only may light pollution affect human physiology but also lack of exposure to natural light is related to high levels of cortisol and lower levels of melatonin at night, and these, in turn, are related to depressive symptoms and poor quality of sleep.     

Isolation and biodiversity in Cytisus villosus Pourret (Fabaceae,Genisteae): enzyme polymorphism in disjunct populations

ABSTRACT

The genetic diversity of isolated populations of Cytisus villosus has been studied by means of enzyme polymorphism analysis. Two types of isolated populations were studied: “terrestrial islands” in Sicily, and “true islands” in the Aeolian archipelago. In the populations of “true islands” the number of alleles and the heterozygosity are lower than in “terrestrial islands”. Isolation amongst Sicilian populations seems to be more recent than isolation of the Aeolian populations, and may be attributed to climatic changes which occurred during the Holocene and/or to human activities. The disjunction of the Aeolian populations seems much more recent than the origin of the isles themselves; the colonization of the archipelago is attributed to a single, recent dispersal event not followed by local evolution. In view of the biological structure of the Aeolian populations, C. villosus must be regarded as a locally endangered species.     

Sexual Interference and Sexual Defense in the Smooth Newt,Triturus vulgaris (Amphibia,Urodela, Salamandridae)

• 1 When a male smooth newt encounters a ♀ who is already engaged in courtship, he may mimic her behaviour during the spermatophore deposition and transfer stages of the courtship. He thereby usurps the courting ♂ and may inseminate the ♀ himself. Such sexual interference depresses the short-term, and perhaps long-term, mating success of the courting ♂.
• 2 In the presence of a potential rival, the courting ♂ alters certain aspects of his sexual behaviour. He displays more intensely to the ♀ and attempts to draw her away from the rival by increasing the duration of his display. He may also “check” that it is the ♀, and not the rival, who will elicit the deposition of a spermatophore from him. These changes in the behaviour of the courting ♂ are interpreted as defense against sexual interference.
• 3 Female smooth newts may be multiply inseminated as a consequence of sexual interference; this may result in sperm competition. However, ♀♀ seem to find competitive interactions between ♂ ♂ “aversive”.
• 4 Sexual interference by ♀-mimicry and associated defensive behaviour patterns are common in the urodele amphibians. Interference can be thought of as a “side-payment” conditional mating strategy.

     

A Partitioning Deletion/Substitution/Addition Algorithm for Creating Survival Risk Groups

Summary Accurately assessing a patient’s risk of a given event is essential in making informed treatment decisions. One approach is to stratify patients into two or more distinct risk groups with respect to a specific outcome using both clinical and demographic variables. Outcomes may be categorical or continuous in nature; important examples in cancer studies might include level of toxicity or time to recurrence. Recursive partitioning methods are ideal for building such risk groups. Two such methods are Classification and Regression Trees (CART) and a more recent competitor known as the partitioning Deletion/Substitution/Addition (partDSA) algorithm, both of which also utilize loss functions (e.g., squared error for a continuous outcome) as the basis for building, selecting, and assessing predictors but differ in the manner by which regression trees are constructed. Recently, we have shown that partDSA often outperforms CART in so‐called “full data” settings (e.g., uncensored outcomes). However, when confronted with censored outcome data, the loss functions used by both procedures must be modified. There have been several attempts to adapt CART for right‐censored data. This article describes two such extensions for partDSA that make use of observed data loss functions constructed using inverse probability of censoring weights. Such loss functions are consistent estimates of their uncensored counterparts provided that the corresponding censoring model is correctly specified. The relative performance of these new methods is evaluated via simulation studies and illustrated through an analysis of clinical trial data on brain cancer patients. The implementation of partDSA for uncensored and right‐censored outcomes is publicly available in the R package, partDSA .     

New insights into the t-complex and control of sperm function

The mouse t-complex, located on chromosome 17, contains genes known to influence male, but not female, fertility. Although some t-complex genes are recessive lethals, t-chromosomes are maintained in the population by transmission ratio distortion. When male mice heterozygous for the t-chromosome mate with wild-type females, most offspring will possess the t-chromosome, indicating a link between t-complex genes and sperm function. Several proteins coded for by t-complex genes have been localised in the sperm flagellum, suggesting roles relating to motility. Another t-complex protein appears able to regulate the adenylyl cyclase/cAMP signal transduction pathway, known to play an important role in capacitation. Defective motility and/or failure to capacitate (“switch on”) would result in poorly fertile or infertile spermatozoa. Given the existence of human homologues for many genes in the t-complex and the prevalence of “male factor” infertility, information obtained about the t-complex not only will provide insight into basic biological mechanisms but may be of future clinical relevance as well. BioEssays 21:304–312, 1999. © 1999 John Wiley & Sons, Inc.     

Distinguishing "or" from "and" and the case for historical identification

The adequacy of a probabilistic interpretation must be judged according to the nature of the event, or thing, being inferred. For example, conditional (frequency) probability is not admissible in the inference of phylogeny, because basic statements of common ancestry do not fulfill the requirements of the relations specified by the probability calculus. The probabilities of the situation peculiar to the time and place of origin of species are unique. Moreover, according to evolutionary theory, an event of species diversification is necessarily unique, because species are parts of a replicator continuum—species arise from ancestral species. Also, these probabilities cannot be ascertained, because the relevant situation cannot be repeated—it is unique. Finally, the applicability of conditional (frequency) probability is denied, because events of common ancestry have already occurred—there is nothing to predict. However, hypotheses of species relationships can be identified objectively according to the degree to which they have survived simultaneous testing with critical evidence, not with generally confirming evidence. The most parsimonious hypothesis of species relationships represents the least disconfirmed, best supported, proposition among the alternatives being compared. That hypothesis does not, however, deserve any special epistemological status beyond serving as the focus of the next round of testing.     

Dynamic prediction of cumulative incidence functions by direct binomial regression

In recent years there have been a series of advances in the field of dynamic prediction. Among those is the development of methods for dynamic prediction of the cumulative incidence function in a competing risk setting. These models enable the predictions to be updated as time progresses and more information becomes available, for example when a patient comes back for a follow‐up visit after completing a year of treatment, the risk of death, and adverse events may have changed since treatment initiation. One approach to model the cumulative incidence function in competing risks is by direct binomial regression, where right censoring of the event times is handled by inverse probability of censoring weights. We extend the approach by combining it with landmarking to enable dynamic prediction of the cumulative incidence function. The proposed models are very flexible, as they allow the covariates to have complex time‐varying effects, and we illustrate how to investigate possible time‐varying structures using Wald tests. The models are fitted using generalized estimating equations. The method is applied to bone marrow transplant data and the performance is investigated in a simulation study.     

EVOLUTIONARY ORIGIN OF A PARTHENOFORM,THE AMAZON MOLLY POECILIA FORMOSA,ON THE BASIS OF A MOLECULAR GENEALOGY

The appearance of vertebrate species that reproduce without genetic recombination has been explained by their origin from a rare hybridization event between members of two distantly related species. For the first recognized vertebrate unisexual, the Amazon molly Poecilia formosa, mostly morphological and biochemical genetic information has been available so far with respect to its evolutionary origin. DNA sequence analyses of transcribed portions of the genome (tyrosine kinase proto-oncogenes) demonstrated its hybrid state unequivocally. Both alleles can be traced in a DNA sequence-based phylogenetic tree to extant species that represent the parental species or that are closely related to the corresponding extinct forms, namely P. mexicana limantouri and a so far taxonomically ill-defined north Mexican subspecies of the P. latipinna/P. velifera complex. A rough estimate from the mutation rates dates the hybridization event further back than would have been predicted on the basis of “Muller's ratchet” for an ecologically successful species.     

A statistical model of the reproduction of aphids

1. The logistic function has been generally used to describe the reproductive process of a “population” of animal. However, this model can not give us any information about the reproductive process of “individuals” in the population. In this study a statistical model on the basis of the reproduction of individuals of barley aphid is presented to find the proportion of the mature individuals, the heterogeneity in reproductive ability of the aphids, etc.
2. The model is constructed as follows:
3. The probability that j insects are found on a plant at time t₀ is represented as Q(j).
4. The probability that h individuals of j have reproductive ability, say, mature individuals, in the period t₀ to t₁ is represented as B(h/j)=_jC_hw^h(1−w)^j−h, where w is the proportion of mature individuals.
5. In a population with a homogeneous reproductive ability, the probability that each parent lays i offspring in the period t₀ to t₁ is represented as P(i/m)=e^−mmⁱ/i!, where m is mean. And, in a population, m changes according to the gamma distribution. Hence the probability that a parent lays i offspring between t₀ and t₁ is represented as , where p and k are parameters of negative binomial distribution. The probability that h parents on a plant lays s offspring is represented as .
6. From the assumptions mentioned above, the probability that s offspring are to be found at time t₁ on a plant with the original j individuals at time t₀ is represented by
7. The experimental populations were demonstrated to fit well to the model.

     

Effects of cyclic spouse separation on conception times

The lengthening of conceptive delays under conditions of natural fertility by cyclic spouse separation is investigated as a problem in renewal processes. Separations are “complete” if they reduce the conditional monthly probability of conception, or fecundability, to zero, and “incomplete” if they merely reduce it, from f to r say. Earlier work respecting cyclic separation by Menken (1979) is extended with formulas for the mean and variance of conceptive delays conditional on T, the ordinal month of the cycle of separation and nonseparation when the woman passes from anovulation into the fecundable state. A simple expression relating fecundabilities f and r and the conditional proportions P_s(T) and P_s-(T) conceiving during separation and nonseparation is obtained.     

The late Cenomanian event in eastern England

The Cenomanian/Turonian boundary event has been fully documented from a series of localities between Flamborough Head in Humberside and Marham in Norfolk. The carbon isotope excursion can be identified and extrapolated to all the studied sections using bed‐by‐bed correlation. Evidence from studies of the isotope data, trace element geochemistry, and the micropalaeontology are presented. The famous “Black Band” is seen to change laterally into a “red” horizon and then a “green” horizon when traced southwards. This appears to represent the “feather‐edge” of the anoxic event when traced towards a palaeo‐high which is located in the region of the Wash. All the events, so‐identified, can be correlated with the A. plenus Marl succession in southern England.     

Perfect temperature for protein structure prediction and folding

We have investigated the influence of the “noise” of inevitable errors in energetic parameters on-protein structure prediction. Because of this noise, only a part of all the interactions operating in a protein chain can be taken into account, and therefore a search for the energy minimum becomes inadequate for protein structure prediction. One can rather rely on statistical mechanics: a calculation carried out at a temperature T_* somewhat below that of protein melting gives the best possible, though always approximate prediction. The early stages of protein folding also “take into account” only a part of all the interactions; consequently, the same temperature T_* is favorable for the self-organization of native-like intermediates in protein folding. © 1995 Wiley-Liss, Inc.     

Empirically-determined statistical significance of the Baillie and Pilcher (1973) t statistic for British Isles oak

The “Belfast method” of statistical crossdating has been widely used in the British Isles since public domain software was released by Baillie and Pilcher (1973). Although the conceptual merits of the approach are accepted, the details of the methodology have been severely criticised, including the fact that serially correlated tree-ring time series violate a fundamental requirement for the use of Students t statistic as a measure of statistical significance. An unfortunate consequence of this has been that t values are often published without reference to the associated probability of the specific value being obtained by chance. Here we present an empirical method for determining statistical significance from analysis of many misaligned inter-site correlations amongst over 2000 dated British Isles oak chronologies. Results indicate that a t value of 3.5 has a probability of about one in 600 for series lengths of 100+ years, but this declines (becomes less rare) as series length decreases.     

On the empirical choice of the time window for restricted mean survival time

The t-year mean survival or restricted mean survival time (RMST) has been used as an appealing summary of the survival distribution within a time window [0, t]. RMST is the patient's life expectancy until time t and can be estimated nonparametrically by the area under the Kaplan-Meier curve up to t. In a comparative study, the difference or ratio of two RMSTs has been utilized to quantify the between-group-difference as a clinically interpretable alternative summary to the hazard ratio. The choice of the time window [0, t] may be prespecified at the design stage of the study based on clinical considerations. On the other hand, after the survival data have been collected, the choice of time point t could be data-dependent. The standard inferential procedures for the corresponding RMST, which is also data-dependent, ignore this subtle yet important issue. In this paper, we clarify how to make inference about a random “parameter.” Moreover, we demonstrate that under a rather mild condition on the censoring distribution, one can make inference about the RMST up to t, where t is less than or even equal to the largest follow-up time (either observed or censored) in the study. This finding reduces the subjectivity of the choice of t empirically. The proposal is illustrated with the survival data from a primary biliary cirrhosis study, and its finite sample properties are investigated via an extensive simulation study.