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)     

Semiparametric estimation of proportional mean residual life model in presence of censoring

A mean residual life function is the average remaining life of a surviving subject, as it varies with time. The proportional mean residual life model was proposed by Oakes and Dasu (1990, Biometrika77, 409-410) in regression analysis to study its association with related covariates in absence of censoring. In this article, we develop some semiparametric estimation procedures to take censoring into account. The proposed methodology is evaluated via simulation studies, and further applied to a clinical trial of chemotherapy in postoperative radiotherapy of lung cancer patients.     

Cholesteryl ester transfer protein gene haplotypes, plasma high-density lipoprotein levels and the risk of coronary heart disease

High-density lipoprotein cholesterol (HDL-C) is a known inverse predictor of coronary heart disease (CHD) and is thus a potential therapeutic target. Cholesteryl ester transfer protein (CETP) is a key protein in HDL-C metabolism such that elevated CETP activity is associated with lower HDL-C. Currently available HDL-C raising drugs are relatively ineffective and evidence suggesting the role of CETP in HDL-C levels has promoted the development of CETP inhibitors as potential therapeutic agents for CHD. We investigated three SNPs in the CETP gene in two cross-sectional community-based populations (n = 1,574 and 1,109) and a population of 556 CHD patients to determine if reduced CETP activity due to genetic variations in the CETP gene would increase HDL-C levels and reduce the risk of CHD. CETP genotypes and haplotypes were tested for association with lipid levels, CETP activity and risk of CHD. Multivariate analysis showed the common AAB2 haplotype defined by the G-2708A, C-629A and TaqIB polymorphisms, was consistently associated with reduced CETP activity and increased HDL-C levels. A mean increase in HDL-C levels of 0.16–0.24 mmol/l was observed in individuals with two copies of the AAB2 haplotype relative to non AAB2 carriers across all three populations (P < 0.001). A case-control study of males indicated no association between single SNPs or haplotypes and the risk of CHD. These results suggest that raising HDL-C via CETP inhibition may not alter risk of CHD. Randomized control trials are needed to determine whether CETP inhibition will in reality reduce risk of CHD by raising HDL-C. Pamela A. McCaskie and John P. Beilby contributed equally to this work.     

Cause‐Specific Cumulative Incidence Estimation and the Fine and Gray Model Under Both Left Truncation and Right Censoring

Summary The standard estimator for the cause‐specific cumulative incidence function in a competing risks setting with left truncated and/or right censored data can be written in two alternative forms. One is a weighted empirical cumulative distribution function and the other a product‐limit estimator. This equivalence suggests an alternative view of the analysis of time‐to‐event data with left truncation and right censoring: individuals who are still at risk or experienced an earlier competing event receive weights from the censoring and truncation mechanisms. As a consequence, inference on the cumulative scale can be performed using weighted versions of standard procedures. This holds for estimation of the cause‐specific cumulative incidence function as well as for estimation of the regression parameters in the Fine and Gray proportional subdistribution hazards model. We show that, with the appropriate filtration, a martingale property holds that allows deriving asymptotic results for the proportional subdistribution hazards model in the same way as for the standard Cox proportional hazards model. Estimation of the cause‐specific cumulative incidence function and regression on the subdistribution hazard can be performed using standard software for survival analysis if the software allows for inclusion of time‐dependent weights. We show the implementation in the R statistical package. The proportional subdistribution hazards model is used to investigate the effect of calendar period as a deterministic external time varying covariate, which can be seen as a special case of left truncation, on AIDS related and non‐AIDS related cumulative mortality.     

Fit and Frailties in Proportional Hazards Regression

We exploit a conjectured equivalence between proportional hazards models with frailties and a particular subclass of non proportional hazards models, specifically those with declining effects, to address the question of fit. A goodness of fit test of the proportional hazards assumption against an alternative of declining regression effect is equivalent to a test for the presence of frailties. Such tests are now widely available in standard software. Although a number of tests of the proportional hazards assumption have been developed there is no test that directly formulates the alternative in terms of a non‐specified monotonic decline in regression effect and that enables a quantification of this in terms of a simple index. The index we obtain lies between zero and one such that, for any given set of covariates, values of the index close to one indicate that the fit cannot essentially be improved by allowing the possibility of regression effects to decline. Values closer to zero and away from one indicate that the fit can be improved by relaxing the proportional hazards constraint in this particular direction. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non‐proportional odds multivariate logistic regression of ordinal family data

Methods to examine whether genetic and/or environmental sources can account for the residual variation in ordinal family data usually assume proportional odds. However, standard software to fit the non‐proportional odds model to ordinal family data is limited because the correlation structure of family data is more complex than for other types of clustered data. To perform these analyses we propose the non‐proportional odds multivariate logistic regression model and take a simulation‐based approach to model fitting using Markov chain Monte Carlo methods, such as partially collapsed Gibbs sampling and the Metropolis algorithm. We applied the proposed methodology to male pattern baldness data from the Victorian Family Heart Study.     

The area under the function: an index for selecting desirable genotypes

The linear regression approach has been widely used for selecting high-yielding and stable genotypes targeted to several environments. The genotype mean yield and the regression coefficient of a genotype's performance on an index of environmental productivity are the two main stability parameters. Using both can often complicate the breeder's decision when comparing high-yielding, less-stable genotypes with low-yielding, stable genotypes. This study proposes to combine the mean yield and regression coefficient into a unified desirability index (D _i). Thus, D _i is defined as the area under the linear regression function divided by the difference between the two extreme environmental indexes. D _i is equal to the mean of the i ^th genotype across all environments plus its slope multiplied by the mean of the environmental indexes of the two extreme environments (symmetry). Desirable genotypes are those with a large D _i. For symmetric trials the desirability index depends largely on the mean yield of the genotype and for asymmetric trials the slope has an important influence on the desirability index. The use of D _i was illustrated by a 20-environments maize yield trial and a 25-environments wheat yield trial. Three maize genotypes out of nine showed values of D _i 's that were significantly larger than a hypothetical, stable genotype. These were considered desirable, even though two of them had slopes significantly greater than 1.0. The results obtained from ranking wheat genotypes on mean yield differ from a ranking based on D _i .     

A three plus three parameters mechanistic model for viral filtration

Viral filtration is an expensive regulatory requirement in downstream processing of monoclonal antibodies (mAbs). This process step is typically operated with an overdesigned filter in order to account for any batch to batch variability in the filter, as well as the feed characteristics. Here, we propose a simple, six‐parameter mechanistic model for viral filtration where three parameters are membrane‐specific while the other three depend on feed characteristics and membrane‐feed interactions. Viruses are considered as passive particles which are retained by the membrane on the basis of size exclusion. The model envisages that the viral filter contains two kind of pores: virus‐retentive, small‐sized pores and non‐retentive, large‐sized pores. The small‐sized pores get blocked during filtration resulting in decrease in active membrane area, while the large‐sized pores get constricted during filtration. The length of constricted part increases during filtration and contributes to increase in hydraulic resistance of the filter. Rate of these processes (blocking and constriction) are assumed to be proportional to the instantaneous rate of retention of the viral particles. The general nature of the model is validated with the experimental data on viral filtration for four different commercial membranes used in biotech industries as well as different model viruses. The proposed model has been demonstrated to describe the behavior of filters with very good accuracy. The best‐fit model parameter values indicate about the various phenomena that are responsible for differences in the behavior of the membranes as well as change in retention and flux with feed concentration. The proposed model can be used for improving design of virus filters as well as in appropriate sizing of the filters during processing. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1538–1547, 2017     

High‐Dimensional Cox Models: The Choice of Penalty as Part of the Model Building Process

The Cox proportional hazards regression model is the most popular approach to model covariate information for survival times. In this context, the development of high‐dimensional models where the number of covariates is much larger than the number of observations ( $p \,{\gg }\, n$ ) is an ongoing challenge. A practicable approach is to use ridge penalized Cox regression in such situations. Beside focussing on finding the best prediction rule, one is often interested in determining a subset of covariates that are the most important ones for prognosis. This could be a gene set in the biostatistical analysis of microarray data. Covariate selection can then, for example, be done by L₁‐penalized Cox regression using the lasso (Tibshirani ( 1997 ). Statistics in Medicine 16 , 385–395). Several approaches beyond the lasso, that incorporate covariate selection, have been developed in recent years. This includes modifications of the lasso as well as nonconvex variants such as smoothly clipped absolute deviation (SCAD) (Fan and Li ( 2001 ). Journal of the American Statistical Association 96 , 1348–1360; Fan and Li ( 2002 ). The Annals of Statistics 30 , 74–99). The purpose of this article is to implement them practically into the model building process when analyzing high‐dimensional data with the Cox proportional hazards model. To evaluate penalized regression models beyond the lasso, we included SCAD variants and the adaptive lasso (Zou ( 2006 ). Journal of the American Statistical Association 101 , 1418–1429). We compare them with “standard” applications such as ridge regression, the lasso, and the elastic net. Predictive accuracy, features of variable selection, and estimation bias will be studied to assess the practical use of these methods. We observed that the performance of SCAD and adaptive lasso is highly dependent on nontrivial preselection procedures. A practical solution to this problem does not yet exist. Since there is high risk of missing relevant covariates when using SCAD or adaptive lasso applied after an inappropriate initial selection step, we recommend to stay with lasso or the elastic net in actual data applications. But with respect to the promising results for truly sparse models, we see some advantage of SCAD and adaptive lasso, if better preselection procedures would be available. This requires further methodological research.     

THE RELATION BETWEEN INFESTATION BY THE STALK BORER, BUSSEOLA FUSCA, AND YIELD OF MAIZE IN EAST AFRICA

The relation between yield and infestation by the maize stalk borer, Busseola fusca Fuller, is expressed as a series of regression lines for crops of different potential yields. The reasons are given for assuming that the regression is rectilinear, and that the regression coefficient b , or rate of fall in yield, is proportional to the maximum expected yield of the crop, that is that b
For the crops examined, the formula for a general regression line of yield, as hundreds of pounds of dry grain per acre, on infestation, as the percentage of plants attacked transformed to angles, is y = 45.1–0.55 x for a high-yielding area, and y = 14.55–0.23 x for a lower yielding crop. This is equivalent to a 35 lb./acre increase in grain yield for every 1% decrease in infestation for the higher yielding group, and 17 lb. increase per 1% decrease for the lower.
The applications of the relationship are discussed, in particular to studies of the economics of control by insecticides, and of the accuracy of methods of sampling infestations.     

Interval estimation of the mean difference in the analysis of over‐dispersed count data

This paper focuses on the development and study of the confidence interval procedures for mean difference between two treatments in the analysis of over‐dispersed count data in order to measure the efficacy of the experimental treatment over the standard treatment in clinical trials. In this study, two simple methods are proposed. One is based on a sandwich estimator of the variance of the regression estimator using the generalized estimating equations (GEEs) approach of Zeger and Liang (1986) and the other is based on an estimator of the variance of a ratio estimator (1977). We also develop three other procedures following the procedures studied by Newcombe (1998) and the procedure studied by Beal (1987). As assessed by Monte Carlo simulations, all the procedures have reasonably well coverage properties. Moreover, the interval procedure based on GEEs outperforms other interval procedures in the sense that it maintains the coverage very close to the nominal coverage level and that it has the shortest interval length, a satisfactory location property, and a very simple form, which can be easily implemented in the applied fields. Illustrative applications in the biological studies for these confidence interval procedures are also presented.     

Molecular pathways linking non‐shivering thermogenesis and obesity: focusing on brown adipose tissue development

An increase in energy intake and/or a decrease in energy expenditure lead to fat storage, causing overweight and obesity phenotypes. The objective of this review was to analyse, for the first time using a systematic approach, all published evidence from the past 8 years regarding the molecular pathways linking non‐shivering thermogenesis and obesity in mammals, focusing on mechanisms involved in brown adipose tissue development. Two major databases were scanned from 2006 to 2013 using ‘brown adipose tissue’ AND ‘uncoupling protein‐1’ AND ‘mammalian thermoregulation’ AND ‘obesity’ as key words. A total of 61 articles were retrieved using the search criteria. The available research used knockout methodologies, various substances, molecules and agonist treatments, or different temperature and diet conditions, to assess the molecular pathways linking non‐shivering thermogenesis and obesity. By integrating the results of the evaluated animal and human studies, our analysis identified specific molecules that enhance non‐shivering thermogenesis and metabolism by: (i) stimulating ‘brite’ (brown‐like) cell development in white adipose tissue; (ii) increasing uncoupling protein‐1 expression in brite adipocytes; and (iii) augmenting brown and/or brite adipose tissue mass. The latter can be also increased through low temperature, hibernation and/or molecules involved in brown adipocyte differentiation. Cold stimuli and/or certain molecules activate uncoupling protein‐1 in the existing brown adipocytes, thus increasing total energy expenditure by a magnitude proportional to the number of available brown adipocytes. Future research should address the interplay between body mass, brown adipose tissue mass, as well as the main molecules involved in brite cell development.     

Sequential Designs for Genetic Epidemiological Linkage or Association Studies A Review of the Literature

Objectives. The cost of a genetic linkage or association study is largely determined by the number of individuals to be recruited, phenotyped, and genotyped. The efficiency can be increased by using a sequential procedure that reduces time and cost on average. Two strategies for sequential designs in genetic epidemiological studies can be distinguished: One approach is to increase the sample size sequentially and to conduct multiple significance tests on accumulating data. If significance or futility can be assumed with a certain probability, the study is stopped. Otherwise, it is carried on to the next stage. The second approach is to conduct early linkage analyses on a coarse marker grid, and to increase marker density in later stages. Interim analyses are performed to select interesting genomic areas for follow up. The aim of this article is to give a review on sequential procedures in the context of genetic linkage and association studies. Methods. A systematic literature search was performed in the Medline and the Linkage Bibliography databases. Articles were defined as relevant if a sequential design was proposed or applied in genetic linkage or association studies. Results. The majority of proposed study designs is developed to meet the demands of specific studies and lacks a theoretical foundation. A second group of procedures is based on simulation results and principally restricted to the specific simulated situations. Finally, some theoretically founded procedures have been proposed that are discussed in detail. Conclusions. Although interesting and promising procedures have been suggested, they still lack realizations for practical purposes. In addition, further developments are required to adapt sequential strategies for optimal use in genetic epidemiological studies.     

Is non‐loglinear allometry a statistical artifact?

The allometric equation, y = ax^b, is commonly fitted to data indirectly by transforming predictor (x) and response (y) variables to logarithms, fitting a straight line to the transformations, and then back‐transforming (exponentiating) the resulting equation to the original arithmetic scale. Sometimes, however, transformation fails to linearize the observations, thereby giving rise to what has come to be known as non‐loglinear allometry. A smooth curve for observations displayed on a log–log plot is usually interpreted to mean that the scaling exponent in the allometric equation is a continuously changing function of body size, whereas a breakpoint between two (or more) linear segments on a log–log plot is typically taken to mean that the exponent changes abruptly, coincident with some important milestone in development. I applied simple graphical and statistical procedures in re‐analyses of three well‐known examples of non‐loglinear allometry, and showed in every instance that the relationship between predictor and response can be described in the original scale by simple functions with constant values for the exponent b. In no instance does the allometric exponent change during the course of development. Transformation of data to logarithms created new distributions that actually obscured the relationships between predictor and response variables in these investigations, and led to erroneous perceptions of growth. Such confounding effects of transformation are not limited to non‐loglinear allometry but are common to all applications of the allometric method. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ?? , ??–??.     

Co‐limitation of photosynthetic capacity by nitrogen and phosphorus in West Africa woodlands

Photosynthetic leaf traits were determined for savanna and forest ecosystems in West Africa, spanning a large range in precipitation. Standardized major axis fits revealed important differences between our data and reported global relationships. Especially for sites in the drier areas, plants showed higher photosynthetic rates for a given N or P when compared with relationships from the global data set. The best multiple regression for the pooled data set estimated V_cmax and J_max from N_DW and S. However, the best regression for different vegetation types varied, suggesting that the scaling of photosynthesis with leaf traits changed with vegetation types. A new model is presented representing independent constraints by N and P on photosynthesis, which can be evaluated with or without interactions with S. It assumes that limitation of photosynthesis will result from the least abundant nutrient, thereby being less sensitive to the allocation of the non‐limiting nutrient to non‐photosynthetic pools. The model predicts an optimum proportionality for N and P, which is distinct for V_cmax and J_max and inversely proportional to S. Initial tests showed the model to predict V_cmax and J_max successfully for other tropical forests characterized by a range of different foliar N and P concentrations.     

Can herbarium records be used to map alien species invasion and native species expansion over the past 100 years?

Aim To determine if the temporal and spatial pattern of alien plant invasion and native plant expansion can be observed using 100 years of herbarium data from Oklahoma, USA, and to eliminate herbarium collection biases in such analyses. Location Oklahoma, USA. Methods Using herbarium records from the Oklahoma Vascular Plants Database from 1903 to 2004, we reconstructed the spatial and temporal collection history of two alien invasive taxa (Lonicera japonica and Tamarix spp.) and three native expansive species (Ambrosia psilostachya, Amphiachyris dracunculoides and Juniperus virginiana). To compare the overall collecting trend, groups of native non‐expansive taxa were selected as counterparts. We recorded the year of the first collection in each township in Oklahoma for all taxa. The cumulative number of occupied townships was log‐transformed, plotted against time and modelled with linear regression. The slope of the linear regression represented collection trend over time for the non‐expansive counterpart group. However, for the invasive and expansive species, the regression slope represented the collection effort plus the invasion or expansion rate. We calculated the proportion of invasive and expansive species to non‐expansive species by dividing the cumulative number of townships for each invasive or expansive species by the cumulative number of townships occupied by the counterpart group (proportion curve). Results Maps of the collection records of invasive and expansive taxa illustrated no discernible spatial invasion or expansion pattern. The slopes of the linear regression for alien invasive taxa were significantly steeper than those of their associated native non‐expansive counterparts, indicating an increase in abundance. Juniperus virginiana, L. japonica and Tamarix spp. exhibited one or more periods during which they were collected at a disproportionately higher rate than their native non‐expansive counterparts. Main conclusions Patterns of species invasion and expansion in Oklahoma were detected using techniques developed for regions with longer collecting plant histories. The proportion curve analysis eliminated some biases inherent in herbarium data by reducing the effect of collecting effort. Both the regression model and proportion curve analyses illustrate the temporal invasion patterns of alien invasive species. The native species did not show a clear expansion pattern. The information found in recently established herbaria may not be sensitive enough to detect the increase in abundance of native species.     

A method of estimating varietal stability for data of long-term trials

Summary A method is proposed to analyze the stability of cultivars in long-term varietal trials. The method involves the following steps: (i) regress a standard variety on environmental means; (ii) regress varieties under test on the standard variety; (iii) transform, through a procedure of reparameterization, the regression computed for each variety under test on the standard variety into the regression of the variety on environmental means. Although this method is proposed to analyze data sets from complex designs, it may also possess some advantages over conventional procedures for simpler designs.     

Inadequacy of blocking in cultivar yield trials

Summary Based on the literature, theoretical considerations and a numerical example on triticale, Complete Randomized Blocks design is shown to be inadequate for cultivar yield trial purposes. Assumptions required for validity and convenience are shown not to be verified throughout most of the published experiments as well as in the present numerical example. It has been referred to the difficulty in forecasting homogeneity within blocks together with heterogeneity between blocks. This is difficult to achieve even in wellknown experimental fields, let alone local fields chosen at random, which leads to unacceptably low correlation between plots from block to block in each trial. Heteroscedasticity, as supported by different regression coefficients in Joint Regression Analysis, does not allow for ANOVA, unless the overall variation of soil fertility level is reduced to an amount comparable with that expected for the unknown errors. In this instance, the loss of degrees of freedom in the two-way ANOVA is known not to be compensated for by block effect deduction. The need to generalize trial results calls attention to the emphasis that should be given to cultivar performance pattern within the area they are to be released. Thus, we advocate the need for precise point evaluations in order to give accurate estimation of that pattern. Genotype-environment interaction, within situations where ecological diversity does not include stress mechanisms of different natures, can be reasonably described through its genotype-fertility level component, since specific instability, related to climatic features, is supposed to be strongly reduced by the screening process of both cultivar production and introduction. Sensitivity of the regression techniques (even through robust methods) requires a broad range of trial fertility levels and, besides an adequate number of degrees of freedom and detection of eventual remaining specific instabilities, demands an experienced evaluation of particular ecological situations; however, randomization is not required except within trials, which should be designed as completely randomized. To carry on trials beyond one year is not an a priori demand and should only be considered when very abnormal seasonal conditions occur.This research was partially supported by the Calouste Gulbenkian Foundation, Lisboa     

Validation of multi‐detector computed tomography as a non‐invasive method for measuring ovarian volume in macaques (Macaca fascicularis)

The purpose of this study was to validate low radiation dose, contrast‐enhanced, multi‐detector computed tomography (MDCT) as a non‐invasive method for measuring ovarian volume in macaques. Computed tomography scans of four known‐volume phantoms and nine mature female cynomolgus macaques were acquired using a previously described, low radiation dose scanning protocol, intravenous contrast enhancement, and a 32‐slice MDCT scanner. Immediately following MDCT, ovaries were surgically removed and the ovarian weights were measured. The ovarian volumes were determined using water displacement. A veterinary radiologist who was unaware of actual volumes measured ovarian CT volumes three times, using a laptop computer, pen display tablet, hand‐traced regions of interest, and free image analysis software. A statistician selected and performed all tests comparing the actual and CT data. Ovaries were successfully located in all MDCT scans. The iliac arteries and veins, uterus, fallopian tubes, cervix, ureters, urinary bladder, rectum, and colon were also consistently visualized. Large antral follicles were detected in six ovaries. Phantom mean CT volume was 0.702±SD 0.504 cc and the mean actual volume was 0.743±SD 0.526 cc. Ovary mean CT volume was 0.258±SD 0.159 cc and mean water displacement volume was 0.257±SD 0.145 cc. For phantoms, the mean coefficient of variation for CT volumes was 2.5%. For ovaries, the least squares mean coefficient of variation for CT volumes was 5.4%. The ovarian CT volume was significantly associated with actual ovarian volume (ICC coefficient 0.79, regression coefficient 0.5, P=0.0006) and the actual ovarian weight (ICC coefficient 0.62, regression coefficient 0.6, P=0.015). There was no association between the CT volume accuracy and mean ovarian CT density (degree of intravenous contrast enhancement), and there was no proportional or fixed bias in the CT volume measurements. Findings from this study indicate that MDCT is a valid non‐invasive technique for measuring the ovarian volume in macaques. Am. J. Primatol. 72:530–538, 2010. © 2010 Wiley‐Liss, Inc.     

A model of temporal distribution of Aphis gossypii (Glover) (Hem., Aphididae) on cotton

The spatio‐temporal distribution of Aphis gossypii (Glover) was studied for a 4‐year period in a plot of Gossypium hirsutum located in Bangui, Central African Republic. A study of the temporal evolution of the number of aphids by means of non‐linear regression indicated a rapid population increase during the first 8 weeks of cotton cultivation. The overdispersion of the aphids was found to be significant during most of the season. We tested three population dispersion models; Iwao's model and Taylor's power law describe the relationship between the mean m and variance σ² for the number of aphids, and the Nachman's model describes the functional dependence between m and the proportion p of non‐infested cotton plants. The results of these statistical tests indicate that only the Taylor's model was not rejected. The aphids’ aggregation increases with population density. The regression parameter confidence intervals for each of the 4 years of observation prove the stability of the Taylor's model. The model σ² = 45m^1.3 is recommended when the environmental and cultural conditions are similar to those of our study.