Predicting the Geographic Distribution of a Species from Presence‐Only Data Subject to Detection Errors

Summary Several models have been developed to predict the geographic distribution of a species by combining measurements of covariates of occurrence at locations where the species is known to be present with measurements of the same covariates at other locations where species occurrence status (presence or absence) is unknown. In the absence of species detection errors, spatial point‐process models and binary‐regression models for case‐augmented surveys provide consistent estimators of a species’ geographic distribution without prior knowledge of species prevalence. In addition, these regression models can be modified to produce estimators of species abundance that are asymptotically equivalent to those of the spatial point‐process models. However, if species presence locations are subject to detection errors, neither class of models provides a consistent estimator of covariate effects unless the covariates of species abundance are distinct and independently distributed from the covariates of species detection probability. These analytical results are illustrated using simulation studies of data sets that contain a wide range of presence‐only sample sizes. Analyses of presence‐only data of three avian species observed in a survey of landbirds in western Montana and northern Idaho are compared with site‐occupancy analyses of detections and nondetections of these species.     

A Comparison of Formulae for Calculating Cost‐Efficient Sample Sizes of Case‐Control Studies with an Internal Validation Scheme

When a case‐control study is planned to include an internal validation study, the sample size of the study and the proportion of validated observations has to be calculated. There are a variety of alternative methods to accomplish this. In this article some possible procedures will be compared in order to clarify whether considerable differences in the suggested optimal designs occur, dependent on the used method.     

Analysis of case-control age-at-onset data using a modified case-cohort method

Case-control designs are widely used in rare disease studies. In a typical case-control study, data are collected from a sample of all available subjects who have experienced a disease (cases) and a sub-sample of subjects who have not experienced the disease (controls) in a study cohort. Cases are oversampled in case-control studies. Logistic regression is a common tool to estimate the relative risks of the disease with respect to a set of covariates. Very often in such a study, information of ages-at-onset of the disease for all cases and ages at survey of controls are known. Standard logistic regression analysis using age as a covariate is based on a dichotomous outcome and does not efficiently use such age-at-onset (time-to-event) information. We propose to analyze age-at-onset data using a modified case-cohort method by treating the control group as an approximation of a subcohort assuming rare events. We investigate the asymptotic bias of this approximation and show that the asymptotic bias of the proposed estimator is small when the disease rate is low. We evaluate the finite sample performance of the proposed method through a simulation study and illustrate the method using a breast cancer case-control data set.     

Analytic power and sample size calculation for the genotypic transmission/disequilibrium test in case‐parent trio studies

Case‐parent trio studies considering genotype data from children affected by a disease and their parents are frequently used to detect single nucleotide polymorphisms (SNPs) associated with disease. The most popular statistical tests for this study design are transmission/disequilibrium tests (TDTs). Several types of these tests have been developed, for example, procedures based on alleles or genotypes. Therefore, it is of great interest to examine which of these tests have the highest statistical power to detect SNPs associated with disease. Comparisons of the allelic and the genotypic TDT for individual SNPs have so far been conducted based on simulation studies, since the test statistic of the genotypic TDT was determined numerically. Recently, however, it has been shown that this test statistic can be presented in closed form. In this article, we employ this analytic solution to derive equations for calculating the statistical power and the required sample size for different types of the genotypic TDT. The power of this test is then compared with the one of the corresponding score test assuming the same mode of inheritance as well as the allelic TDT based on a multiplicative mode of inheritance, which is equivalent to the score test assuming an additive mode of inheritance. This is, thus, the first time the power of these tests are compared based on equations, yielding instant results and omitting the need for time‐consuming simulation studies. This comparison reveals that these tests have almost the same power, with the score test being slightly more powerful.     

An 'unconditional-like' structure for the conditional estimator of odds ratio from 2 x 2 tables

In the estimation of the odds ratio (OR), the conditional maximum-likelihood estimate (cMLE) is preferred to the more readily computed unconditional one (uMLE). However, the exact cMLE does not have a closed form to help divine it from the uMLE or to understand in what circumstances the difference between the two is appreciable. Here, the cMLE is shown to have the same 'ratio of cross-products' structure as its unconditional counterpart, but with two of the cell frequencies augmented, so as to shrink the unconditional estimator towards unity. The augmentation involves a factor, similar to the finite population correction, derived from the minimum of the marginal totals.     

Inference of haplotype effects in case-control studies using unphased genotype and environmental data

A retrospective likelihood-based approach was proposed to test and estimate the effect of haplotype on disease risk using unphased genotype data with adjustment for environmental covariates. The proposed method was also extended to handle the data in which the haplotype and environmental covariates are not independent. Likelihood ratio tests were constructed to test the effects of haplotype and gene-environment interaction. The model parameters such as haplotype effect size was estimated using an Expectation Conditional-Maximization (ECM) algorithm developed by Meng and Rubin (1993). Model-based variance estimates were derived using the observed information matrix. Simulation studies were conducted for three different genetic effect models, including dominant effect, recessive effect, and additive effect. The results showed that the proposed method generated unbiased parameter estimates, proper type I error, and true beta coverage probabilities. The model performed well with small or large sample sizes, as well as short or long haplotypes.     

Estimating Propensity Scores and Causal Survival Functions Using Prevalent Survival Data

Summary This article develops semiparametric approaches for estimation of propensity scores and causal survival functions from prevalent survival data. The analytical problem arises when the prevalent sampling is adopted for collecting failure times and, as a result, the covariates are incompletely observed due to their association with failure time. The proposed procedure for estimating propensity scores shares interesting features similar to the likelihood formulation in case‐control study, but in our case it requires additional consideration in the intercept term. The result shows that the corrected propensity scores in logistic regression setting can be obtained through standard estimation procedure with specific adjustments on the intercept term. For causal estimation, two different types of missing sources are encountered in our model: one can be explained by potential outcome framework; the other is caused by the prevalent sampling scheme. Statistical analysis without adjusting bias from both sources of missingness will lead to biased results in causal inference. The proposed methods were partly motivated by and applied to the Surveillance, Epidemiology, and End Results (SEER)‐Medicare linked data for women diagnosed with breast cancer.     

Choice of Scores in Trend Tests for Case‐Control Studies of Candidate‐Gene Associations

When applying the Cochran‐Armitage (CA) trend test for an association between a candidate allele and a disease in a case‐control study, a set of scores must be assigned to the genotypes. Sasieni (1997, Biometrics 53 , 1253–1261) suggested scores for the recessive, additive, and dominant models but did not examine their statistical properties. Using the criteria of minimizing the required sample size of the CA trend test to achieve prespecified type I and type II errors, we show that the scores given by Sasieni (1997) are optimal for the recessive and dominant models and locally optimal for the additive one. Moreover, the additive scores are shown to be locally optimal for the multiplicative model. The tests are applied to a real dataset.     

Case–Control Studies of Gene–Environment Interaction: Bayesian Design and Analysis

Summary With increasing frequency, epidemiologic studies are addressing hypotheses regarding gene‐environment interaction. In many well‐studied candidate genes and for standard dietary and behavioral epidemiologic exposures, there is often substantial prior information available that may be used to analyze current data as well as for designing a new study. In this article, first, we propose a proper full Bayesian approach for analyzing studies of gene–environment interaction. The Bayesian approach provides a natural way to incorporate uncertainties around the assumption of gene–environment independence, often used in such an analysis. We then consider Bayesian sample size determination criteria for both estimation and hypothesis testing regarding the multiplicative gene–environment interaction parameter. We illustrate our proposed methods using data from a large ongoing case–control study of colorectal cancer investigating the interaction of N‐acetyl transferase type 2 (NAT2) with smoking and red meat consumption. We use the existing data to elicit a design prior and show how to use this information in allocating cases and controls in planning a future study that investigates the same interaction parameters. The Bayesian design and analysis strategies are compared with their corresponding frequentist counterparts.     

Portrait of the Patient as a Young Man: An Exploration of the Use of Photographs in Hospital

The display of personal photographs in hospital is a common practice that has yet to be rigorously examined. The photographs displayed are subject to interpretation by the viewer and may lead to misunderstandings or miscommunication if clarification of meaning is not sought. This paper explores a range of possible meanings that the display of photographs in hospital may hold, based on a case study of a 15 year old boy hospitalised with a life threatening illness. Further research is needed into the actual meanings attributed to the display of photographs in hospital by patients and family members.     

A mathematical model to design a lignocellulosic biofuel supply chain system with a case study based on a region in Central Texas

This study formulates a model to maximize the profit of a lignocellulosic biofuel supply chain ranging from feedstock suppliers to biofuel customers. The model deals with a time-staged, multi-commodity, production/distribution system, prescribing facility locations and capacities, technologies, and material flows. A case study based on a region in Central Texas demonstrates application of the proposed model to design the most profitable biofuel supply chain under each of several scenarios. A sensitivity analysis identifies that ethanol (ETOH) price is the most significant factor in the economic viability of a lignocellulosic biofuel supply chain.     

Introducing the Multivariate Dale Model in Population‐Based Genetic Association Studies

Until recently, the most common parametric approaches to study the combined effects of several genetic polymorphisms located within a gene or in a small genomic region are, at the genotype level, logistic regressions and at the haplotype level, haplotype analyses. An alternative modeling approach, based on the case/control principle, is to regard exposures (e.g., genetic data such as derived from Single Nucleotide Polymorphisms – SNPs) as random and disease status as fixed and to use a marginal multivariate model that accounts for inter‐relationships between exposures. One such model is the multivariate Dale model. This model is based on multiple logistic regressions. That is why the model, applied in a case/control setting, leads to straightforward interpretations that are similar to those drawn in a classical logistic modeling framework. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)