A Regression-Based Method for Estimating Risks and Relative Risks in Case-Base Studies

Both the absolute risk and the relative risk (RR) have a crucial role to play in epidemiology. RR is often approximated by odds ratio (OR) under the rare-disease assumption in conventional case-control study; however, such a study design does not provide an estimate for absolute risk. The case-base study is an alternative approach which readily produces RR estimation without resorting to the rare-disease assumption. However, previous researchers only considered one single dichotomous exposure and did not elaborate how absolute risks can be estimated in a case-base study. In this paper, the authors propose a logistic model for the case-base study. The model is flexible enough to admit multiple exposures in any measurement scale—binary, categorical or continuous. It can be easily fitted using common statistical packages. With one additional step of simple calculations of the model parameters, one readily obtains relative and absolute risk estimates as well as their confidence intervals. Monte-Carlo simulations show that the proposed method can produce unbiased estimates and adequate-coverage confidence intervals, for ORs, RRs and absolute risks. The case-base study with all its desirable properties and its methods of analysis fully developed in this paper may become a mainstay in epidemiology.     

Potential Biases in Estimating Absolute and Relative Case-Fatality Risks during Outbreaks

Estimating the case-fatality risk (CFR)—the probability that a person dies from an infection given that they are a case—is a high priority in epidemiologic investigation of newly emerging infectious diseases and sometimes in new outbreaks of known infectious diseases. The data available to estimate the overall CFR are often gathered for other purposes (e.g., surveillance) in challenging circumstances. We describe two forms of bias that may affect the estimation of the overall CFR—preferential ascertainment of severe cases and bias from reporting delays—and review solutions that have been proposed and implemented in past epidemics. Also of interest is the estimation of the causal impact of specific interventions (e.g., hospitalization, or hospitalization at a particular hospital) on survival, which can be estimated as a relative CFR for two or more groups. When observational data are used for this purpose, three more sources of bias may arise: confounding, survivorship bias, and selection due to preferential inclusion in surveillance datasets of those who are hospitalized and/or die. We illustrate these biases and caution against causal interpretation of differential CFR among those receiving different interventions in observational datasets. Again, we discuss ways to reduce these biases, particularly by estimating outcomes in smaller but more systematically defined cohorts ascertained before the onset of symptoms, such as those identified by forward contact tracing. Finally, we discuss the circumstances in which these biases may affect non-causal interpretation of risk factors for death among cases.The case-fatality risk (CFR) is a key quantity in characterizing new infectious agents and new outbreaks of known agents. The CFR can be defined as the probability that a case dies from the infection. Several variations of the definition of “case” are used for different infections, as discussed in Box 1. Under all these definitions, the CFR characterizes the severity of an infection and is useful for planning and determining the intensity of a response to an outbreak [1,2]. Moreover, the CFR may be compared between cases who do and do not receive particular treatments as a way of trying to estimate the causal impact of these treatments on survival. Such causal inference might ideally be done in a randomized trial in which individuals are randomly assigned to treatments, but this is often not possible during an outbreak for logistical, ethical, and other reasons [3]. Therefore, observational estimates of CFR under different treatment conditions may be the only available means to assess the impact of various treatments.

Box 1. Definition of the CFR.

The CFR itself is an ambiguous term, as its definition and value depend on what qualifies an individual to be a “case.” Several different precise definitions of CFR have been used in practice, as have several imprecise ones. The infection-fatality risk (sometimes written IFR) defines a case as a person who has shown evidence of infection, either by clinical detection of the pathogen or by seroconversion or other immune response. Such individuals may or may not be symptomatic, though asymptomatic ones may go undetected. The symptomatic case-fatality risk (sCFR) defines a case as someone who is infected and shows certain symptoms. Infection in many outbreaks is given several gradations, including confirmed (definitive laboratory confirmation), probable (high degree of suspicion, by various clinical and epidemiologic criteria, without laboratory confirmation), and possible or suspected (lower degree of suspicion). This paper describes issues in estimating any of these risks or comparing them across groups, but does not go into the details of each possible definition.Furthermore, unlike risks commonly used in epidemiologic research (e.g., the 5-year mortality risk), the length of the period during which deaths are counted for the CFR is rarely explicit, probably because it is considered to be short enough to avoid ambiguity in the definition of CFR. However, a precise definition of the CFR would need to include the risk period, e.g., the 1-month CFR of Ebola. Clearly, the definition of CFR for a particular investigation should be specified as precisely as possible.However, observational studies conducted in the early phases of an outbreak, when public health authorities are appropriately concentrating on crisis response and not on rigorous study design, are challenging. A common problem is that disease severity of the cases recorded in a surveillance database will differ, perhaps substantially, from that of all cases in the population. This issue has arisen in the present epidemic of Ebola virus disease in West Africa and in many previous outbreaks and epidemics [4–9] and will continue to arise in future ones.Here we outline two biases that may occur when estimating the CFR in a population from a surveillance database, and three more biases that may occur when comparing the CFR between subgroups to estimate the causal effect of medical interventions. We also briefly consider the applicability of these biases to a different application: comparing the CFR across different groups of people, for example, by geography, sex, age, comorbidities, and other “unchangeable” risk factors. Such factors are “unchangeable” in the sense that they are not candidates for intervention in the setting of the outbreak, though some could, of course, change over longer timescales. The goal of estimating the CFR in groups defined by such unchangeable factors is not to understand the causal role of these factors in mortality, but to develop a predictive model for mortality that might be used to improve prognostic accuracy or identify disparities. Such predictions may be affected by survivorship bias and selection bias, but not by confounding, as we discuss.     

Estimating Bacterial Diversity for Ecological Studies: Methods,Metrics, and Assumptions

Methods to estimate microbial diversity have developed rapidly in an effort to understand the distribution and diversity of microorganisms in natural environments. For bacterial communities, the 16S rRNA gene is the phylogenetic marker gene of choice, but most studies select only a specific region of the 16S rRNA to estimate bacterial diversity. Whereas biases derived from from DNA extraction, primer choice and PCR amplification are well documented, we here address how the choice of variable region can influence a wide range of standard ecological metrics, such as species richness, phylogenetic diversity, β-diversity and rank-abundance distributions. We have used Illumina paired-end sequencing to estimate the bacterial diversity of 20 natural lakes across Switzerland derived from three trimmed variable 16S rRNA regions (V3, V4, V5). Species richness, phylogenetic diversity, community composition, β-diversity, and rank-abundance distributions differed significantly between 16S rRNA regions. Overall, patterns of diversity quantified by the V3 and V5 regions were more similar to one another than those assessed by the V4 region. Similar results were obtained when analyzing the datasets with different sequence similarity thresholds used during sequences clustering and when the same analysis was used on a reference dataset of sequences from the Greengenes database. In addition we also measured species richness from the same lake samples using ARISA Fingerprinting, but did not find a strong relationship between species richness estimated by Illumina and ARISA. We conclude that the selection of 16S rRNA region significantly influences the estimation of bacterial diversity and species distributions and that caution is warranted when comparing data from different variable regions as well as when using different sequencing techniques.     

Gene-Gene and Gene-Environment Interactions in Meta-Analysis of Genetic Association Studies

Extensive genetic studies have identified a large number of causal genetic variations in many human phenotypes; however, these could not completely explain heritability in complex diseases. Some researchers have proposed that the “missing heritability” may be attributable to gene–gene and gene–environment interactions. Because there are billions of potential interaction combinations, the statistical power of a single study is often ineffective in detecting these interactions. Meta-analysis is a common method of increasing detection power; however, accessing individual data could be difficult. This study presents a simple method that employs aggregated summary values from a “case” group to detect these specific interactions that based on rare disease and independence assumptions. However, these assumptions, particularly the rare disease assumption, may be violated in real situations; therefore, this study further investigated the robustness of our proposed method when it violates the assumptions. In conclusion, we observed that the rare disease assumption is relatively nonessential, whereas the independence assumption is an essential component. Because single nucleotide polymorphisms (SNPs) are often unrelated to environmental factors and SNPs on other chromosomes, researchers should use this method to investigate gene–gene and gene–environment interactions when they are unable to obtain detailed individual patient data.     

A Platform for the Remote Conduct of Gene-Environment Interaction Studies

Background

Gene-environment interaction studies offer the prospect of robust causal inference through both gene identification and instrumental variable approaches. As such they are a major and much needed development. However, conducting these studies using traditional methods, which require direct participant contact, is resource intensive. The ability to conduct gene-environment interaction studies remotely would reduce costs and increase capacity.

Aim

To develop a platform for the remote conduct of gene-environment interaction studies.

Methods

A random sample of 15,000 men and women aged 50+ years and living in Cardiff, South Wales, of whom 6,012 were estimated to have internet connectivity, were mailed inviting them to visit a web-site to join a study of successful ageing. Online consent was obtained for questionnaire completion, cognitive testing, re-contact, record linkage and genotyping. Cognitive testing was conducted using the Cardiff Cognitive Battery. Bio-sampling was randomised to blood spot, buccal cell or no request.

Results

A heterogeneous sample of 663 (4.5% of mailed sample and 11% of internet connected sample) men and women (47% female) aged 50–87 years (median = 61 yrs) from diverse backgrounds (representing the full range of deprivation scores) was recruited. Bio-samples were donated by 70% of those agreeing to do so. Self report questionnaires and cognitive tests showed comparable distributions to those collected using face-to-face methods. Record linkage was achieved for 99.9% of participants.

Conclusion

This study has demonstrated that remote methods are suitable for the conduct of gene-environment interaction studies. Up-scaling these methods provides the opportunity to increase capacity for large-scale gene-environment interaction studies.     

Tests of the Critical Assumptions of the Dilution Method for Estimating Bacterivory by Microeucaryotes

The critical assumptions of the dilution method for estimating grazing rates of microzooplankton were tested by using a community from the sediment-water interface of Lake Anna, Va. Determination of the appropriate computational model was achieved by regression analysis; the exponential model was appropriate for bacterial growth at Lake Anna. The assumption that the change in grazing pressure is linearly proportional to the dilution factor was tested by analysis of variance with a lack-of-fit test. There was a significant (P < 0.0001) linear (P > 0.05) relationship between the dilution factor and time-dependent change in ln bacterial abundance. The assumption that bacterial growth is not altered by possible substrate enrichment in the dilution treatment was tested by amending diluted water with various amounts of dissolved organic carbon (either yeast extract or extracted carbon from lake sediments). Additions of carbon did not significantly alter bacterial growth rates during the incubation period (24 h). On the basis of these results, the assumptions of the dilution method proved to be valid for the system examined.     

On the Interpretation of Equilibrium Binding Studies

Abstract

Equilibrium binding curves are discussed on the basis of their fundamental equations. The shape of these curves is not influenced by the number of conformational states of the receptor-ligand complexes. In contrast, the number of binding sites determines the shape of the equilibrium binding curve. For example, a curved Scat-chard plot establishes the existence of more than one binding site at the receptor but cannot yield information on the number of conformational states. If there are discrepancies between equilibrium binding and equilibrium dose-response curves they indicate that the response is not initiated by the overall binding process. They may be explained assuming that only one particular receptor-ligand complex (e.g. the fully saturated one) will initiate the physiological response.     

Hardy-Weinberg定律在专科教学中的课堂设计

Hardy-Weinberg定律是群体遗传学的第一理论基石,也是现代进化论、现代优生学和群体育种的理论基础,是遗传学教学中的重难点内容,但通过合理的教学设计可帮助学生全面理解、掌握并应用该定律,为后续学习奠定基础。     

Estimating the Global Prevalence of Inadequate Zinc Intake from National Food Balance Sheets: Effects of Methodological Assumptions

Background

The prevalence of inadequate zinc intake in a population can be estimated by comparing the zinc content of the food supply with the population’s theoretical requirement for zinc. However, assumptions regarding the nutrient composition of foods, zinc requirements, and zinc absorption may affect prevalence estimates. These analyses were conducted to: (1) evaluate the effect of varying methodological assumptions on country-specific estimates of the prevalence of dietary zinc inadequacy and (2) generate a model considered to provide the best estimates.

Methodology and Principal Findings

National food balance data were obtained from the Food and Agriculture Organization of the United Nations. Zinc and phytate contents of these foods were estimated from three nutrient composition databases. Zinc absorption was predicted using a mathematical model (Miller equation). Theoretical mean daily per capita physiological and dietary requirements for zinc were calculated using recommendations from the Food and Nutrition Board of the Institute of Medicine and the International Zinc Nutrition Consultative Group. The estimated global prevalence of inadequate zinc intake varied between 12–66%, depending on which methodological assumptions were applied. However, country-specific rank order of the estimated prevalence of inadequate intake was conserved across all models (r = 0.57–0.99, P<0.01). A “best-estimate” model, comprised of zinc and phytate data from a composite nutrient database and IZiNCG physiological requirements for absorbed zinc, estimated the global prevalence of inadequate zinc intake to be 17.3%.

Conclusions and Significance

Given the multiple sources of uncertainty in this method, caution must be taken in the interpretation of the estimated prevalence figures. However, the results of all models indicate that inadequate zinc intake may be fairly common globally. Inferences regarding the relative likelihood of zinc deficiency as a public health problem in different countries can be drawn based on the country-specific rank order of estimated prevalence of inadequate zinc intake.     

Genomewide Transmission/Disequilibrium Testing-Consideration of the Genotypic Relative Risks at Disease Loci

Genomewide association studies are set to become the tool of the future for detection of small-effect genes in complex diseases. It will therefore be necessary to calculate sufficient sample sizes with which to perform them. In this paper I illustrate how to calculate the required number of families for general genotypic relative risks (GRRs). I show the superior sensitivity of the genomewide association study over the standard genomewide affected-sib-pair linkage analysis, for a range of different underlying GRR patterns. I also illustrate the extent of change in the sample sizes that is necessary for a genomewide association analysis depending on the pattern of the GRRs at the disease locus. In many cases, the comparative numbers of families required under different genetic mechanisms vary by several orders of magnitude. These sometimes dramatic differences have important implications for the determination of the size of the collection of samples prior to analysis and for the types of effects that are likely--and unlikely--to be detected by such an analysis.     

Multiple Imputation Methods for Estimating Regression Coefficients in the Competing Risks Model with Missing Cause of Failure

We propose a method to estimate the regression coefficients in a competing risks model where the cause-specific hazard for the cause of interest is related to covariates through a proportional hazards relationship and when cause of failure is missing for some individuals. We use multiple imputation procedures to impute missing cause of failure, where the probability that a missing cause is the cause of interest may depend on auxiliary covariates, and combine the maximum partial likelihood estimators computed from several imputed data sets into an estimator that is consistent and asymptotically normal. A consistent estimator for the asymptotic variance is also derived. Simulation results suggest the relevance of the theory in finite samples. Results are also illustrated with data from a breast cancer study.     

On Estimation of Relative Risk in Case Control Studies

An estimator of relative risk in a case control study has been proposed in terms of observed cell frequencies and the probability of disease. The bias of the usual estimator i.e odds ratio as compared to the new estimator has been workedout. The expression of Mean Square Error of proposed estimator has been derived in situations where probability of disease is exactly known and when it is estimated through an independent survey. It has been observed that there is a serious error using odds ratio as an estimate of relative risk when probability of disease is not negligible. In such situations the proposed estimator can be used with advantage.     

Estimating the Relative Roles of Recombination and Point Mutation in the Generation of Single Locus Variants in Campylobacter jejuni and Campylobacter coli

Single locus variants (SLVs) are bacterial sequence types that differ at only one of the seven canonical multilocus sequence typing (MLST) loci. Estimating the relative roles of recombination and point mutation in the generation of new alleles that lead to SLVs is helpful in understanding how organisms evolve. The relative rates of recombination and mutation for Campylobacter jejuni and Campylobacter coli were estimated at seven different housekeeping loci from publically available MLST data. The probability of recombination generating a new allele that leads to an SLV is estimated to be roughly seven times more than that of mutation for C. jejuni, but for C. coli recombination and mutation were estimated to have a similar contribution to the generation of SLVs. The majority of nucleotide differences (98?% for C. jejuni and 85?% for C. coli) between strains that make up an SLV are attributable to recombination. These estimates are much larger than estimates of the relative rate of recombination to mutation calculated from more distantly related isolates using MLST data. One explanation for this is that purifying selection plays an important role in the evolution of Campylobacter. A simulation study was performed to test the performance of our method under a range of biologically realistic parameters. We found that our method performed well when the recombination tract length was longer than 3?kb. For situations in which recombination may occur with shorter tract lengths, our estimates are likely to be an underestimate of the ratio of recombination to mutation, and of the importance of recombination for creating diversity in closely related isolates. A parametric bootstrap method was applied to calculate the uncertainty of these estimates.     

An Evaluation of Different Methods in Epidemiologic Studies of Radiation Risks

The probability of detecting possible late effects of ionizing radiation in human populations depends on the size of exposure in the study population and on the epidemiologic evaluation method used. This is not only due to the mathematical or statistical properties of the method, but also to the choice of the control population, which may be either external (usually large) or internal (usually not so large). Moreover, the use of a large external control population often results in an increasing influence of selection factors expressing themselves e.g. through the ‘healthy worker’ effect. In this paper three different methods usually employed in follow-up studies are reviewed: the calculation of Standardized Mortality Ratios (SMR), a contingency table analysis based on Person-Years (PY) and the comparison of Cumulative Mean Doses (CMD) within different subcohorts. The methods are illustrated with a simple radiation risk model; nevertheless, most of the conclusions apply to non-radiation risk studies as well. The CMD-method is shown to be heavily selection sensitive.     

Estimation of Hardy-Weinberg and pairwise disequilibrium in the apolipoprotein AI-CIII-AIV gene cluster.

Departures from Hardy-Weinberg (HW) equilibria and pairwise disequilibria were estimated in a sample of unrelated healthy individuals typed for six RFLPs in the apo AI-CIII-AIV gene region. The sample was composed of males and females, selected for health, from two populations, those of exclusively French-Canadian (FC) and those of some non-French-Canadian (NFC) ancestry. An approach suggested by Weir and Cockerham, which includes estimates of nonrandom association (disequilibria) between three and four alleles at two loci as well as the traditional associations between two alleles, at two loci was used. The pattern of departures from HW equilibria suggested that the genetic structures of the FC and NFC are different. Departure from HW equilibrium at an RFLP locus could not be predicted from information about other loci in the same gene region. Nonrandom associations were also evident from the pairwise analyses. Two pairs of loci had significant diallelic disequilibria, while two other pairs had significant triallelic disequilibria. All of the RFLP pairs had at least one measure of disequilibrium at its maximum value determined by allele frequencies. Inferences about pairwise disequilibria depended on the statistical approach used. Sizes of the pairwise disequilibria were not correlated with the physical distance between loci. The impact of these disequilibria on RFLP-phenotype association studies is discussed.