Rare Disease Assumption Research Articles

Risk ratio and risk difference estimation in case-cohort studies.

In case-cohort studies with binary outcomes, ordinary logistic regression analyses have been widely used because of their computational simplicity. However, the resultant odds-ratio estimates cannot be interpreted as relative risk measures unless the event rate is low. The risk ratio and risk difference are more favorable outcome measures that are directly interpreted as effect measures without the rare disease assumption. We provide pseudo-Poisson and pseudo-normal linear regression methods for estimating the risk ratio and risk difference in analyses of case-cohort studies. These multivariate regression models are fitted by weighting the inverses of sampling probabilities. Also, the precisions of the risk ratio and risk difference estimators can be improved using auxiliary variable information, specifically by adapting the calibrated or estimated weights, which are readily measured on all samples from the whole cohort. Finally, we provide computational code in R (R Foundation for Statistical Computing, Vienna, Austria) that can easily perform these methods. Through numerical analyses of artificially simulated data and the National Wilms Tumor Study data, accurate risk ratio and risk difference estimates were obtained by the pseudo-Poisson and pseudo-normal linear regression methods. Also, using the auxiliary variable information from the whole cohort, precisions of these estimators were markedly improved. The ordinary logistic regression analyses may provide uninterpretable effect measure estimates, and the risk ratio and risk difference estimation methods are effective alternative approaches for case-cohort studies. These methods are especially recommended under situations in which the event rate is not low.

A unified mediation analysis framework for integrative cancer proteogenomics with clinical outcomes.

Multilevel molecular profiling of tumors and the integrative analysis with clinical outcomes have enabled a deeper characterization of cancer treatment. Mediation analysis has emerged as a promising statistical tool to identify and quantify the intermediate mechanisms by which a gene affects an outcome. However, existing methods lack a unified approach to handle various types of outcome variables, making them unsuitable for high-throughput molecular profiling data with highly interconnected variables. We develop a general mediation analysis framework for proteogenomic data that include multiple exposures, multivariate mediators on various scales of effects as appropriate for continuous, binary and survival outcomes. Our estimation method avoids imposing constraints on model parameters such as the rare disease assumption, while accommodating multiple exposures and high-dimensional mediators. We compare our approach to other methods in extensive simulation studies at a range of sample sizes, disease prevalence and number of false mediators. Using kidney renal clear cell carcinoma proteogenomic data, we identify genes that are mediated by proteins and the underlying mechanisms on various survival outcomes that capture short- and long-term disease-specific clinical characteristics. Software is made available in an R package (https://github.com/longjp/mediateR). Supplementary data are available at Bioinformatics online.

Estimation of vaccine efficacy for variants that emerge afterthe placebo group is vaccinated.

SARS‐CoV‐2 continues to evolve and the vaccine efficacy against variants is challenging to estimate. It is now common in phase III vaccine trials to provide vaccine to those randomized to placebo once efficacy has been demonstrated, precluding a direct assessment of placebo controlled vaccine efficacy after placebo vaccination. In this work, we extend methods developed for estimating vaccine efficacy post placebo vaccination to allow variant specific time varying vaccine efficacy, where time is measured since vaccination. The key idea is to infer counterfactual strain specific placebo case counts by using surveillance data that provide the proportions of the different strains. This blending of clinical trial and observational data allows estimation of strain‐specific time varying vaccine efficacy, or sieve effects, including for strains that emerge after placebo vaccination. The key requirements are that the surveillance strain distribution accurately reflects the strain distribution for a placebo group throughout follow‐up after placebo group vaccination, and that at least one strain is present before and after placebo vaccination. For illustration, we develop a Poisson approach for an idealized design under a rare disease assumption and then use a proportional hazards model to address staggered entry, staggered crossover, and smoothly varying strain specific vaccine efficacy. We evaluate these methods by theoretical work and simulations, and demonstrate that useful estimation of the efficacy profile is possible for strains that emerge after vaccination of the placebo group. An important principle is to incorporate sensitivity analyses to guard against misspecification of the strain distribution.

Interpretation of clinical trial results: a committee opinion

This document provides guidance, background, and tips on how to recognize quality trials and focuses on evaluating the validity, importance, and relevance of clinical trial results. This document replaces the document of the same name, last published in 2008 (Fertil Steril® 2008;90:S114-20).

Invited Commentary: Two-Phase, Generalized Case-Control Designs for Quantitative Longitudinal Outcomes and Evolution of the Case-Control Study.

The case-control study design has evolved substantially over the past half century. The design has long been recognized as a way to increase efficiency by studying fewer subjects than would be required for a full cohort study. Historically, it was thought that case-control studies required a rare disease assumption for valid risk ratio estimation, but it was later realized that rare disease was not necessary. Over time, the design and analysis methods were further modified to allow estimation of rate ratios or to allow each person to serve as his/her own control (as we see with case-cohort and case-crossover studies, for example). We now understand that efficiency can be increased through the use of outcome-dependent sampling not only for dichotomous outcomes but also for continuous outcomes in longitudinal studies with repeated outcome measurement during follow-up. In their accompanying paper, Schildcrout et al. (Am J Epidemiol. 2019;000(00):000-000) contribute to our understanding, clearly summarizing many recent advances in study design and analyses that allow more general and efficient use of case-control studies. Their simulations demonstrate that improved efficiency is achieved with these methods when the goal is to estimate associations of exposure with trajectories and patterns of change over time. Here we comment on application of some of these generalized case-control methods to causal inference.

Examining the rare disease assumption used to justify HWE testing with control samples.

Many statistical methods for analyzing genetic data, such as those used in genome-wide association studies, assume Hardy-Weinberg Equilibrium (HWE). Therefore, to use such methods, one must check whether the HWE assumption is valid. For a case-control study, researchers have recognized that Hardy Weinberg proportions will be distorted if the marker being tested happens to be associated with the disease. To alleviate this problem, many studies carry out HWE testing on controls only. A number of papers in the literature have justified this practice by making the rare disease assumption without providing rigorous theoretical basis for this justification. Even though many of the diseases studied today are common, whether it is justifiable to use controls to test for HWE when the disease is indeed rare remains an outstanding issue. In this study, we address the rare disease assumption as well as potential problems associated with testing for HWE using controls only, regardless of the prevalence of the disease. We carried out theoretical derivations and numerical studies; the latter were performed using simulated genotypes as well as data from the 1000 Genomes Project. The results from our study are striking: the type I error can be severely inflated, regardless of whether the disease being investigated is rare or common. This study shows that, based on the common practice of using controls only to test for HWE, many genetic variants will be discarded erroneously, wasting valuable information and hindering the ability to detect disease-associated variants.

Adjusted time-varying population attributable hazard in case-control studies.

Population attributable fraction is a widely used measure for quantifying the disease burden associated with a modifiable exposure of interest at the population level. It has been extended to a time-varying measure, population attributable hazard function, to provide additional information on when and how the exposure's impact varies over time. However, like the classic population attributable fraction, the population attributable hazard is generally biased if confounders are present. In this article, we provide a natural definition of adjusted population attributable hazard to take into account the effects of confounders, and its alternative that is identifiable from case-control studies under the rare disease assumption. We propose a novel estimator, which combines the odds ratio estimator from logistic regression model, and the conditional density function estimator of the exposure and confounding variables distribution given the failure times of cases or the current times of controls from a kernel smoother. We show that the proposed estimators are consistent and asymptotically normal with variance that can be estimated empirically from the data. Simulation studies demonstrate that the proposed estimators perform well in finite sample sizes. Finally, we illustrate the method by an analysis of a case-control study of colorectal cancer. Supplementary materials for this article are available online.

A semiparametric efficient estimator in case-control studies for gene–environment independent models

Case-controls studies are popular epidemiological designs for detecting gene–environment interactions in the etiology of complex diseases, where the genetic susceptibility and environmental exposures may often be reasonably assumed independent in the source population. Various papers have presented analytical methods exploiting gene–environment independence to achieve better efficiency, all of which require either a rare disease assumption or a distributional assumption on the genetic variables. We relax both assumptions. We construct a semiparametric estimator in case-control studies exploiting gene–environment independence, while the distributions of genetic susceptibility and environmental exposures are both unspecified and the disease rate is assumed unknown and is not required to be close to zero. The resulting estimator is semiparametric efficient and its superiority over prospective logistic regression, the usual analysis in case-control studies, is demonstrated in various numerical illustrations.

Mediation analysis for common binary outcomes.

Mediation analysis provides an attractive causal inference framework to decompose the total effect of an exposure on an outcome into natural direct effects and natural indirect effects acting through a mediator. For binary outcomes, mediation analysis methods have been developed using logistic regression when the binary outcome is rare. These methods will not hold in practice when a disease is common. In this paper, we develop mediation analysis methods that relax the rare disease assumption when using logistic regression. We calculate the natural direct and indirect effects for common diseases by exploiting the relationship between logit and probit models. Specifically, we derive closed-form expressions for the natural direct and indirect effects on the odds ratio scale. Mediation models for both continuous and binary mediators are considered. We demonstrate through simulation that the proposed method performs well for common binary outcomes. We apply the proposed methods to analyze the Normative Aging Study to identify DNA methylation sites that are mediators of smoking behavior on the outcome of obstructed airway function.

Case-only approach to identifying markers predicting treatment effects on the relative risk scale.

Retrospectively measuring markers on stored baseline samples from participants in a randomized controlled trial (RCT) may provide high quality evidence as to the value of the markers for treatment selection. Originally developed for approximating gene-environment interactions in the odds ratio scale, the case-only method has recently been advocated for assessing gene-treatment interactions on rare disease endpoints in randomized clinical trials. In this article, the case-only approach is shown to provide a consistent and efficient estimator of marker by treatment interactions and marker-specific treatment effects on the relative risk scale. The prohibitive rare-disease assumption is no longer needed, broadening the utility of the case-only approach. The case-only method is resource-efficient as markers only need to be measured in cases only. It eliminates the need to model the marker's main effect, and can be used with any parametric or nonparametric learning method. The utility of this approach is illustrated by an application to genetic data in the Women's Health Initiative (WHI) hormone therapy trial.

Self-controlled case series with multiple event types

Self-controlled case series methods for events that may be classified as one of several types are described. When the event is non-recurrent, the different types correspond to competing risks. It is shown that, under circumstances that are likely to arise in practical applications, the SCCS multi-type likelihood reduces to the product of the type-specific likelihoods. For recurrent events, this applies whether or not the marginal type-specific counts are dependent. As for the standard SCCS method, a rare disease assumption is required for non-recurrent events. Several forms of this assumption are investigated by simulation. The methods are applied to data on MMR vaccine and convulsions (febrile and non-febrile), and to data on thiazolidinediones and fractures (at different sites).

Testing for Sufficient-Cause Gene-Environment Interactions Under the Assumptions of Independence and Hardy-Weinberg Equilibrium.

To detect gene-environment interactions, a logistic regression model is typically fitted to a set of case-control data, and the focus is on testing of the cross-product terms (gene × environment) in the model. A significant result is indicative of a gene-environment interaction under a multiplicative model for disease odds. Based on the sufficient-cause model for rates, in this paper we put forward a general approach to testing for sufficient-cause gene-environment interactions in case-control studies. The proposed tests can be tailored to detect a particular type of sufficient-cause gene-environment interaction with greater sensitivity. These tests include testing for autosomal dominant, autosomal recessive, and gene-dosage interactions. The tests can also detect trend interactions (e.g., a larger gene-environment interaction with a higher level of environmental exposure) and threshold interactions (e.g., gene-environment interaction occurs only when environmental exposure reaches a certain threshold level). Two assumptions are necessary for the validity of the tests: 1) the rare-disease assumption and 2) the no-redundancy assumption. Another 2 assumptions are optional but, if imposed correctly, can boost the statistical powers of the tests: 3) the gene-environment independence assumption and 4) the Hardy-Weinberg equilibrium assumption. SAS code (SAS Institute, Inc., Cary, North Carolina) for implementing the methods is provided.

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.

Analysis of case-cohort designs with binary outcomes: Improving efficiency using whole-cohort auxiliary information.

The case-cohort design has been widely adopted for reducing the cost of covariate measurements in large prospective cohort studies. Under the case-cohort design, complete covariate data are collected only on randomly sampled cases and a subcohort randomly selected from the whole cohort. For the analysis of case-cohort studies with binary outcomes, logistic regression analysis has been routinely used. However, in many applications, certain covariates are readily measured on all samples from the whole cohort, and the case-cohort design may be regarded as a two-phase sampling design. Using this auxiliary covariate information, estimators for the regression parameters can be substantially improved. In this article, we discuss the theoretical basis of the case-cohort design derived from the formulation of the two-phase design and the improved estimators using whole-cohort auxiliary variable information. In particular, we show that the sampling scheme of the case-cohort design is substantially equivalent to that of conventional two-phase case-control studies (also known as two-stage case-control studies for epidemiologists), i.e., the methodologies of two-phase case-control studies can be directly applied to case-cohort data. Under this framework, we review and apply the following improved estimators to the case-cohort design with binary outcomes: (i) weighted estimators, (ii) a semiparametric maximum likelihood estimator, and (iii) a multiple imputation estimator. In addition, based on the framework of the two-phase design, we can obtain risk ratio and risk difference estimators without the rare-disease assumption. We illustrate these methodologies via simulations and the National Wilms Tumor Study data.

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.

Intensity Of Smoking Increases The Odds Of Acute Myeloid Leukemia In Adult Smokers

IntroductionA number of risk factors for the development of acute myeloid leukemia (AML) have been previously described. The role of smoking in the development of AML has been postulated as a potential environmental risk factor. This association has been studied in previous observational reports; however, the dose-response relation between smoking and AML has not been evaluated. The primary objective of this meta-analysis is to evaluate the dose-relationship between smoking and the development of AML. Secondary objectives were to identify potential gender and/or geographical disparities. MethodsA PubMed search from January 1, 1993 to December 31, 2012 was undertaken using the keywords: “(smoking OR tobacco OR cigarette) AND leukemia”. Prospective cohort and case-control studies reporting on the incidence of AML were included. Studies reporting on acute promyelocytic leukemia, acute leukemia or myeloid leukemia without specifying subtype and cross-sectional studies were excluded. Studies included in a previous meta-analysis by Brownson et al. (1993) were also excluded. The outcome of interest was the odds ratio (OR) with 95% confidence interval (CI) of developing AML in smokers compared to never smokers. Because the overall risk of AML in the general population is low, the relative risk mathematically approximates the OR, allowing the pooling of cohort and case-control studies (rare disease assumption). The random effects model (REM), which accounts for intra and inter-study heterogeneity, was used to estimate the combined outcome. Heterogeneity was also quantified by the I2statistic. Publication bias was assessed by the trim-and-fill analysis. Stratified analyses were performed in current smokers and ever smokers. Subset analyses were performed by sex, study design, geographical region, number of cigarettes smoked, number of years of smoking and cumulative smoking in pack-years. The quality of the studies was assessed by the Newcastle-Ottawa scale (NOS). Literature search, data gathering and quality assessment were performed independently by at least two of the investigators. All calculations and graphs were obtained using Comprehensive Meta-Analysis version 2.2.050 (Biostat, Englewood, NJ, USA). ResultsOur initial search yielded 573 articles, from which 16 case-control and 6 cohort studies were included in our final analysis; 10 studies were from Europe, 9 from North America and 3 from Asia. All the studies were considered of intermediate and high quality, based on the NOS score. Ever smokers had an OR of 1.26 (95% CI 1.15-1.38; p<0.01). The OR of AML in male and female ever smokers was 1.45 (95% CI 1.14-1.85; p<0.01) and 1.14 (95% CI 1.00-1.29; p=0.05), respectively. Current smokers had an OR of 1.42 (95% CI 1.24-1.62; p<0.01). Male and female current smokers had an OR 1.42 (95% CI 1.12-1.81; p<0.01) and 1.28 (95% CI 1.03-1.60; p=0.03), respectively. The odds of AML were increased in ever and current smokers regardless of the study design and the geographical region. Heterogeneity was minimal to moderate and publication bias analysis would have not changed our results. The dose-response analysis showed that smoking >20 cigarettes per day was associated with OR 1.76 (95% CI 1.41-2.18; p<0.01) while smoking <20 cigarettes with OR 1.38 (95% CI 1.23-1.55; p<0.01) of developing AML. Smoking >20 years showed OR of 1.35 (95% CI 1.16-1.57; p<0.01) but smoking <20 years was not associated with increased odds of AML (OR 1.04, 95% CI 0.90-1.20; p=0.56). ConclusionsThere is a 26% increase in the odds of developing of AML in those who have ever smoked compared to never smokers. In those who are current smokers the odds are increased by 42%. The odds of AML in male smokers appear somewhat higher than in female smokers but there does not appear to be a geographical disparity in the odds of AML based on smoking status. The dose-response analysis supports that the intensity of smoking might be a stronger driver of the odds of AML than the duration of smoking in adult individuals. Disclosures:No relevant conflicts of interest to declare.

Case-control studies: basic concepts

The purpose of this article is to present in elementary mathematical and statistical terms a simple way to quickly and effectively teach and understand case-control studies, as they are commonly done in dynamic populations-without using the rare disease assumption. Our focus is on case-control studies of disease incidence ('incident case-control studies'); we will not consider the situation of case-control studies of prevalent disease, which are published much less frequently.

The case-cohort design in outbreak investigations

The use of the case-cohort design for outbreak investigations has been limited. Here we discuss its strengths and limitations based on real and fictitious examples. The case-cohort is a case–control study where controls are sampled from the initial population at risk, and may thus include both cases and non-cases. An advantage of the design, compared to traditional case-control studies, is that risk ratios can easily be obtained directly from the cross-product of exposed and unexposed cases and controls (rare disease assumption is not required). We illustrate this in the context of point source gastrointestinal outbreaks and in field studies on vaccine effectiveness. The design is also useful to investigate multiple outcomes with a unique sample of controls or to test hypotheses when different case-definitions (from the most sensitive to the most specific) are used for a particular outcome. Strengths and limitations are presented, and discussed in the context of outbreak investigations.

Estimation and testing of the relative risk of disease in case-control studies with a set of k matched controls per case with known prevalence of disease.

The analysis of case-control studies with matched controls per case is well documented in the medical literature. Of primary interest is the estimation of the relative risk of disease. Matched case-control studies fall into two scenarios: the probability of exposure is constant within each of the case and control groups, or the probability of exposure varies within each group. Numerous estimation procedures have been developed for both scenarios. Often these procedures are developed under the rare disease assumption, where the relative risk of disease is approximated by the odds ratio. In this paper, without making the rare disease assumption, we develop consistent estimators of the relative risk of disease for both scenarios. Exact derivations of the relative risk of disease are provided. Estimators, confidence intervals, and test statistics for the relative risk of disease are developed. We then make the following observations based on extensive simulations. First, our estimators are as close or closer to the relative risk of disease than other estimators. Second, our estimators produce mean square errors for the relative risk of disease that are as good as or better than these other estimators. Third, our confidence intervals provide accurate coverage probabilities. Therefore, these new estimators, confidence intervals, and test statistics can be used to either estimate or test the relative risk of disease in matched case-control studies.

Inference From a Multiplicative Model of Joint Genetic Effects for Ovarian Cancer Risk

Inference From a Multiplicative Model of Joint Genetic Effects for Ovarian Cancer Risk