Empirical comparisons of heterogeneity magnitudes of the risk difference, relative risk, and odds ratio.
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ABSTRACT:
SUBMITTER: Zhao Y
PROVIDER: S-EPMC8840324 | biostudies-literature | 2022 Feb
REPOSITORIES: biostudies-literature
Publications
Empirical comparisons of heterogeneity magnitudes of the risk difference, relative risk, and odds ratio.
Zhao Yuxi Y Slate Elizabeth H EH Xu Chang C Chu Haitao H Lin Lifeng L
Systematic reviews 20220212 1
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Project description:For comparison of proportions, there are three commonly used measurements: the difference, the relative risk, and the odds ratio. Significant effort has been spent on exact confidence intervals for the difference. In this article, we focus on the relative risk and the odds ratio when data are collected from a matched-pairs design or a two-arm independent binomial experiment. Exact one-sided and two-sided confidence intervals are proposed for each configuration of two measurements and two types of data. The one-sided intervals are constructed using an inductive order, they are the smallest under the order, and are admissible under the set inclusion criterion. The two-sided intervals are the intersection of two one-sided intervals. R codes are developed to implement the intervals. Supplementary materials for this article are available online.
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Project description:BackgroundIn 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.MethodsWe provide pseudo-Poisson and pseudo-normal linear regression methods for estimating risk ratios and risk differences 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.ResultsThrough numerical analyses of artificially simulated data and the National Wilms Tumor Study data, accurate risk ratio and risk difference estimates were obtained using 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.ConclusionThe 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.
| S-EPMC10483099 | biostudies-literature
Project description:In this paper we consider three-arm non-inferiority (NI) trial that includes an experimental, a reference, and a placebo arm. While for binary outcomes the risk difference (RD) is the most common and well explored functional form for testing efficacy (or effectiveness), recent FDA guideline suggested other measures such as relative risk (RR) and odds ratio (OR) on the basis of which NI of an experimental treatment can be claimed. However, developing test based on these different functions of binary outcomes are challenging since the construction and interpretation of NI margin for such functions are not trivial extensions of RD based approach. Recently, we have proposed Frequentist approaches for testing NI for these functionals. In this article we further develop Bayesian approaches for testing NI based on effect retention approach for RR and OR. Bayesian paradigm provides a natural path to integrate historical trials' information, as well as it allows the usage of patients'/clinicians' opinions as prior information via sequential learning. In addition we discuss, in detail, the sample size/power calculation which could be readily used while designing such trials in practice.
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Project description:BACKGROUND:Population attributable fractions (PAF) measure the proportion of disease prevalence that would be avoided in a hypothetical population, similar to the population of interest, but where a particular risk factor is eliminated. They are extensively used in epidemiology to quantify and compare disease burden due to various risk factors, and directly influence public policy regarding possible health interventions. In contrast to individual specific metrics such as relative risks and odds ratios, attributable fractions depend jointly on both risk factor prevalence and relative risk. The relative contributions of these two components is important, and usually needs to be presented in summary tables that are presented together with the attributable fraction calculation. However, representing PAF in an accessible graphical format, that captures both prevalence and relative risk, may assist interpretation. METHODS:Taylor-series approximations to PAF in terms of risk factor prevalence and log-odds ratio are derived that facilitate simultaneous representation of PAF, risk factor prevalence and risk-factor/disease log-odds ratios on a single co-ordinate axis. Methods are developed for binary, multi-category and continuous exposure variables. RESULTS:The methods are demonstrated using INTERSTROKE, a large international case control dataset focused on risk factors for stroke. CONCLUSIONS:The described methods could be used as a complement to tables summarizing prevalence, odds ratios and PAF, and may convey the same information in a more intuitive and visually appealing manner. The suggested nomogram can also be used to visually estimate the effects of health interventions which only partially reduce risk factor prevalence. Finally, in the binary risk factor case, the approximations can also be used to quickly convert logistic regression coefficients for a risk factor into approximate PAFs.
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Project description:In clinical trials and observational studies, the effect of an intervention or exposure can be reported as an absolute or relative comparative measure such as risk difference, odds ratio or risk ratio, or at the group level with the estimated risk of disease in each group. For meta-analysis of results with covariate adjustment, the log of the odds ratio (log odds ratio), with its standard error, is a commonly used measure of effect. However, extracting the adjusted log odds ratio from the reported estimates of disease risk in each group is not straightforward. Here, we propose a method to transform the adjusted probability of the event in each group to the log of the odds ratio and obtain the appropriate (approximate) standard error, which can then be used in a meta-analysis. We also use example data to compare our method with two other methods and show that our method is superior in calculating the standard error of the log odds ratio.
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Project description:For estimation of heterogeneity variance τ2 in meta-analysis of log-odds-ratio, we derive new mean- and median-unbiased point estimators and new interval estimators based on a generalized Q statistic, QF , in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators based on the inverse-variance-weights version of Q , QIV. In an extensive simulation, we studied the bias (including median bias) of the point estimators and the coverage (including left and right coverage error) of the confidence intervals. Most estimators add 0.5 to each cell of the 2×2 table when one cell contains a zero count; we include a version that always adds 0.5 . The results show that: two of the new point estimators and two of the familiar point estimators are almost unbiased when the total sample size n≥250 and the probability in the Control arm ( piC ) is 0.1, and when n≥100 and piC is 0.2 or 0.5; for 0.1≤τ2≤1 , all estimators have negative bias for small to medium sample sizes, but for larger sample sizes some of the new median-unbiased estimators are almost median-unbiased; choices of interval estimators depend on values of parameters, but one of the new estimators is reasonable when piC=0.1 and another, when piC=0.2 or piC=0.5 ; and lack of balance between left and right coverage errors for small n and/or piC implies that the available approximations for the distributions of QIV and QF are accurate only for larger sample sizes.
| S-EPMC10946484 | biostudies-literature
Project description:Three-arm non-inferiority (NI) trial including the experimental treatment, an active reference treatment, and a placebo where the outcome of interest is binary are considered. While the risk difference (RD) is the most common and well explored functional form for testing efficacy (or effectiveness), however, recent FDA guideline suggested measures such as relative risk (RR), odds ratio (OR), number needed to treat (NNT) among others, on the basis of which NI can be claimed for binary outcome. Albeit, developing test based on these different functions of binary outcome are challenging. This is because the construction and interpretation of NI margin for such functions are non-trivial extensions of RD based approach. A Frequentist test based on traditional fraction margin approach for RR, OR and NNT are proposed first. Furthermore a conditional testing approach is developed by incorporating assay sensitivity (AS) condition directly into NI testing. A detailed discussion of sample size/power calculation are also put forward which could be readily used while designing such trials in practice. A clinical trial data is reanalyzed to demonstrate the presented approach.
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Project description:A key step in implementing the GRADE (Grading of Recommendations Assessment, Development and Evaluation) system is the estimation of a risk difference based on estimates of the baseline risk and the relative risk estimated from different sources. In this paper we describe a simple and effective method to calculate confidence intervals (CIs) for the risk difference for this situation. Whenever an independent source is available to estimate the baseline risk for the population to which the effect estimates should be applied, this source should be used and CIs for the absolute risk difference should be calculated taking all sources of uncertainty into account.
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Project description:The individual sample heterogeneity is one of the biggest obstacles in biomarker identification for complex diseases such as cancers. Current statistical models to identify differentially expressed genes between disease and control groups often overlook the substantial human sample heterogeneity. Meanwhile, traditional nonparametric tests lose detailed data information and sacrifice the analysis power, although they are distribution free and robust to heterogeneity. Here, we propose an empirical likelihood ratio test with a mean-variance relationship constraint (ELTSeq) for the differential expression analysis of RNA sequencing (RNA-seq). As a distribution-free nonparametric model, ELTSeq handles individual heterogeneity by estimating an empirical probability for each observation without making any assumption about read-count distribution. It also incorporates a constraint for the read-count overdispersion, which is widely observed in RNA-seq data. ELTSeq demonstrates a significant improvement over existing methods such as edgeR, DESeq, t-tests, Wilcoxon tests and the classic empirical likelihood-ratio test when handling heterogeneous groups. It will significantly advance the transcriptomics studies of cancers and other complex disease.
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Project description:A large body of literature shows that non-human animals master a variety of numerical tasks, but studies involving proportional discrimination are sparse and primarily done with mature animals. Here we trained 4-day-old domestic chicks (Gallus gallus) to respond to stimuli depicting multiple examples of the proportion 4:1 when compared with the proportion 2:1. Stimuli were composed of green and red dot arrays; for the rewarded 4:1 proportion, 4 green dots for every red dot (e.g. ratios: 32:8, 12:3, and 44:11). The birds continued to discriminate when presented with new ratios at test (such as 20:5), characterized by new numbers of dots and new spatial configurations (Experiment 1). This indicates that chicks can extract the common proportional value shared by different ratios and apply it to new ones. In Experiment 2, chicks identified a specific proportion (2:1) from either a smaller (4:1) or a larger one (1:1), demonstrating an ability to represent the specific, and not relative, value of a particular proportion. Again, at test, chicks selectively responded to the previously reinforced proportion from new ratios. These findings provide strong evidence for very young animals' ability to extract, identify, and productively use proportion information across a range of different amounts.
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