Maximum type I error rate inflation from sample size reassessment when investigators are blind to treatment labels

Consider a parallel group trial for the comparison of an experimental treatment to a control, where the second‐stage sample size may depend on the blinded primary endpoint data as well as on additional blinded data from a secondary endpoint. For the setting of normally distributed endpoints, we demonstrate that this may lead to an inflation of the type I error rate if the null hypothesis holds for the primary but not the secondary endpoint. We derive upper bounds for the inflation of the type I error rate, both for trials that employ random allocation and for those that use block randomization. We illustrate the worst‐case sample size reassessment rule in a case study. For both randomization strategies, the maximum type I error rate increases with the effect size in the secondary endpoint and the correlation between endpoints. The maximum inflation increases with smaller block sizes if information on the block size is used in the reassessment rule. Based on our findings, we do not question the well‐established use of blinded sample size reassessment methods with nuisance parameter estimates computed from the blinded interim data of the primary endpoint. However, we demonstrate that the type I error rate control of these methods relies on the application of specific, binding, pre‐planned and fully algorithmic sample size reassessment rules and does not extend to general or unplanned sample size adjustments based on blinded data. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

An evaluation of constrained randomization for the design and analysis of group‐randomized trials

In group‐randomized trials, a frequent practical limitation to adopting rigorous research designs is that only a small number of groups may be available, and therefore, simple randomization cannot be relied upon to balance key group‐level prognostic factors across the comparison arms. Constrained randomization is an allocation technique proposed for ensuring balance and can be used together with a permutation test for randomization‐based inference. However, several statistical issues have not been thoroughly studied when constrained randomization is considered. Therefore, we used simulations to evaluate key issues including the following: the impact of the choice of the candidate set size and the balance metric used to guide randomization; the choice of adjusted versus unadjusted analysis; and the use of model‐based versus randomization‐based tests. We conducted a simulation study to compare the type I error and power of the F‐test and the permutation test in the presence of group‐level potential confounders. Our results indicate that the adjusted F‐test and the permutation test perform similarly and slightly better for constrained randomization relative to simple randomization in terms of power, and the candidate set size does not substantially affect their power. Under constrained randomization, however, the unadjusted F‐test is conservative, while the unadjusted permutation test carries the desired type I error rate as long as the candidate set size is not too small; the unadjusted permutation test is consistently more powerful than the unadjusted F‐test and gains power as candidate set size changes. Finally, we caution against the inappropriate specification of permutation distribution under constrained randomization. An ongoing group‐randomized trial is used as an illustrative example for the constrained randomization design. Copyright © 2015 John Wiley & Sons, Ltd.     

Validity and power considerations on hypothesis testing under minimization

Minimization, a dynamic allocation method, is gaining popularity especially in cancer clinical trials. Aiming to achieve balance on all important prognostic factors simultaneously, this procedure can lead to a substantial reduction in covariate imbalance compared with conventional randomization in small clinical trials. While minimization has generated enthusiasm, some controversy exists over the proper analysis of such a trial. Critics argue that standard testing methods that do not account for the dynamic allocation algorithm can lead to invalid statistical inference. Acknowledging this limitation, the International Conference on Harmonization E9 guideline suggests that ‘the complexity of the logistics and potential impact on analyses be carefully evaluated when considering dynamic allocation’. In this article, we investigate the proper analysis approaches to inference in a minimization design for both continuous and time‐to‐event endpoints and evaluate the validity and power of these approaches under a variety of scenarios both theoretically and empirically. Published 2016. This article is a U.S. Government work and is in the public domain in the USA     

Assessing the Genetic Predisposition of Education on Myopia: A Mendelian Randomization Study

Myopia is the largest cause of uncorrected visual impairments globally and its recent dramatic increase in the population has made it a major public health problem. In observational studies, educational attainment has been consistently reported to be correlated to myopia. Nonetheless, correlation does not imply causation. Observational studies do not tell us if education causes myopia or if instead there are confounding factors underlying the association. In this work, we use a two‐step least squares instrumental‐variable (IV) approach to estimate the causal effect of education on refractive error, specifically myopia. We used the results from the educational attainment GWAS from the Social Science Genetic Association Consortium to define a polygenic risk score (PGRS) in three cohorts of late middle age and elderly Caucasian individuals (N = 5,649). In a meta‐analysis of the three cohorts, using the PGRS as an IV, we estimated that each z‐score increase in education (approximately 2 years of education) results in a reduction of 0.92 ± 0.29 diopters (P = 1.04 × 10^?3). Our estimate of the effect of education on myopia was higher (P = 0.01) than the observed estimate (0.25 ± 0.03 diopters reduction per education z‐score [～2 years] increase). This suggests that observational studies may actually underestimate the true effect. Our Mendelian Randomization (MR) analysis provides new evidence for a causal role of educational attainment on refractive error.     

Polygenic Epidemiology

Much of the genetic basis of complex traits is present on current genotyping products, but the individual variants that affect the traits have largely not been identified. Several traditional problems in genetic epidemiology have recently been addressed by assuming a polygenic basis for disease and treating it as a single entity. Here I briefly review some of these applications, which collectively may be termed polygenic epidemiology. Methodologies in this area include polygenic scoring, linear mixed models, and linkage disequilibrium scoring. They have been used to establish a polygenic effect, estimate genetic correlation between traits, estimate how many variants affect a trait, stratify cases into subphenotypes, predict individual disease risks, and infer causal effects using Mendelian randomization. Polygenic epidemiology will continue to yield useful applications even while much of the specific variation underlying complex traits remains undiscovered.     

Causal associations of intelligence with schizophrenia and bipolar disorder: A Mendelian randomization analysis

BackgroundIntelligence is inversely associated with schizophrenia (SCZ) and bipolar disorder (BD); it remains unclear whether low intelligence is a cause or consequence. We investigated causal associations of intelligence with SCZ or BD risk and a shared risk between SCZ and BD and SCZ-specific risk.MethodsTo estimate putative causal associations, we performed multi-single nucleotide polymorphism (SNP) Mendelian randomization (MR) using generalized summary-data-based MR (GSMR). Summary-level datasets from five GWASs (intelligence, SCZ vs. control [CON], BD vs. CON, SCZ + BD vs. CON, and SCZ vs. BD; sample sizes of up to 269,867) were utilized.ResultsA strong bidirectional association between risks for SCZ and BD was observed (odds ratio; OR_SCZ → BD = 1.47, p = 2.89 × 10⁻⁴¹, OR_BD → SCZ = 1.44, p = 1.85 × 10⁻⁵²). Low intelligence was bidirectionally associated with a high risk for SCZ, with a stronger effect of intelligence on SCZ risk (OR_{lower intelligence → SCZ} = 1.62, p = 3.23 × 10⁻¹⁴) than the reverse (OR_{SCZ → lower intelligence} = 1.06, p = 3.70 × 10⁻²³). Furthermore, low intelligence affected a shared risk between SCZ and BD (OR _{lower intelligence → SCZ + BD} = 1.23, p = 3.41 × 10⁻⁵) and SCZ-specific risk (OR_{lower intelligence → SCZvsBD} = 1.64, p = 9.72 × 10⁻¹⁰); the shared risk (OR_{SCZ + BD → lower intelligence} = 1.04, p = 3.09 × 10⁻¹⁴) but not SCZ-specific risk (OR_{SCZvsBD → lower intelligence} = 1.00, p = 0.88) weakly affected low intelligence. Conversely, there was no significant causal association between intelligence and BD risk (p > 0.05).ConclusionsThese findings support observational studies showing that patients with SCZ display impairment in premorbid intelligence and intelligence decline. Moreover, a shared factor between SCZ and BD might contribute to impairment in premorbid intelligence and intelligence decline but SCZ-specific factors might be affected by impairment in premorbid intelligence. We suggest that patients with these genetic factors should be categorized as having a cognitive disorder SCZ or BD subtype.     

弓形虫感染与精神分裂症的两样本孟德尔随机化研究

目的 采用两样本孟德尔随机化方法探究弓形虫感染和精神分裂症之间的因果关系.方法 利用汇总的大样本GWAS数据提取与弓形虫血清抗体密切相关的遗传位点作为工具变量,分别运用MR-Egger回归、加权中位数和逆方差加权法进行孟德尔随机化分析,以OR值及95％CI评价弓形虫感染与精神分裂症之间是否存在关联.采用Egger-in...     

Mitochondrial DNA copy number and cancer risks: A comprehensive Mendelian randomization analysis

Mitochondrial DNA plays a critical role in the pathophysiology of cancer. However, the associations between mitochondrial DNA copy number (mtDNA-CN) and cancer risk are controversial. Mendelian randomization (MR) analyses were performed using three independent instrumental variables (IVs) to explore potential associations between mtDNA-CN and 20 types of cancer. The three sets of IVs were primarily obtained from participants in the UK Biobank and the Cohorts for Heart and Aging Research in Genomic Epidemiology consortium using different methods. The outcome data of cancers were investigated using summary statistics from the FinnGen cohort. The potential causal associations were evaluated using the MR-Egger regression, weighted median, inverse-variance weighted (IVW), and weighted mode methods. The robustness of IVW estimates was validated using leave-one-out sensitivity analysis. Additionally, a meta-analysis was conducted to pool results from three sets of IVs. The results revealed that genetically predicted mtDNA-CN was not associated with cancer risk (odds ratio = 1.02; 95% confidence interval: 0.95–1.10). Subgroup analyses indicated no causal association between mtDNA-CN and breast, lung, prostate, skin, colorectal, gastric, liver, cervical uteri, esophageal, thyroid, bladder, pancreas, kidney, corpus uteri, ovary, brain, larynx, and anus cancers. It was observed that mtDNA-CN was associated with lip, oral cavity, and testis cancers. However, these results should be interpreted with caution because a small number of patients with lip and oral cavity or testis cancers were included. The comprehensive MR analysis demonstrated that mtDNA-CN is not a suitable biomarker for tumor risk assessment.