Simple Algorithms to Calculate Asymptotic Null Distributions of Robust Tests in Case-Control Genetic Association Studies in R

The case-control study is an important design for testing association between genetic markers and a disease. The Cochran-Armitage trend test (CATT) is one of the most commonly used statistics for the analysis of case-control genetic association studies. The asymptotically optimal CATT can be used when the underlying genetic model (mode of inheritance) is known. However, for most complex diseases, the underlying genetic models are unknown. Thus, tests robust to genetic model misspecification are preferable to the model-dependant CATT. Two robust tests, MAX3 and the genetic model selection (GMS), were recently proposed. Their asymptotic null distributions are often obtained by Monte-Carlo simulations, because they either have not been fully studied or involve multiple integrations. In this article, we study how components of each robust statistic are correlated, and find a linear dependence among the components. Using this new finding, we propose simple algorithms to calculate asymptotic null distributions for MAX3 and GMS, which greatly reduce the computing intensity. Furthermore, we have developed the R package Rassoc implementing the proposed algorithms to calculate the empirical and asymptotic p values for MAX3 and GMS as well as other commonly used tests in case-control association studies. For illustration, Rassoc is applied to the analysis of case-control data of 17 most significant SNPs reported in four genome-wide association studies.

Optimal sequential enrichment designs for phase II clinical trials

In the early phase development of molecularly targeted agents (MTAs), a commonly encountered situation is that the MTA is expected to be more effective for a certain biomarker subgroup, say marker-positive patients, but there is no adequate evidence to show that the MTA does not work for the other subgroup, that is, marker-negative patients. After establishing that marker-positive patients benefit from the treatment, it is often of great clinical interest to determine whether the treatment benefit extends to marker-negative patients. The authors propose optimal sequential enrichment (OSE) designs to address this practical issue in the context of phase II clinical trials. The OSE designs evaluate the treatment effect first in marker-positive patients and then in marker-negative patients if needed. The designs are optimal in the sense that they minimize the expected sample size or the maximum sample size under the null hypothesis that the MTA is futile. An efficient, accurate optimization algorithm is proposed to find the optimal design parameters. One important advantage of the OSE design is that the go/no-go interim decision rules are specified prior to the trial conduct, which makes the design particularly easy to use in practice. A simulation study shows that the OSE designs perform well and are ethically more desirable than the commonly used marker-stratified design. The OSE design is applied to an endometrial carcinoma trial

A Bayesian adaptive marker‐stratified design for molecularly targeted agents with customized hierarchical modeling

It is well known that the treatment effect of a molecularly targeted agent (MTA) may vary dramatically, depending on each patient's biomarker profile. Therefore, for a clinical trial evaluating MTA, it is more reasonable to evaluate its treatment effect within different marker subgroups rather than evaluating the average treatment effect for the overall population. The marker‐stratified design (MSD) provides a useful tool to evaluate the subgroup treatment effects of MTAs. Under the Bayesian framework, the beta‐binomial model is conventionally used under the MSD to estimate the response rate and test the hypothesis. However, this conventional model ignores the fact that the biomarker used in the MSD is, in general, predictive only for the MTA. The response rates for the standard treatment can be approximately consistent across different subgroups stratified by the biomarker. In this paper, we proposed a Bayesian hierarchical model incorporating this biomarker information into consideration. The proposed model uses a hierarchical prior to borrow strength across different subgroups of patients receiving the standard treatment and, therefore, improve the efficiency of the design. Prior informativeness is determined by solving a “customized” equation reflecting the physician's professional opinion. We developed a Bayesian adaptive design based on the proposed hierarchical model to guide the treatment allocation and test the subgroup treatment effect as well as the predictive marker effect. Simulation studies and a real trial application demonstrate that the proposed design yields desirable operating characteristics and outperforms the existing designs

A Bayesian adaptive phase II clinical trial design accounting for spatial variation

Conventional phase II clinical trials evaluate the treatment effects under the assumption of patient homogeneity. However, due to inter-patient heterogeneity, the effect of a treatment may differ remarkably among subgroups of patients. Besides patient’s individual characteristics such as age, gender, and biomarker status, a substantial amount of this heterogeneity could be due to the spatial variation across geographic regions because of unmeasured or unknown spatially varying environmental and social exposures. In this article, we propose a hierarchical Bayesian adaptive design for two-arm randomized phase II clinical trials that accounts for the spatial variation as well as patient’s individual characteristics. We treat the treatment efficacy as an ordinal outcome and quantify the desirability of each possible category of the ordinal efficacy using a utility function. A cumulative probit mixed model is used to relate efficacy to patient-specific covariates and geographic region spatial effects. Spatial dependence between regions is induced through the conditional autoregressive priors on the spatial effects. A two-stage design is proposed to adaptively assign patients to desirable treatments according to each patient’s spatial information and individual covariates and make treatment recommendations at the end of the trial based on the overall treatment effect. Simulation studies show that our proposed design has good operating characteristics and significantly outperforms an alternative phase II trial design that ignores the spatial variation

A robust two-stage design identifying the optimal biological dose for phase I/II clinical trials

We propose a robust two-stage design to identify the optimal biological dose for phase I/II clinical trials evaluating both toxicity and efficacy outcomes. In the first stage of dose finding, we use the Bayesian model averaging continual reassessment method to monitor the toxicity outcomes and adopt an isotonic regression method based on the efficacy outcomes to guide dose escalation. When the first stage ends, we use the Dirichlet-multinomial distribution to jointly model the toxicity and efficacy outcomes and pick the candidate doses based on a three-dimensional volume ratio. The selected candidate doses are then seamlessly advanced to the second stage for dose validation. Both toxicity and efficacy outcomes are continuously monitored so that any overly toxic and/or less efficacious dose can be dropped from the study as the trial continues. When the phase I/II trial ends, we select the optimal biological dose as the dose obtaining the minimal value of the volume ratio within the candidate set. An advantage of the proposed design is that it does not impose a monotonically increasing assumption on the shape of the dose-efficacy curve. We conduct extensive simulation studies to examine the operating characteristics of the proposed design. The simulation results show that the proposed design has desirable operating characteristics across different shapes of the underlying true dose-toxicity and dose-efficacy curves. The software to implement the proposed design is available upon request

Robust tests for matched case-control genetic association studies

<p>Abstract</p> <p>Background</p> <p>The Cochran-Armitage trend test (CATT) is powerful in detecting association between a susceptible marker and a disease. This test, however, may suffer from a substantial loss of power when the underlying genetic model is unknown and incorrectly specified. Thus, it is useful to derive tests obtaining the plausible power against all common genetic models. For this purpose, the genetic model selection (GMS) and genetic model exclusion (GME) methods were proposed recently. Simulation results showed that GMS and GME can obtain the plausible power against three common genetic models while the overall type I error is well controlled.</p> <p>Results</p> <p>Although GMS and GME are powerful statistically, they could be seriously affected by known confounding factors such as gender, age and race. Therefore, in this paper, via comparing the difference of Hardy-Weinberg disequilibrium coefficients between the cases and the controls within each sub-population, we propose the stratified genetic model selection (SGMS) and exclusion (SGME) methods which could eliminate the effect of confounding factors by adopting a matching framework. Our goal in this paper is to investigate the robustness of the proposed statistics and compare them with other commonly used efficiency robust tests such as MAX3 and <it>χ</it>²with 2 degrees of freedom (df) test in matched case-control association designs through simulation studies.</p> <p>Conclusion</p> <p>Simulation results showed that if the mean genetic effect of the heterozygous genotype is between those of the two homozygous genotypes, then the proposed tests and MAX3 are preferred. Otherwise, <it>χ</it>²with 2 df test may be used. To illustrate the robust procedures, the proposed tests are applied to a real matched pair case-control etiologic study of sarcoidosis.</p

Effect of rolling process parameters on stability of rolling mill vibration with nonlinear friction

Friction-induced vibration is a typical self-excited phenomenon in the rolling process. Since its important industrial relevance, a rolling mill vertical-torsional-horizontal coupled vibration model with the consideration of the nonlinear friction has been established by coupling the dynamic rolling process model and the rolling mill structural model. Based on this model, the system stability domain is determined according to Hurwitz algebraic criterion. Subsequently, the Hopf bifurcation types at different bifurcation points are judged. Finally, the influences of rolling process parameters on the system stability domain are analyzed in detail. The results show that the critical boundaries of vertical vibration modal, horizontal vibration modal and torsional vibration modal will move with the change of rolling process parameters, and the system stability domain will change simultaneously. Among the parameters, the reduction ratio has the most significant effect on the stability of the system. And when rolling the thin strip, the system stability domain may be only enclosed by the critical boundaries of vertical vibration modal and torsional vibration modal. In that case, the system instability induced by horizontal vibration modal would not occur. The study is helpful for proposing a reasonable rolling process planning to reduce the possibility of vibration, as well as selecting an optimal rolling process parameter to design a controller to control the rolling mill vibration

Simple Algorithms to Calculate Asymptotic Null Distributions of Robust Tests in Case-Control Genetic Association Studies in R

The case-control study is an important design for testing association between genetic markers and a disease. The Cochran-Armitage trend test (CATT) is one of the most commonly used statistics for the analysis of case-control genetic association studies. The asymptotically optimal CATT can be used when the underlying genetic model (mode of inheritance) is known. However, for most complex diseases, the underlying genetic models are unknown. Thus, tests robust to genetic model misspecification are preferable to the model-dependant CATT. Two robust tests, MAX3 and the genetic model selection (GMS), were recently proposed. Their asymptotic null distributions are often obtained by Monte-Carlo simulations, because they either have not been fully studied or involve multiple integrations. In this article, we study how components of each robust statistic are correlated, and find a linear dependence among the components. Using this new finding, we propose simple algorithms to calculate asymptotic null distributions for MAX3 and GMS, which greatly reduce the computing intensity. Furthermore, we have developed the R package <b>Rassoc</b> implementing the proposed algorithms to calculate the empirical and asymptotic <i>p</i> values for MAX3 and GMS as well as other commonly used tests in case-control association studies. For illustration, <b>Rassoc</b> is applied to the analysis of case-control data of 17 most significant SNPs reported in four genome-wide association studies

9,9-Dimethyl-12-phenyl-8,9-dihydro-12H-benzo[a]xanthen-11(10H)-one

The title compound, C25H22O2, was synthesized via the three-component coupling of benzaldehyde, 2-naphthol and 5,5-dimethyl­cyclo­hexane-1,3-dione. In the crystal structure, centrosymmetrically related mol­ecules are linked into dimers by pairs of inter­molecular C—H⋯O hydrogen bonds. The dimers are further connected into a three-dimensional network by π–π aromatic stacking inter­actions involving the naphthalene ring system, with centroid–centroid separations of 3.695 (7) Å

Rolling mill chatter mechanism based on the unsteady lubrication performance

The unsteady lubrication is one of the major causes for self-excited vibration in rolling. But it is difficult to build a rolling chatter model which considers the unsteady lubrication state in roll bite. Using the regression exponential function model of rolling friction coefficient, a dynamic rolling process model was built. Coupling the dynamic rolling process model with a mill stand structure model, a chatter model which considers the unsteady lubrication state at roll bite was established. Based on the proposed chatter model, the friction coefficient, rolling force and critical velocity of a rolling mill stand under different working conditions were calculated. The computed results were compared to the test results. And it proves the validity of the proposed model. With the proposed chatter model, the effects of rolling process parameters and emulsion lubricant characteristic parameters on friction coefficient and critical velocity were both analyzed and discussed. The chatter model successfully introduces the unsteady friction model into the rolling mill chatter model. It better explains the negative damping effect of the rolling chatter and reflects the rolling mill dynamic vibration characteristic