Gender Influence on Statistics Anxiety among Graduate Students

The present study was conducted to further explore gender-based differences in the experience of statistics anxiety among graduate students. A sample of 75 graduate students from a mid-sized research university in the southeastern United States were recruited to participate in a survey concerning statistics anxiety. Data were analyzed using multivariate analysis of covariance and discriminant analysis. Using the Statistics Anxiety Rating Scale, students’ statistics anxiety was measured. After accounting for age, the findings revealed a significant gender difference in statistics anxiety. A significant covariate effect of age indicated that older graduate students reported experiencing higher levels of anxiety as compared to their younger peers. Age accounted for 21% of variance in the combined statistics anxiety subscales. Analysis further revealed that males experienced higher levels of anxiety when seeking statistics help from a fellow student or a professor than did females. Implications for the design of statistics courses are discussed.

A comparative study on the unified model based multifactor dimensionality reduction methods for identifying gene-gene interactions associated with the survival phenotype

Background For gene-gene interaction analysis, the multifactor dimensionality reduction (MDR) method has been widely employed to reduce multi-levels of gene-gene interactions into high- or low-risk groups using a binary attribute. For the survival phenotype, the Cox-MDR method has been proposed using a martingale residual of a Cox model since Surv-MDR was first proposed using a log-rank test statistic. Recently, the KM-MDR method was proposed using the Kaplan-Meier median survival time as a classifier. All three methods used the cross-validation procedure to identify single nucleotide polymorphism (SNP) using SNP interactions among all possible SNP pairs. Furthermore, these methods require the permutation test to verify the significance of the selected SNP pairs. However, the unified model-based multifactor dimensionality reduction method (UM-MDR) overcomes this shortcoming of MDR by unifying the significance testing with the MDR algorithm within the framework of the regression model. Neither cross-validation nor permutation testing is required to identify SNP by SNP interactions in the UM-MDR method. The UM-MDR method comprises two steps: in the first step, multi-level genotypes are classified into high- or low-risk groups, and an indicator variable for the high-risk group is defined. In the second step, the significance of the indicator variable of the high-risk group is tested in the regression model included with other adjusting covariates. The Cox-UMMDR method was recently proposed by combining Cox-MDR with UM-MDR to identify gene-gene interactions associated with the survival phenotype. In this study, we propose two simple methods either by combining KM-MDR with UM-MDR, called KM-UMMDR or by modifying Cox-UMMDR by adjusting for the covariate effect in step 1, rather than in step 2, a process called Cox2-UMMDR. The KM-UMMDR method allows the covariate effect to be adjusted for in the regression model of step 2, although KM-MDR cannot adjust for the covariate effect in the classification procedure of step 1. In contrast, Cox2-UMMDR differs from Cox-UMMDR in the sense that the martingale residuals are obtained from a Cox model by adjusting for the covariate effect in step 1 of Cox2-UMMDR whereas Cox-UMMDR adjusts for the covariate effect in the regression model in step 2. We performed simulation studies to compare the power of several methods such as KM-UMMDR, Cox-UMMDR, Cox2-UMMDR, Cox-MDR, and KM-MDR by considering the effect of covariates and the marginal effect of SNPs. We also analyzed a real example of Korean leukemia patient data for illustration and a short discussion is provided. Results In the simulation study, two different scenarios are considered: the first scenario compares the power of the cases with and without the covariate effect. The second scenario is to compare the power of cases with the main effect of SNPs versus without the main effect of SNPs. From the simulation results, Cox-UMMDR performs the best across all scenarios among KM-UMMDR, Cox2-UMMDR, Cox-MDR and KM-MDR. As expected, both Cox-UMMDR and Cox-MDR perform better than KM-UMMDR and KM-MDR when a covariate effect exists because the former adjusts for the covariate effect but the latter cannot. However, Cox2-UMMDR behaves similarly to KM-UMMDR and KM-MDR even though there is a covariate effect. This implies that the covariate effect would be more efficiently adjusted for in the regression model of the second step rather than under the classification procedure of the first step. When there is a main effect of any SNP, Cox-UMMDR, Cox2-UMMDR and KM-UMMDR perform better than Cox-MDR and KM-MDR if the main effects of SNPs are properly adjusted for in the regression model. From the simulation results of two different scenarios, Cox-UMMDR seems to be the most robust when there is either any covariate effect adjusting for or any SNP that has a main effect on the survival phenotype. In addition, the power of all methods decreased as the censoring fraction increased from 0.1 to 0.3, as heritability increased. The power of all methods seems to be greater under MAF = 0.2 than under MAF = 0.4. For illustration, both KM-UMMDR and Cox2-UMMDR were applied to identify SNP by SNP interactions with the survival phenotype to a real dataset of Korean leukemia patients. Conclusion Both KM-UMMDR and Cox2-UMMDR were easily implemented by combining KM-MDR and Cox-MDR with UM-MDR, respectively, to detect significant gene-gene interactions associated with survival time without cross-validation and permutation testing. The simulation results demonstrate the utility of KM-UMMDR, Cox2-UMMDR and Cox-UMMDR, which outperforms Cox-MDR and KM-MDR when some SNPs with only marginal effects might mask the detection of causal epistasis. In addition, Cox-UMMDR, Cox2-UMMDR and Cox-MDR performed better than KM-UMMDR and KM-MDR when there were potentially confounding covariate effects.

A comparative study on the unified model based multifactor dimensionality reduction methods for identifying gene-gene interactions associated with the survival phenotype

Background: For gene-gene interaction analysis, the multifactor dimensionality reduction (MDR) method has been widely employed to reduce multi-levels of gene-gene interactions into high- or low-risk groups using a binary attribute. For the survival phenotype, the Cox-MDR method has been proposed using a martingale residual of a Cox model since Surv-MDR was first proposed using a log-rank test statistic. Recently, the KM-MDR method was proposed using the Kaplan-Meier median survival time as a classifier. All three methods used the cross-validation procedure to identify single nucleotide polymorphism (SNP) using SNP interactions among all possible SNP pairs. Furthermore, these methods require the permutation test to verify the significance of the selected SNP pairs. However, the unified model-based multifactor dimensionality reduction method (UM-MDR) overcomes this shortcoming of MDR by unifying the significance testing with the MDR algorithm within the framework of the regression model. Neither cross-validation nor permutation testing is required to identify SNP by SNP interactions in the UM-MDR method. The UM-MDR method comprises two steps: in the first step, multi-level genotypes are classified into high- or low-risk groups, and an indicator variable for the high-risk group is defined. In the second step, the significance of the indicator variable of the high-risk group is tested in the regression model included with other adjusting covariates. The Cox-UMMDR method was recently proposed by combining Cox-MDR with UM-MDR to identify gene-gene interactions associated with the survival phenotype. In this study, we propose two simple methods either by combining KM-MDR with UM-MDR, called KM-UMMDR or by modifying Cox-UMMDR by adjusting for the covariate effect in step 1, rather than in step 2, a process called Cox2-UMMDR. The KM-UMMDR method allows the covariate effect to be adjusted for in the regression model of step 2, although KM-MDR cannot adjust for the covariate effect in the classification procedure of step 1. In contrast, Cox2-UMMDR differs from Cox-UMMDR in the sense that the martingale residuals are obtained from a Cox model by adjusting for the covariate effect in step 1 of Cox2-UMMDR whereas Cox-UMMDR adjusts for the covariate effect in the regression model in step 2. We performed simulation studies to compare the power of several methods such as KM-UMMDR, Cox-UMMDR, Cox2-UMMDR, Cox-MDR, and KM-MDR by considering the effect of covariates and the marginal effect of SNPs. We also analyzed a real example of Korean leukemia patient data for illustration and a short discussion is provided.Results: In the simulation study, two different scenarios are considered: the first scenario compares the power of the cases with and without the covariate effect. The second scenario is to compare the power of cases with the main effect of SNPs versus without the main effect of SNPs. From the simulation results, Cox-UMMDR performs the best across all scenarios among KM-UMMDR, Cox2-UMMDR, Cox-MDR and KM-MDR. As expected, both Cox-UMMDR and Cox-MDR perform better than KM-UMMDR and KM-MDR when a covariate effect exists because the former adjusts for the covariate effect but the latter cannot. However, Cox2-UMMDR behaves similarly to KM-UMMDR and KM-MDR even though there is a covariate effect. This implies that the covariate effect would be more efficiently adjusted for in the regression model of the second step rather than under the classification procedure of the first step. When there is a main effect of any SNP, Cox-UMMDR, Cox2-UMMDR and KM-UMMDR perform better than Cox-MDR and KM-MDR if the main effects of SNPs are properly adjusted for in the regression model. From the simulation results of two different scenarios, Cox-UMMDR seems to be the most robust when there is either any covariate effect adjusting for or any SNP that has a main effect on the survival phenotype. In addition, the power of all methods decreased as the censoring fraction increased from 0.1 to 0.3, as heritability increased. The power of all methods seems to be greater under MAF = 0.2 than under MAF = 0.4. For illustration, both KM-UMMDR and Cox2-UMMDR were applied to identify SNP by SNP interactions with the survival phenotype to a real dataset of Korean leukemia patients.Conclusion: Both KM-UMMDR and Cox2-UMMDR were easily implemented by combining KM-MDR and Cox-MDR with UM-MDR, respectively, to detect significant gene-gene interactions associated with survival time without cross-validation and permutation testing. The simulation results demonstrate the utility of KM-UMMDR, Cox2-UMMDR and Cox-UMMDR, which outperforms Cox-MDR and KM-MDR when some SNPs with only marginal effects might mask the detection of causal epistasis. In addition, Cox-UMMDR, Cox2-UMMDR and Cox-MDR performed better than KM-UMMDR and KM-MDR when there were potentially confounding covariate effects.

A comparative study on the unified model based multifactor dimensionality reduction methods for identifying gene-gene interactions associated with the survival phenotype

BackgroundFor gene-gene interaction analysis, the multifactor dimensionality reduction (MDR) method has been widely employed to reduce multi-levels of gene-gene interactions into high- or low-risk groups using a binary attribute. For the survival phenotype, the Cox-MDR method has been proposed using a martingale residual of a Cox model since Surv-MDR was first proposed using a log-rank test statistic. Recently, the KM-MDR method was proposed using the Kaplan-Meier median survival time as a classifier. All three methods used the cross-validation procedure to identify single nucleotide polymorphism (SNP) using SNP interactions among all possible SNP pairs. Furthermore, these methods require the permutation test to verify the significance of the selected SNP pairs. However, the unified model-based multifactor dimensionality reduction method (UM-MDR) overcomes this shortcoming of MDR by unifying the significance testing with the MDR algorithm within the framework of the regression model. Neither cross-validation nor permutation testing is required to identify SNP by SNP interactions in the UM-MDR method. The UM-MDR method comprises two steps: in the first step, multi-level genotypes are classified into high- or low-risk groups, and an indicator variable for the high-risk group is defined. In the second step, the significance of the indicator variable of the high-risk group is tested in the regression model included with other adjusting covariates. The Cox-UMMDR method was recently proposed by combining Cox-MDR with UM-MDR to identify gene-gene interactions associated with the survival phenotype. In this study, we propose two simple methods either by combining KM-MDR with UM-MDR, called KM-UMMDR or by modifying Cox-UMMDR by adjusting for the covariate effect in step 1, rather than in step 2, a process called Cox2-UMMDR. The KM-UMMDR method allows the covariate effect to be adjusted for in the regression model of step 2, although KM-MDR cannot adjust for the covariate effect in the classification procedure of step 1. In contrast, Cox2-UMMDR differs from Cox-UMMDR in the sense that the martingale residuals are obtained from a Cox model by adjusting for the covariate effect in step 1 of Cox2-UMMDR whereas Cox-UMMDR adjusts for the covariate effect in the regression model in step 2. We performed simulation studies to compare the power of several methods such as KM-UMMDR, Cox-UMMDR, Cox2-UMMDR, Cox-MDR, and KM-MDR by considering the effect of covariates and the marginal effect of SNPs. We also analyzed a real example of Korean leukemia patient data for illustration and a short discussion is provided.ResultsIn the simulation study, two different scenarios are considered: the first scenario compares the power of the cases with and without the covariate effect. The second scenario is to compare the power of cases with the main effect of SNPs versus without the main effect of SNPs. From the simulation results, Cox-UMMDR performs the best across all scenarios among KM-UMMDR, Cox2-UMMDR, Cox-MDR and KM-MDR. As expected, both Cox-UMMDR and Cox-MDR perform better than KM-UMMDR and KM-MDR when a covariate effect exists because the former adjusts for the covariate effect but the latter cannot. However, Cox2-UMMDR behaves similarly to KM-UMMDR and KM-MDR even though there is a covariate effect. This implies that the covariate effect would be more efficiently adjusted for in the regression model of the second step rather than under the classification procedure of the first step. When there is a main effect of any SNP, Cox-UMMDR, Cox2-UMMDR and KM-UMMDR perform better than Cox-MDR and KM-MDR if the main effects of SNPs are properly adjusted for in the regression model. From the simulation results of two different scenarios, Cox-UMMDR seems to be the most robust when there is either any covariate effect adjusting for or any SNP that has a main effect on the survival phenotype. In addition, the power of all methods decreased as the censoring fraction increased from 0.1 to 0.3, but increased as heritability increased. The power of all methods seems to be greater under MAF = 0.2 than under MAF = 0.4. For illustration, both KM-UMMDR and Cox2-UMMDR were applied to identify SNP by SNP interactions with the survival phenotype to a real dataset of Korean leukemia patients.ConclusionBoth KM-UMMDR and Cox2-UMMDR were easily implemented by combining KM-MDR and Cox-MDR with UM-MDR, respectively, to detect significant gene-gene interactions associated with survival time without cross-validation and permutation testing. The intensive simulation results demonstrate the utility of KM-UMMDR, Cox2-UMMDR and Cox-UMMDR, which outperforms Cox-MDR and KM-MDR when some SNPs with only marginal effects might mask the detection of causal epistasis. In addition, Cox-UMMDR, Cox2-UMMDR and Cox-MDR performed better than KM-UMMDR and KM-MDR when there were potentially confounding covariate effects.

Definition and Estimation of Covariate Effect Types in the Context of Treatment Effectiveness

In some clinical studies, assessing covariate effect types indicating whether a covariate is predictive and/or prognostic is of interest, in addition to the study endpoint. Recently, for a case with a binary outcome, Chiba (Clinical Trials, 2019; 16: 237–245) proposed the new concept of covariate effect type, which is assessed in terms of four response types, and showed that standard subgroup or regression analysis is applicable only in certain cases. Although this concept could be useful for supplementing conventional standard analysis, its application is limited to cases with a binary outcome. In this article, we aim to generalize Chiba’s concept to continuous and time-to-event outcomes. We define covariate effect types based on four response types. It is difficult to estimate the response types from the observed data without making certain assumptions, so we propose a simple method to estimate them under the assumption of independent potential outcomes. Our approach is illustrated using data from a clinical study with a time-to-event outcome.

Testing Measurement Invariance Across Unobserved Groups: The Role of Covariates in Factor Mixture Modeling

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration was investigated via Monte Carlo simulations. Data were generated based on FMM models with (1) a zero covariate effect, (2) a covariate effect on the latent class variable, and (3) covariate effects on both the latent class variable and the factor. For each population model, different analysis models that excluded or misspecified covariate effects were fitted. Results highlighted the importance of including proper covariates in measurement invariance testing and evidenced the utility of a model comparison approach in searching for the correct specification of covariate effects and the level of measurement invariance. This approach was demonstrated using an empirical data set. Implications for methodological and applied research are discussed.

Survival analysis with change-points in covariate effects

We apply a maximal likelihood ratio test for the presence of multiple change-points in the covariate effects based on the Cox regression model. The covariate effect is assumed to change smoothly at one or more unknown change-points. The number of change-points is inferred by a sequential approach. Confidence intervals for the regression and change-point parameters are constructed by a bootstrap method based on Bernstein polynomials conditionally on the number of change-points. The methods are assessed by simulations and are applied to two datasets.

Exposure-Response and Clinical Outcome Modeling of Inhaled Budesonide/Formoterol Combination in Asthma Patients

Exposure-response and clinical outcome (CO) model for inhaled budesonide/formoterol was developed to quantify the relationship among pharmacokinetics (PK), pharmacodynamics (PD) and CO of the drugs and evaluate the covariate effect on model parameters. Sputum eosinophils cationic proteins (ECP) and forced expiratory volume (FEV1) were selected as PD markers and asthma control score was used as a clinical outcome. One- and two-compartment models were used to describe the PK of budesonide and formoterol, respectively. The indirect response model (IDR) was used to describe the PD effect for ECP and FEV1. In addition, the symptomatic effect on the disease progression model for CO was connected with IDR on each PD response. The slope for the effect of ECP and FEV1 to disease progression were estimated as 0.00008 and 0.644, respectively. Total five covariates (ex. ADRB2 genotype etc.) were searched using a stepwise covariate modeling method, however, there was no significant covariate effect. The results from the simulation study were showed that a 1 puff b.i.d. had a comparable effect of asthma control with a 2 puff b.i.d. As a result, the 1 puff b.i.d. of combination drug could be suggested as a standardized dose to minimize the side effects and obtain desired control of disease compared to the 2 puff b.i.d.