Effect of nonnormal random components on level and power in group-randomized trials

The use of group-randomized trials is particularly widespread in the evaluation of health care, educational, and screening strategies. Group-randomized trials represent a subset of a larger class of designs often labeled nested, hierarchical, or multilevel and are characterized by the randomization of intact social units or groups, rather than individuals. The application of random effects models to group-randomized trials requires the specification of fixed and random components of the model. The underlying assumption is usually that these random components are normally distributed. This research is intended to determine if the Type I error rate and power are affected when the assumption of normality for the random component representing the group effect is violated. ^ In this study, simulated data are used to examine the Type I error rate, power, bias and mean squared error of the estimates of the fixed effect and the observed intraclass correlation coefficient (ICC) when the random component representing the group effect possess distributions with non-normal characteristics, such as heavy tails or severe skewness. The simulated data are generated with various characteristics (e.g. number of schools per condition, number of students per school, and several within school ICCs) observed in most small, school-based, group-randomized trials. The analysis is carried out using SAS PROC MIXED, Version 6.12, with random effects specified in a random statement and restricted maximum likelihood (REML) estimation specified. The results from the non-normally distributed data are compared to the results obtained from the analysis of data with similar design characteristics but normally distributed random effects. ^ The results suggest that the violation of the normality assumption for the group component by a skewed or heavy-tailed distribution does not appear to influence the estimation of the fixed effect, Type I error, and power. Negative biases were detected when estimating the sample ICC and dramatically increased in magnitude as the true ICC increased. These biases were not as pronounced when the true ICC was within the range observed in most group-randomized trials (i.e. 0.00 to 0.05). The normally distributed group effect also resulted in bias ICC estimates when the true ICC was greater than 0.05. However, this may be a result of higher correlation within the data. ^

Change Detection Memory in Rhesus Monkeys and Humans

Visual short-term memory (VSTM) is the storage of visual information over a brief time period (usually a few seconds or less). Over the past decade, the most popular task for studying VSTM in humans has been the change detection task. In this task, subjects must remember several visual items per trial in order to identify a change following a brief delay interval. Results from change detection tasks have shown that VSTM is limited; humans are only able to accurately hold a few visual items in mind over a brief delay. However, there has been much debate in regard to the structure or cause of these limitations. The two most popular conceptualizations of VSTM limitations in recent years have been the fixed-capacity model and the continuous-resource model. The fixed-capacity model proposes a discrete limit on the total number of visual items that can be stored in VSTM. The continuous-resource model proposes a continuous-resource that can be allocated among many visual items in VSTM, with noise in item memory increasing as the number of items to be remembered increases. While VSTM is far from being completely understood in humans, even less is known about VSTM in non-human animals, including the rhesus monkey (Macaca mulatta). Given that rhesus monkeys are the premier medical model for humans, it is important to understand their VSTM if they are to contribute to understanding human memory. The primary goals of this study were to train and test rhesus monkeys and humans in change detection in order to directly compare VSTM between the two species and explore the possibility that direct species comparison might shed light on the fixed-capacity vs. continuous-resource models of VSTM. The comparative results suggest qualitatively similar VSTM for the two species through converging evidence supporting the continuous-resource model and thereby establish rhesus monkeys as a good system for exploring neurophysiological correlates of VSTM.

Bayesian joint modeling of longitudinal and survival data

The joint modeling of longitudinal and survival data is a new approach to many applications such as HIV, cancer vaccine trials and quality of life studies. There are recent developments of the methodologies with respect to each of the components of the joint model as well as statistical processes that link them together. Among these, second order polynomial random effect models and linear mixed effects models are the most commonly used for the longitudinal trajectory function. In this study, we first relax the parametric constraints for polynomial random effect models by using Dirichlet process priors, then three longitudinal markers rather than only one marker are considered in one joint model. Second, we use a linear mixed effect model for the longitudinal process in a joint model analyzing the three markers. In this research these methods were applied to the Primary Biliary Cirrhosis sequential data, which were collected from a clinical trial of primary biliary cirrhosis (PBC) of the liver. This trial was conducted between 1974 and 1984 at the Mayo Clinic. The effects of three longitudinal markers (1) Total Serum Bilirubin, (2) Serum Albumin and (3) Serum Glutamic-Oxaloacetic transaminase (SGOT) on patients' survival were investigated. Proportion of treatment effect will also be studied using the proposed joint modeling approaches. ^ Based on the results, we conclude that the proposed modeling approaches yield better fit to the data and give less biased parameter estimates for these trajectory functions than previous methods. Model fit is also improved after considering three longitudinal markers instead of one marker only. The results from analysis of proportion of treatment effects from these joint models indicate same conclusion as that from the final model of Fleming and Harrington (1991), which is Bilirubin and Albumin together has stronger impact in predicting patients' survival and as a surrogate endpoints for treatment. ^

The determinants of improvements in health outcomes and of cost reduction in hospital inpatient care

This study aims to address two research questions. First, ‘Can we identify factors that are determinants both of improved health outcomes and of reduced costs for hospitalized patients with one of six common diagnoses?’ Second, ‘Can we identify other factors that are determinants of improved health outcomes for such hospitalized patients but which are not associated with costs?’ The Healthcare Cost and Utilization Project (HCUP) Nationwide Inpatient Sample (NIS) database from 2003 to 2006 was employed in this study. The total study sample consisted of hospitals which had at least 30 patients each year for the given diagnosis: 954 hospitals for acute myocardial infarction (AMI), 1552 hospitals for congestive heart failure (CHF), 1120 hospitals for stroke (STR), 1283 hospitals for gastrointestinal hemorrhage (GIH), 979 hospitals for hip fracture (HIP), and 1716 hospitals for pneumonia (PNE). This study used simultaneous equations models to investigate the determinants of improvement in health outcomes and of cost reduction in hospital inpatient care for these six common diagnoses. In addition, the study used instrumental variables and two-stage least squares random effect model for unbalanced panel data estimation. The study concluded that a few factors were determinants of high quality and low cost. Specifically, high specialty was the determinant of high quality and low costs for CHF patients; small hospital size was the determinant of high quality and low costs for AMI patients. Furthermore, CHF patients who were treated in Midwest, South, and West region hospitals had better health outcomes and lower hospital costs than patients who were treated in Northeast region hospitals. Gastrointestinal hemorrhage and pneumonia patients who were treated in South region hospitals also had better health outcomes and lower hospital costs than patients who were treated in Northeast region hospitals. This study found that six non-cost factors were related to health outcomes for a few diagnoses: hospital volume, percentage emergency room admissions for a given diagnosis, hospital competition, specialty, bed size, and hospital region.^

Effect of a lifestyle physical activity intervention on transtheoretical model variables

Purpose. To determine the effect a stage-based, lifestyle physical activity intervention has on Transtheoretical Model variables in a population of breast cancer survivors. ^ Methods. Sedentary breast cancer survivors (N=60) were randomized to either a standard care study condition or to a 6-month, 21-session intervention. The Transtheoretical Model variables stage of change, self-efficacy, decisional balance (pros and cons to exercise), and processes of change were measured at baseline, 3 months, and 6 months. ^ Results. Women in the lifestyle group had significantly higher self-efficacy than women in the standard care group (F=9.55, p=0.003). Although there was not a significant difference between the two groups for perceived pros of exercise, there was a significant difference between the groups for perceived cons of exercise. Women in the lifestyle group perceived significantly fewer cons of exercise at both 3 and 6 months compared with women in the standard care condition (F=5.416, p=0.025). Between baseline and the 6 month assessment, the intervention also had an effect on three of the processes of change, while seven of the processes were not significantly affected by the intervention. ^ Conclusions. Data from the pilot study suggest that a stage-based, lifestyle physical activity intervention has an effect on Transtheoretical Model variables, which have been shown to facilitate exercise adoption, and should be tested in a larger trial. ^

The effect of African Americans' ethnographic paradigms and cultural explanatory model of breast cancer in framing the male partner's attitudes and behaviors about the woman's breast cancer diagnosis

The disparate burden of breast cancer-related morbidity and mortality experienced by African American women compared with women of other races is a topic of intense debate in the medical and public health arenas. The anomaly is consistently attributed to the fact that at diagnosis, a large proportion of African American women have advanced-stage disease. Extensive research has documented the impacts of cultural factors and of socioeconomic factors in shaping African American women's breast-health practices; however, there is another factor of a more subtle influence that might have some role in establishing these women's vulnerability to this disease: the lack of or perceived lack of partner support. Themes expressed in the research literature reflect that many African American breast cancer patients and survivors consider their male partners as being apathetic and nonsupportive. ^ The purpose of this study was to learn how African American couples' ethnographic paradigms and cultural explanatory model of breast cancer frame the male partners' responses to the women's diagnosis and to assess his ability to cope and willingness to adapt to the subsequent challenges. The goal of the study was to determine whether these men's coping and adaptation skills positively or negatively affect the women's self-care attitudes and behaviors. ^ This study involved 4 African American couples in which the woman was a breast cancer survivor. Participants were recruited through a community-based cancer support group and a church-based cancer support group. Recruitment sessions were held at regular meetings of these organizations. Accrual took 2 months. In separate sessions, each male partner and each survivor completed a demographic survey and a questionnaire and were interviewed. Additionally, the couples were asked to participate in a communications activity (Adinkra). This activity was not done to fulfill any part of the study purpose and was not included in the data analysis; rather, it was done to assess its potential use as an intervention to promote dialogue between African American partners about the experience of breast cancer. ^ The questionnaire was analyzed on the basis of a coding schema and the interview responses were analyzed on the principles of hermeneutic phenomenology. In both cases, the instruments were used to determine whether the partner's coping skills reflected a compassionate attitude (positive response) versus an apathetic attitude (negative response) and whether his adaptation skills reflected supportive behaviors (the positive response) versus nonsupportive behaviors (the negative response). Overall, the women's responses showed that they perceived of their partners as being compassionate, yet nonsupportive, and the partner's perceived of themselves likewise. Only half of the women said that their partners' coping and adaptation abilities enabled them to relinquish traditional concepts of control and focus on their own well-being. ^ The themes that emerged indicate that African American men's attitudes and behaviors regarding his female partner's diagnosis of breast cancer and his ability to cope and willingness to adapt are influenced by their ritualistic mantras, folk beliefs, religious teachings/spiritual values, existential ideologies, socioeconomic status, and environmental factors and by their established perceptions of what causes breast cancer, what the treatments and outcomes are, and how the disease affects the entire family, particularly him. These findings imply that a culturally specific intervention might be useful in educating African American men about breast cancer and their roles in supporting their female partners, physically and psychologically, during diagnosis, treatment, and recovery. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

Application of the general linear model to assess the effect of missing data on bone marrow mononuclear cell therapy with infusion timing and follow-up MRI

With most clinical trials, missing data presents a statistical problem in evaluating a treatment's efficacy. There are many methods commonly used to assess missing data; however, these methods leave room for bias to enter the study. This thesis was a secondary analysis on data taken from TIME, a phase 2 randomized clinical trial conducted to evaluate the safety and effect of the administration timing of bone marrow mononuclear cells (BMMNC) for subjects with acute myocardial infarction (AMI).^ We evaluated the effect of missing data by comparing the variance inflation factor (VIF) of the effect of therapy between all subjects and only subjects with complete data. Through the general linear model, an unbiased solution was made for the VIF of the treatment's efficacy using the weighted least squares method to incorporate missing data. Two groups were identified from the TIME data: 1) all subjects and 2) subjects with complete data (baseline and follow-up measurements). After the general solution was found for the VIF, it was migrated Excel 2010 to evaluate data from TIME. The resulting numerical value from the two groups was compared to assess the effect of missing data.^ The VIF values from the TIME study were considerably less in the group with missing data. By design, we varied the correlation factor in order to evaluate the VIFs of both groups. As the correlation factor increased, the VIF values increased at a faster rate in the group with only complete data. Furthermore, while varying the correlation factor, the number of subjects with missing data was also varied to see how missing data affects the VIF. When subjects with only baseline data was increased, we saw a significant rate increase in VIF values in the group with only complete data while the group with missing data saw a steady and consistent increase in the VIF. The same was seen when we varied the group with follow-up only data. This essentially showed that the VIFs steadily increased when missing data is not ignored. When missing data is ignored as with our comparison group, the VIF values sharply increase as correlation increases.^

Robust effect sizes and their confidence intervals for group difference between trajectories in hierarchical linear growth model

Hierarchical linear growth model (HLGM), as a flexible and powerful analytic method, has played an increased important role in psychology, public health and medical sciences in recent decades. Mostly, researchers who conduct HLGM are interested in the treatment effect on individual trajectories, which can be indicated by the cross-level interaction effects. However, the statistical hypothesis test for the effect of cross-level interaction in HLGM only show us whether there is a significant group difference in the average rate of change, rate of acceleration or higher polynomial effect; it fails to convey information about the magnitude of the difference between the group trajectories at specific time point. Thus, reporting and interpreting effect sizes have been increased emphases in HLGM in recent years, due to the limitations and increased criticisms for statistical hypothesis testing. However, most researchers fail to report these model-implied effect sizes for group trajectories comparison and their corresponding confidence intervals in HLGM analysis, since lack of appropriate and standard functions to estimate effect sizes associated with the model-implied difference between grouping trajectories in HLGM, and also lack of computing packages in the popular statistical software to automatically calculate them. ^ The present project is the first to establish the appropriate computing functions to assess the standard difference between grouping trajectories in HLGM. We proposed the two functions to estimate effect sizes on model-based grouping trajectories difference at specific time, we also suggested the robust effect sizes to reduce the bias of estimated effect sizes. Then, we applied the proposed functions to estimate the population effect sizes (d ) and robust effect sizes (du) on the cross-level interaction in HLGM by using the three simulated datasets, and also we compared the three methods of constructing confidence intervals around d and du recommended the best one for application. At the end, we constructed 95% confidence intervals with the suitable method for the effect sizes what we obtained with the three simulated datasets. ^ The effect sizes between grouping trajectories for the three simulated longitudinal datasets indicated that even though the statistical hypothesis test shows no significant difference between grouping trajectories, effect sizes between these grouping trajectories can still be large at some time points. Therefore, effect sizes between grouping trajectories in HLGM analysis provide us additional and meaningful information to assess group effect on individual trajectories. In addition, we also compared the three methods to construct 95% confident intervals around corresponding effect sizes in this project, which handled with the uncertainty of effect sizes to population parameter. We suggested the noncentral t-distribution based method when the assumptions held, and the bootstrap bias-corrected and accelerated method when the assumptions are not met.^