A hybrid method in combining treatment effects from matched and unmatched studies

In the biomedical studies, the general data structures have been the matched (paired) and unmatched designs. Recently, many researchers are interested in Meta-Analysis to obtain a better understanding from several clinical data of a medical treatment. The hybrid design, which is combined two data structures, may create the fundamental question for statistical methods and the challenges for statistical inferences. The applied methods are depending on the underlying distribution. If the outcomes are normally distributed, we would use the classic paired and two independent sample T-tests on the matched and unmatched cases. If not, we can apply Wilcoxon signed rank and rank sum test on each case. ^ To assess an overall treatment effect on a hybrid design, we can apply the inverse variance weight method used in Meta-Analysis. On the nonparametric case, we can use a test statistic which is combined on two Wilcoxon test statistics. However, these two test statistics are not in same scale. We propose the Hybrid Test Statistic based on the Hodges-Lehmann estimates of the treatment effects, which are medians in the same scale.^ To compare the proposed method, we use the classic meta-analysis T-test statistic on the combined the estimates of the treatment effects from two T-test statistics. Theoretically, the efficiency of two unbiased estimators of a parameter is the ratio of their variances. With the concept of Asymptotic Relative Efficiency (ARE) developed by Pitman, we show ARE of the hybrid test statistic relative to classic meta-analysis T-test statistic using the Hodges-Lemann estimators associated with two test statistics.^ From several simulation studies, we calculate the empirical type I error rate and power of the test statistics. The proposed statistic would provide effective tool to evaluate and understand the treatment effect in various public health studies as well as clinical trials.^

Multivariate methods for correlated effects sizes

Current statistical methods for estimation of parametric effect sizes from a series of experiments are generally restricted to univariate comparisons of standardized mean differences between two treatments. Multivariate methods are presented for the case in which effect size is a vector of standardized multivariate mean differences and the number of treatment groups is two or more. The proposed methods employ a vector of independent sample means for each response variable that leads to a covariance structure which depends only on correlations among the $p$ responses on each subject. Using weighted least squares theory and the assumption that the observations are from normally distributed populations, multivariate hypotheses analogous to common hypotheses used for testing effect sizes were formulated and tested for treatment effects which are correlated through a common control group, through multiple response variables observed on each subject, or both conditions.^ The asymptotic multivariate distribution for correlated effect sizes is obtained by extending univariate methods for estimating effect sizes which are correlated through common control groups. The joint distribution of vectors of effect sizes (from $p$ responses on each subject) from one treatment and one control group and from several treatment groups sharing a common control group are derived. Methods are given for estimation of linear combinations of effect sizes when certain homogeneity conditions are met, and for estimation of vectors of effect sizes and confidence intervals from $p$ responses on each subject. Computational illustrations are provided using data from studies of effects of electric field exposure on small laboratory animals. ^

The effect of thyroxine and triiodothyronine on fatigue, depression, and memory in a hypothyroid population

Background. This study was planned at a time when important questions were being raised about the adequacy of using one hormone to treat hypothyroidism instead of two. Specifically, this trial aimed to replicate prior findings which suggested that substituting 12.5 μg of liothyronine for 50 μg of levothyroxine might improve mood, cognition, and physical symptoms. Additionally, this trial aimed to extend findings to fatigue. ^ Methods. A randomized, double-blind, two-period, crossover design was used. Hypothyroid patients stabilized on levothyroxine were invited to participate. Thirty subjects were recruited and randomized. Sequence one received their standard levothyroxine dose in one capsule and placebo in another during the first six weeks. Sequence two received their usual levothyroxine dose minus 50 μg in one capsule and 10 μg of liothyronine in another. At the end of the first six week period, subjects were crossed over. T tests were used to assess carry-over and treatment effects. ^ Results. Twenty-seven subjects completed the trial. The majority of completers had an autoimmune etiology. Mean baseline levothyroxine dose was 121 μg/d (±26.0). Subjects reported small increases in fatigue as measured by the Piper Fatigue Scale (0.9, p = 0.09) and in symptoms of depression measured by the Beck Depression Inventory-II (2.3, p = 0.16) as well as the General Health Questionnaire-30 (4.7, p = 0.14) while treated with substitution treatment. However, none of these differences was statistically significant. Measures of working memory were essentially unchanged between treatments. Thyroid stimulating hormone was about twice as high during substitution treatment (p = 0.16). Free thyroxine index was reduced by 0.7 (p < 0.001), and total serum thyroxine was reduced by 3.0 (p < 0.001) while serum triiodothyronine was increased by 20.5 (p < 0.001) on substitution treatment. ^ Conclusions. Substituting an equivalent amount of liothyronine for a portion of levothyroxine in patients with hypothyroidism does not decrease fatigue, symptoms of depression, or improve working memory. However, due to changes in serum hormone levels and small increments in fatigue and depression symptoms on substitution treatment, a question was raised about the role of T3 in the serum. ^

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. ^

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^

Interim analysis of clinical trials: Simulation studies of fractional Brownian motion

Interim clinical trial monitoring procedures were motivated by ethical and economic considerations. Classical Brownian motion (Bm) techniques for statistical monitoring of clinical trials were widely used. Conditional power argument and α-spending function based boundary crossing probabilities are popular statistical hypothesis testing procedures under the assumption of Brownian motion. However, it is not rare that the assumptions of Brownian motion are only partially met for trial data. Therefore, I used a more generalized form of stochastic process, called fractional Brownian motion (fBm), to model the test statistics. Fractional Brownian motion does not hold Markov property and future observations depend not only on the present observations but also on the past ones. In this dissertation, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5< H <1, with treatment effects vs. without treatment effects. Then the performance of conditional power and boundary-crossing based interim analyses were compared by assuming that the data follow Bm or fBm. Our simulation study suggested that the conditional power or boundaries under fBm assumptions are generally higher than those under Bm assumptions when H > 0.5 and also matches better with the empirical results. ^

Effects of treatment on orienting in Parkinson disease

Parkinson disease (PD) is a movement disorder affecting over one million Americans, and 1% of our population over 60 years of age. Currently, PD has an unknown cause, no predictive biomarker, and no cure, yet there are effective treatments (medicine and surgery) to chronically manage the motor symptoms. But, PD patients also develop cognitive symptoms (e.g., distractibility, executive dysfunction) that remain untreated or may decline as a result of treating the motor symptoms. To address this important issue, I measured covert orienting of attention and overt eye movements in PD patients to assess the patients' ability to automatically detect stimuli in their visual field, to predict and attend to where the stimuli would appear, and to volitionally look somewhere else. ^ PD patients completed the cognitive tasks under multiple treatment conditions, and their performance was compared to healthy adults. PD patients first completed the tasks after they had withdrawn from medication. Their unmedicated performance revealed exaggerated automatic orienting, poor predictability, and weak volitional orienting. PD patients then repeated the tasks while medication was giving its peak benefit. The medication returned automatic covert orienting toward normal but did not improve volitional covert orienting. Several PD patients completed the tasks a third time after receiving surgery (specifically, implantation of stimulating electrodes in a subcortical brain region to alleviate motor symptoms). The stimulation (without medication) returned automatic orienting toward normal, did not change predictability, and further impaired volitional orienting. Taken together, treatments prescribed to alleviate the motor symptoms (a patient's primary concern) only improve some cognitive functions. Future studies may establish criteria to predict which patients are more likely to have cognitive benefit from medication over surgery, or vice versa. ^ I have also hypothesized an anatomical model relating orienting circuitry to abnormal PD circuitry and the therapeutic targets. My results suggest medication is more effective restoring the orienting circuitry than stimulation. Further, automatic and volitional orienting abilities seem to be modulated independently, which differs from an earlier model proposing a dependent, inverse relationship. My results are further discussed in terms of response inhibition, response selection, and the location of the selection. ^

Quantitative comparison of late effects following photon versus proton external-beam radiation therapies: Toward an evidence-based approach to selecting a treatment modality

Radiation therapy has been used as an effective treatment for malignancies in pediatric patients. However, in many cases, the side effects of radiation diminish these patients’ quality of life. In order to develop strategies to minimize radiogenic complications, one must first quantitatively estimate pediatric patients’ relative risk for radiogenic late effects, which has not become feasible till recently because of the calculational complexity. The goals of this work were to calculate the dose delivered to tissues and organs in pediatric patients during contemporary photon and proton radiotherapies; to estimate the corresponding risk of radiogenic second cancer and cardiac toxicity based on the calculated doses and on dose-risk models from the literature; to test for the statistical significance of the difference between predicted risks after photon versus proton radiotherapies; and to provide a prototype of an evidence-based approach to selecting treatment modalities for pediatric patients, taking second cancer and cardiac toxicity into account. The results showed that proton therapy confers a lower predicted risk of radiogenic second cancer, and lower risks of radiogenic cardiac toxicities, compared to photon therapy. An uncertainty analysis revealed that the qualitative findings of this study are insensitive to changes in a wide variety of host and treatment related factors.