Design and analysis for three level hierarchical structures with count response

In numerous intervention studies and education field trials, random assignment to treatment occurs in clusters rather than at the level of observation. This departure of random assignment of units may be due to logistics, political feasibility, or ecological validity. Data within the same cluster or grouping are often correlated. Application of traditional regression techniques, which assume independence between observations, to clustered data produce consistent parameter estimates. However such estimators are often inefficient as compared to methods which incorporate the clustered nature of the data into the estimation procedure (Neuhaus 1993).1 Multilevel models, also known as random effects or random components models, can be used to account for the clustering of data by estimating higher level, or group, as well as lower level, or individual variation. Designing a study, in which the unit of observation is nested within higher level groupings, requires the determination of sample sizes at each level. This study investigates the design and analysis of various sampling strategies for a 3-level repeated measures design on the parameter estimates when the outcome variable of interest follows a Poisson distribution. ^ Results study suggest that second order PQL estimation produces the least biased estimates in the 3-level multilevel Poisson model followed by first order PQL and then second and first order MQL. The MQL estimates of both fixed and random parameters are generally satisfactory when the level 2 and level 3 variation is less than 0.10. However, as the higher level error variance increases, the MQL estimates become increasingly biased. If convergence of the estimation algorithm is not obtained by PQL procedure and higher level error variance is large, the estimates may be significantly biased. In this case bias correction techniques such as bootstrapping should be considered as an alternative procedure. For larger sample sizes, those structures with 20 or more units sampled at levels with normally distributed random errors produced more stable estimates with less sampling variance than structures with an increased number of level 1 units. For small sample sizes, sampling fewer units at the level with Poisson variation produces less sampling variation, however this criterion is no longer important when sample sizes are large. ^ 1Neuhaus J (1993). “Estimation efficiency and Tests of Covariate Effects with Clustered Binary Data”. Biometrics , 49, 989–996^

The design and evaluation of a 2D dose verification system for intensity modulated radiotherapy

The usage of intensity modulated radiotherapy (IMRT) treatments necessitates a significant amount of patient-specific quality assurance (QA). This research has investigated the precision and accuracy of Kodak EDR2 film measurements for IMRT verifications, the use of comparisons between 2D dose calculations and measurements to improve treatment plan beam models, and the dosimetric impact of delivery errors. New measurement techniques and software were developed and used clinically at M. D. Anderson Cancer Center. The software implemented two new dose comparison parameters, the 2D normalized agreement test (NAT) and the scalar NAT index. A single-film calibration technique using multileaf collimator (MLC) delivery was developed. EDR2 film's optical density response was found to be sensitive to several factors: radiation time, length of time between exposure and processing, and phantom material. Precision of EDR2 film measurements was found to be better than 1%. For IMRT verification, EDR2 film measurements agreed with ion chamber results to 2%/2mm accuracy for single-beam fluence map verifications and to 5%/2mm for transverse plane measurements of complete plan dose distributions. The same system was used to quantitatively optimize the radiation field offset and MLC transmission beam modeling parameters for Varian MLCs. While scalar dose comparison metrics can work well for optimization purposes, the influence of external parameters on the dose discrepancies must be minimized. The ability of 2D verifications to detect delivery errors was tested with simulated data. The dosimetric characteristics of delivery errors were compared to patient-specific clinical IMRT verifications. For the clinical verifications, the NAT index and percent of pixels failing the gamma index were exponentially distributed and dependent upon the measurement phantom but not the treatment site. Delivery errors affecting all beams in the treatment plan were flagged by the NAT index, although delivery errors impacting only one beam could not be differentiated from routine clinical verification discrepancies. Clinical use of this system will flag outliers, allow physicists to examine their causes, and perhaps improve the level of agreement between radiation dose distribution measurements and calculations. The principles used to design and evaluate this system are extensible to future multidimensional dose measurements and comparisons. ^

Simulation study of joint transition and Weibull survival model with shared parameters

This study investigates a theoretical model where a longitudinal process, that is a stationary Markov-Chain, and a Weibull survival process share a bivariate random effect. Furthermore, a Quality-of-Life adjusted survival is calculated as the weighted sum of survival time. Theoretical values of population mean adjusted survival of the described model are computed numerically. The parameters of the bivariate random effect do significantly affect theoretical values of population mean. Maximum-Likelihood and Bayesian methods are applied on simulated data to estimate the model parameters. Based on the parameter estimates, predicated population mean adjusted survival can then be calculated numerically and compared with the theoretical values. Bayesian method and Maximum-Likelihood method provide parameter estimations and population mean prediction with comparable accuracy; however Bayesian method suffers from poor convergence due to autocorrelation and inter-variable correlation. ^

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. ^

An ordinal logistic regression model with misclassification of the outcome variable and categorical covariate

Ordinal outcomes are frequently employed in diagnosis and clinical trials. Clinical trials of Alzheimer's disease (AD) treatments are a case in point using the status of mild, moderate or severe disease as outcome measures. As in many other outcome oriented studies, the disease status may be misclassified. This study estimates the extent of misclassification in an ordinal outcome such as disease status. Also, this study estimates the extent of misclassification of a predictor variable such as genotype status. An ordinal logistic regression model is commonly used to model the relationship between disease status, the effect of treatment, and other predictive factors. A simulation study was done. First, data based on a set of hypothetical parameters and hypothetical rates of misclassification was created. Next, the maximum likelihood method was employed to generate likelihood equations accounting for misclassification. The Nelder-Mead Simplex method was used to solve for the misclassification and model parameters. Finally, this method was applied to an AD dataset to detect the amount of misclassification present. The estimates of the ordinal regression model parameters were close to the hypothetical parameters. β1 was hypothesized at 0.50 and the mean estimate was 0.488, β2 was hypothesized at 0.04 and the mean of the estimates was 0.04. Although the estimates for the rates of misclassification of X1 were not as close as β1 and β2, they validate this method. X 1 0-1 misclassification was hypothesized as 2.98% and the mean of the simulated estimates was 1.54% and, in the best case, the misclassification of k from high to medium was hypothesized at 4.87% and had a sample mean of 3.62%. In the AD dataset, the estimate for the odds ratio of X 1 of having both copies of the APOE 4 allele changed from an estimate of 1.377 to an estimate 1.418, demonstrating that the estimates of the odds ratio changed when the analysis includes adjustment for misclassification. ^

Biomarker circadian rhythm profiles in critically ill mechanically ventilated patients

Objective: To explore the natural trajectory of core body temperature (CBT) and cortisol (CORT) circadian rhythms in mechanically ventilated intensive care unit (MV ICU) patients. ^ Design: Prospective, observational, time-series pilot study. ^ Setting: Medical-surgical and pulmonary ICUs in a tertiary care hospital. ^ Sample: Nine (F = 3, M = 6) adults who were mechanically ventilated within 12 hrs of ICU admission with mean ± SD age of 65.2 ± 14 years old. ^ Measurements: Core body temperature and environmental measures of light, sound, temperature, and relative humidity were logged in 1-min intervals. Hourly urine specimens and 2-hr interval blood specimens were collected for up to 7 consecutive days for CORT assay. Mechanical ventilation days, ICU length of stay, and ICU mortality were documented. Acute Physiology and Chronic Health Evaluation (APACHE) II scores were computed for each study day. The data of each biologic and environmental variable were analyzed using single cosinor analysis of 24-hr serial segments. One patient did not complete the study because mortality occurred within 8 hrs of enrollment. Nine ICU patients completed the study in 1.6 to 7.0 days. ^ Results: No normal circadian rhythm pattern was found when the cosinor-derived parameters of amplitude (one-half the peak-trough variability) and acrophase (peak time) were compared with cosinor-derived parameter reference ranges of healthy, diurnally active humans, although 83% of patient-day CBT segments showed statistically significant (p ≤ .05) and biologically meaningful (R2≥ 0.30) 24-hr rhythms with abnormal cosinor parameters. Cosinor parameters of the environmental temporal profiles showed 27% of light, 76% of ambient temperature, and 78% of relative humidity serial segments had a significant and meaningful 24-hr diurnal pattern. Average daily light intensity varied from 34 to 187 lx with a maximum light exposure of 1877 lx. No sound measurement segment had a statistically significant cosine pattern, and numerous 1-minute interval peaks ≥ 60 dB occurred around the clock. Average daily ambient temperature and relative humidity varied from 19 to 24°C and from 25% to 61%, respectively. There was no statistically significant association between CBT or clinical outcomes and cosinor-derived parameters of the environmental variables. Circadian rhythms of urine and plasma CORT were deferred for later analysis. ^ Conclusions: The natural trajectory of the CBT circadian rhythm in MV ICU patients demonstrated persistent cosinor parameter alteration, even when a significant and meaningful 24-hr rhythm was present. The ICU environmental measures showed erratic light and sound exposures. Room temperature and relative humidity data produced the highest rate of significant and meaningful diurnal 24-hr patterns. Additional research is needed to clarify relations among the CBT biomarker of the circadian clock and environmental variables of MV ICU patients. ^

Circadian rhythm profiles in porcine ICU subjects

Purpose: To explore the natural trajectory of circadian rhythms of sedation requirement, core body temperature (CBT), pulmonary mechanics (PM), and gas exchange (GE) in mechanically ventilated swine, as these variables affect the duration of mechanical ventilation. ^ Design: A secondary analysis to describe and compare circadian rhythms of study variables in swine mechanically ventilated for ≤ 7 days. ^ Setting: Porcine Intensive Care Unit (ICU).^ Sample: Six male swine. ^ Methods: Sedation requirements were recorded hourly and the CBT, PM and GE variables were sampled every 1 s – 1 min for ≤ 7 days. The data sets for each pig with > 5 days ICU length of stay were divided into one section representing the first 3 days and one section representing subsequent days. The Lomb periodogram was used to estimate the circadian time period for each variable, and cosinor analysis with the estimated time period to obtain amplitude and mesor. Circadian to ultradian bandpower ratio to assess rhythm quality and stability over time and goodness-of-fit index to describe biological significance of a rhythm were used. Together, these two parameters were used to define rhythm robustness over time. The masking effect of sedation as a potential confounder of the circadian rhythms of CBT, PM, and GE was explored, and circadian rhythm profiles of CBT of pigs in the ICU setting were compared with those of the same pigs in the ambulatory setting. ^ Results: All pigs had significant rhythms in CBT, respiratory rate, and peripheral oxygen saturation across ICU data sets. Healthier pigs had more robust rhythms of study variables over time. Sedation did not appear to mask the circadian rhythms of CBT, PM, and GE. The circadian rhythm of CBT was less robust in the ICU setting than in the ambulatory setting. ^ Conclusions: Individual subject observations provided preliminary evidence that robustness of rhythms varies with subject acuity. Comparison of profiles of circadian rhythms among ICU subjects with similar acuity and disease processes is warranted to determine if the profiles in the present study are reproducible. Identification of consistent patterns may provide insight into subject morbidity and timing of such therapeutic interventions as weaning from mechanical ventilation. ^

A simulation study of the standard design, the rolling six design, the CRM, and the modified CRM in Phase I clinical trials

The Phase I clinical trial is considered the "first in human" study in medical research to examine the toxicity of a new agent. It determines the maximum tolerable dose (MTD) of a new agent, i.e., the highest dose in which toxicity is still acceptable. Several phase I clinical trial designs have been proposed in the past 30 years. The well known standard method, so called the 3+3 design, is widely accepted by clinicians since it is the easiest to implement and it does not need a statistical calculation. Continual reassessment method (CRM), a design uses Bayesian method, has been rising in popularity in the last two decades. Several variants of the CRM design have also been suggested in numerous statistical literatures. Rolling six is a new method introduced in pediatric oncology in 2008, which claims to shorten the trial duration as compared to the 3+3 design. The goal of the present research was to simulate clinical trials and compare these phase I clinical trial designs. Patient population was created by discrete event simulation (DES) method. The characteristics of the patients were generated by several distributions with the parameters derived from a historical phase I clinical trial data review. Patients were then selected and enrolled in clinical trials, each of which uses the 3+3 design, the rolling six, or the CRM design. Five scenarios of dose-toxicity relationship were used to compare the performance of the phase I clinical trial designs. One thousand trials were simulated per phase I clinical trial design per dose-toxicity scenario. The results showed the rolling six design was not superior to the 3+3 design in terms of trial duration. The time to trial completion was comparable between the rolling six and the 3+3 design. However, they both shorten the duration as compared to the two CRM designs. Both CRMs were superior to the 3+3 design and the rolling six in accuracy of MTD estimation. The 3+3 design and rolling six tended to assign more patients to undesired lower dose levels. The toxicities were slightly greater in the CRMs.^

Adaptive clinical trial design for targeted therapy development

The development of targeted therapy involve many challenges. Our study will address some of the key issues involved in biomarker identification and clinical trial design. In our study, we propose two biomarker selection methods, and then apply them in two different clinical trial designs for targeted therapy development. In particular, we propose a Bayesian two-step lasso procedure for biomarker selection in the proportional hazards model in Chapter 2. In the first step of this strategy, we use the Bayesian group lasso to identify the important marker groups, wherein each group contains the main effect of a single marker and its interactions with treatments. In the second step, we zoom in to select each individual marker and the interactions between markers and treatments in order to identify prognostic or predictive markers using the Bayesian adaptive lasso. In Chapter 3, we propose a Bayesian two-stage adaptive design for targeted therapy development while implementing the variable selection method given in Chapter 2. In Chapter 4, we proposed an alternate frequentist adaptive randomization strategy for situations where a large number of biomarkers need to be incorporated in the study design. We also propose a new adaptive randomization rule, which takes into account the variations associated with the point estimates of survival times. In all of our designs, we seek to identify the key markers that are either prognostic or predictive with respect to treatment. We are going to use extensive simulation to evaluate the operating characteristics of our methods.^