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. ^

‘The best thing I’ve ever done is ring these people…’: Making a Difference through Family Support

Effective family support strategies offer early intervention and help for families and children at risk of experiencing social exclusion and maltreatment. This paper reports a study which evaluated client outcomes from participation in an Intensive Family Support Service by comparing views of workers and service users on perceived benefits. It profiles the characteristics and circumstances of families recruited to service, services and interventions delivered and the potential of IFSS to lead to safe and positive outcomes for children and families. Findings discussed highlight the individualized and collaborative approach and the high degree of engagement with service users that facilitated gains in the domains of child and family functioning targeted. Implications of the findings for policy and practice in responding to vulnerable families and children are discussed.

Comparison of Tumor Shrinkage and Cumulative Dose Distribution for Lung Cancers

Background: The physical characteristic of protons is that they deliver most of their radiation dose to the target volume and deliver no dose to the normal tissue distal to the tumor. Previously, numerous studies have shown unique advantages of proton therapy over intensity-modulated radiation therapy (IMRT) in conforming dose to the tumor and sparing dose to the surrounding normal tissues and the critical structures in many clinical sites. However, proton therapy is known to be more sensitive to treatment uncertainties such as inter- and intra-fractional variations in patient anatomy. To date, no study has clearly demonstrated the effectiveness of proton therapy compared with the conventional IMRT under the consideration of both respiratory motion and tumor shrinkage in non-small cell lung cancer (NSCLC) patients. Purpose: This thesis investigated two questions for establishing a clinically relevant comparison of the two different modalities (IMRT and proton therapy). The first question was whether or not there are any differences in tumor shrinkage between patients randomized to IMRT versus passively scattered proton therapy (PSPT). Tumor shrinkage is considered a standard measure of radiation therapy response that has been widely used to gauge a short-term progression of radiation therapy. The second question was whether or not there are any differences between the planned dose and 5D dose under the influence of inter- and intra-fractional variations in the patient anatomy for both modalities. Methods: A total of 45 patients (25 IMRT patients and 20 PSPT patients) were used to quantify the tumor shrinkage in terms of the change of the primary gross tumor volume (GTVp). All patients were randomized to receive either IMRT or PSPT for NSCLC. Treatment planning goals were identical for both groups. All patients received 5 to 8 weekly repeated 4-dimensional computed tomography (4DCT) scans during the course of radiation treatments. The original GTVp contours were propagated to T50 of weekly 4DCT images using deformable image registration and their absolute volumes were measured. Statistical analysis was performed to compare the distribution of tumor shrinkage between the two population groups. In order to investigate the difference between the planned dose and the 5D dose with consideration of both breathing motion and anatomical change, we re-calculated new dose distributions at every phase of the breathing cycle for all available weekly 4DCT data sets which resulted 50 to 80 individual dose calculations for each of the 7 patients presented in this thesis. The newly calculated dose distributions were then deformed and accumulated to T50 of the planning 4DCT for comparison with the planned dose distribution. Results: At the end of the treatment, both IMRT and PSPT groups showed mean tumor volume reductions of 23.6% ( 19.2%) and 20.9% ( 17.0 %) respectively. Moreover, the mean difference in tumor shrinkage between two groups is 3% along with the corresponding 95% confidence interval, [-8%, 14%]. The rate of tumor shrinkage was highly correlated with the initial tumor volume size. For the planning dose and 5D dose comparison study, all 7 patients showed a mean difference of 1 % in terms of target coverage for both IMRT and PSPT treatment plans. Conclusions: The results of the tumor shrinkage investigation showed no statistically significant difference in tumor shrinkage between the IMRT and PSPT patients, and the tumor shrinkage between the two modalities is similar based on the 95% confidence interval. From the pilot study of comparing the planned dose with the 5D dose, we found the difference to be only 1%. Overall impression of the two modalities in terms of treatment response as measured by the tumor shrinkage and 5D dose under the influence of anatomical change that were designed under the same protocol (i.e. randomized trial) showed similar result.

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.^