Introduction: The structural components variance estimator proposed by DeLong et al. (1988) is a popular approach used when comparing two correlated AUCs. However, this variance estimator is biased and could be problematic with small sample sizes. Methods: A U-statistics based variance estimator approach is presented and compared with the structural components variance estimator through a large-scale simulation study under different finite-sample size configurations. Results: The U-statistics variance estimator was unbiased for the true variance of the difference between correlated AUCs regardless of the sample size and had lower RMSE than the structural components variance estimator, providing better type 1 error control and larger power. The structural components variance estimator provided increasingly biased variance estimates as the correlation between biomarkers increased. Discussion: When comparing two correlated AUCs, it is recommended that the U-Statistics variance estimator be used whenever possible, especially for finite sample sizes and highly correlated biomarkers.

Two-arm group sequential designs have been widely used for over forty years, especially for studies with mortality endpoints. The natural generalization of such designs to trials with multiple treatment arms and a common control (MAMS designs) has, however, been implemented rarely. While the statistical methodology for this extension is clear, the main limitation has been an efficient way to perform the computations. Past efforts were hampered by algorithms that were computationally explosive. With the increasing interest in adaptive designs, platform designs, and other innovative designs that involve multiple comparisons over multiple stages, the importance of MAMS designs is growing rapidly. This dissertation proposes a group sequential approach to design MAMS trial where the test statistic is the maximum of the cumulative score statistics for each pair-wise comparison, and is evaluated at each analysis time point with respect to efficacy and futility stopping boundaries while maintaining strong control of the family wise error rate (FWER). In this dissertation we start with a break-through algorithm that will enable us to compute MAMS boundaries rapidly. This algorithm will make MAMS design a practical reality. For designs with efficacy-only boundaries, the computational effort increases linearly with number of arms and number of stages. For designs with both efficacy and futility boundaries the computational effort doubles with successive increases in number of stages. Previous attempts to obtain MAMS boundaries were confined to smaller problems because their computational effort grew exponentially with number of arms and number of stages. We will next extend our proposed group sequential MAMS design to permit adaptive changes such as dropping treatment arms and increasing the sample size at each interim analysis time point. In order to control the FWER in the presence of these adaptations the early stopping boundaries must be re-computed by invoking the conditional error rate principle and the closed testing principle. This adaptive MAMS design is immensely useful in phase~2 and phase~3 settings. An alternative to the group sequential approach for MAMS design is the p-value combination approach. This approach has been in place for the last fifteen years.This alternative MAMS approach is based on combining independent p-values from the incremental data of each stage. Strong control of the FWER for this alternative approach is achieved by closed testing. We will compare the operating characteristics of the two approaches both analytically and empirically via simulation. In this dissertation we will demonstrate that the MAMS group sequential approach dominates the traditional p-value combination approach in terms of statistical power.

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal.

Pharmaceutical drug development is a costly and time consuming process. Reportedly, it takes about 10-15 years and ~900 million dollars of investment to launch a new drug in the world market. Any measure that increases the power and also decreases uncertainty about that power also increases drug net present value. For some time now, it has been argued that judicious utilization of available data might lead to more efficient use of resources during drug development. Conventionally, assessment of effectiveness has been based on comparing change from baseline at some pre-specified time for the control and test treatment (SPA). The last observation carry forward (LOCF) is a widely used technique if the data are missing due to any reason. Although, LOCF is known to introduce bias, the direction and magnitude is debatable.The primary aim of the proposed simulation experiments was to assess the properties of the random effects model (REM) and mixed model repeated measures (MMRM) methods that utilize all the data collected during pivotal trials. A total of 43 scenarios based on disease progression, magnitude of drug effect, between and within subject variability and patient drop-outs were analyzed. Three analysis methods, viz. SPA, REM and MMRM, were investigated. For the SPA method, the missing data were imputed with four different methods, such as LOCF, mean imputation, population and individual regression. The false-positive, false-negative inferences and bias in estimating the effect size for each method was assessed.The most important finding of this report is that the REM and MMRM methods are efficient alternatives to the SPA methods with ~50% savings on sample size. These methods are based on sound scientific principles and provide stronger evidence against the null hypothesis. The choice of the REM versus MMRM method is dependent on the purpose of the analysis and data gathered from the experimental design. The results support the use of likelihood-based MMRM methods for regulatory decision making. The REM methods are useful in understanding the time course of the disease and drug effect, making predictions based on the data and gaining insights into time to steady state effect for rational decision making. The SPA methods are less powerful across all the scenarios. The SPA-LOCF yielded anticonservative results in some cases with type-1 error rate exceeding 15% if data were missing due to toxicity. On the other hand, the drug effect was consistently underestimated (~40%), if data were missing due to lack of effectiveness. The results demonstrate that the SPA-LOCF methods make it practically impossible to establish effectiveness in these areas with a reasonable sample size.

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal