Dose response signal detection under model uncertainty

Bayesian model averaging of longitudinal dose-response models

Selecting a safe and clinically beneficial dose can be difficult in drug development. Dose justification often relies on dose-response modeling where parametric assumptions are made in advance which may not adequately fit the data. This is especially problematic in longitudinal dose-response models, where additional parametric assumptions must be made. This paper proposes a class of longitudinal dose-response models to be used in the Bayesian model averaging paradigm which improve trial operating characteristics while maintaining flexibility a priori. A new longitudinal model for non-monotonic longitudinal profiles is proposed. The benefits and trade-offs of the proposed approach are demonstrated through a case study and simulation.

cLRT-Mod: An efficient methodology for pharmacometric model-based analysis of longitudinal phase II dose finding studies under model uncertainty

Within the challenging context of phase II dose-finding trials, longitudinal analyses may increase drug effect detection power compared to an end-of-treatment analysis. This work proposes cLRT-Mod, a pharmacometric adaptation of the MCP-Mod methodology, which allows the use of nonlinear mixed effect models to first detect a dose-response signal and then identify the doses for the confirmatory phase while accounting for model structure uncertainty. The method was evaluated through extensive clinical trial simulations of a hypothetical phase II dose-finding trial using different scenarios and comparing different methods such as MCP-Mod. The results show an increase in power using cLRT with longitudinal data compared to an EOT multiple contrast tests for scenarios with small sample size and weak drug effect while maintaining pre-specifiability of the models prior to data analysis and the nominal type I error. This work shows how model averaging provides better coverage probability of the drug effect in the prediction step, and avoids under-estimation of the size of the confidence interval. Finally, for illustration purpose cLRT-Mod was applied to the analysis of a real phase II dose-finding trial.

The Tukey trend test: Multiplicity adjustment using multiple marginal models

In dose-response analysis, it is a challenge to choose appropriate linear or curvilinear shapes when considering multiple, differently scaled endpoints. It has been proposed to fit several marginal regression models that try sets of different transformations of the dose levels as explanatory variables for each endpoint. However, the multiple testing problem underlying this approach, involving correlated parameter estimates for the dose effect between and within endpoints, could only be adjusted heuristically. An asymptotic correction for multiple testing can be derived from the score functions of the marginal regression models. Based on a multivariate t-distribution, the correction provides a one-step adjustment of p-values that accounts for the correlation between estimates from different marginal models. The advantages of the proposed methodology are demonstrated through three example datasets, involving generalized linear models with differently scaled endpoints, differing covariates, and a mixed effect model and through simulation results. The methodology is implemented in an R package.

Generalized multiple contrast tests in dose-response studies

In the process of developing drugs, proof-of-concept studies can be helpful in determining whether there is any evidence of a dose-response relationship. A global test for this purpose that has gained popularity is a component of the multiple comparisons procedure with modeling techniques (MCP-Mod), which involves the specification of a candidate set of several plausible dose-response models. For each model, a test is performed for significance of an optimally chosen contrast among the sample means. An overall P-value is obtained from the distribution of the maximum of the contrast statistics. This is equivalent to basing the test on the minimum of the P-values arising from these contrast statistics and, hence, can be viewed as a method for combining dependent P-values. We generalize this idea to the use of different statistics for combining the dependent P-values, such as Fisher's combination method or the inverse normal combination method. Simulation studies show that the generalized multiple contrast tests (GMCTs) based on the Fisher and inverse normal methods are generally more powerful than the MCP-Mod procedure based on the minimum of the P-values except for cases where the true dose-response model is, in a sense, near the extremes of the candidate set of dose-response models. The proposed GMCTs can also be used for model selection and dosage selection by employing a closed testing procedure.

Comparison of different approaches for dose response analysis

Characterizing an appropriate dose-response relationship and identifying the right dose in a clinical trial are two main goals of early drug-development. MCP-Mod is one of the pioneer approaches developed within the last 10 years that combines the modeling techniques with multiple comparison procedures to address the above goals in clinical drug development. The MCP-Mod approach begins with a set of potential dose-response models, tests for a significant dose-response effect (proof of concept, PoC) using multiple linear contrasts tests and selects the "best" model among those with a significant contrast test. A disadvantage of the method is that the parameter values of the candidate models need to be fixed a priori for the contrasts tests. This may lead to a loss in power and unreliable model selection. For this reason, several variations of the MCP-Mod approach and a hierarchical model selection approach have been suggested where the parameter values need not be fixed in the proof of concept testing step and can be estimated after the model selection step. This paper provides a numerical comparison of the different MCP-Mod variants and the hierarchical model selection approach with regard to their ability of detecting the dose-response trend, their potential to select the correct model and their accuracy in estimating the dose response shape and minimum effective dose. Additionally, as one of the approaches is based on two-sided model comparisons only, we make it more consistent with the common goals of a PoC study, by extending it to one-sided comparisons between the constant and alternative candidate models in the proof of concept step.