Design considerations and analysis planning of a phase 2a proof of concept study in rheumatoid arthritis in the presence of possible non-monotonicity

Discretizing multiple continuous predictors with U-shaped relationships with lnOR: introducing the recursive gradient scanning method in clinical and epidemiological research

BACKGROUND

Assuming a linear relationship between continuous predictors and outcomes in clinical prediction models is often inappropriate, as true linear relationships are rare, potentially resulting in biased estimates and inaccurate conclusions. Our research group addressed a single U-shaped independent variable before. Multiple U-shaped predictors can improve predictive accuracy by capturing nuanced relationships, but they also introduce challenges like increased complexity and potential overfitting. This study aims to extend the applicability of our previous research results to more common scenarios, thereby facilitating more comprehensive and practical investigations.

METHODS

In this study, we proposed a novel approach called the Recursive Gradient Scanning Method (RGS) for discretizing multiple continuous variables that exhibit U-shaped relationships with the natural logarithm of the odds ratio (lnOR). The RGS method involves a two-step approach: first, it conducts fine screening from the 2.5th to 97.5th percentiles of the lnOR. Then, it utilizes an iterative process that compares AIC metrics to identify optimal categorical variables. We conducted a Monte Carlo simulation study to investigate the performance of the RGS method. Different correlation levels, sample sizes, missing rates, and symmetry levels of U-shaped relationships were considered in the simulation process. To compare the RGS method with other common approaches (such as median, Q1-Q3, minimum P-value method), we assessed both the predictive ability (e.g., AUC) and goodness of fit (e.g., AIC) of logistic regression models with variables discretized at different cut-points using a real dataset.

RESULTS

Both simulation and empirical studies have consistently demonstrated the effectiveness of the RGS method. In simulation studies, the RGS method showed superior performance compared to other common discretization methods in discrimination ability and overall performance for logistic regression models across various U-shaped scenarios (with varying correlation levels, sample sizes, missing rates, and symmetry levels of U-shaped relationships). Similarly, empirical study showed that the optimal cut-points identified by RGS have superior clinical predictive power, as measured by metrics such as AUC, compared to other traditional methods.

CONCLUSIONS

The simulation and empirical study demonstrated that the RGS method outperformed other common discretization methods in terms of goodness of fit and predictive ability. However, in the future, we will focus on addressing challenges related to separation or missing binary responses, and we will require more data to validate our method.

Comparison of hierarchical EMAX and NDLM models in dose-response for early phase clinical trials

Background

Phase II clinical trials primarily aim to find the optimal dose and investigate the relationship between dose and efficacy relative to standard of care (control). Therefore, before moving forward to a phase III confirmatory trial, the most effective dose is needed to be identified.

Methods

The primary endpoint of a phase II trial is typically a binary endpoint of success or failure. The EMAX model, ubiquitous in pharmacology research, was fit for many compounds and described the data well, except for a single compound, which had nonmonotone dose–response (Thomas et al., Stat Biopharmaceutical Res. 6:302-317 2014). To mitigate the risk of nonmonotone dose response one of the alternative options is a Bayesian hierarchical EMAX model (Gajewski et al., Stat Med. 38:3123-3138 2019). The hierarchical EMAX adapts to its environment.

Results

When the dose-response curve is monotonic it enjoys the efficiency of EMAX. When the dose-response curve is non-monotonic the additional random effect hyperprior makes the hierarchical EMAX model more adjustable and flexible. However, the normal dynamic linear model (NDLM) is a useful model to explore dose-response relationships in that the efficacy at the current dose depends on the efficacy of the previous dose(s). Previous research has compared the EMAX to the hierarchical EMAX (Gajewski et al., Stat Med. 38:3123-3138 2019) and the EMAX to the NDLM (Liu et al., BMC Med Res Method 17:149 2017), however, the hierarchical EMAX has not been directly compared to the NDLM.

Conclusions

The focus of this paper is to compare these models and discuss the relative merit for each of their uses for an ongoing early phase dose selection study.