Partial Conjunction Analysis in Neuroimaging: A Comparative Study

Abstract

Replicability is a cornerstone of science. The partial conjunction (PC) hypothesis testing framework objectively quantifies replicability across disciplines. Although several statistical methodologies for testing PC hypotheses exist, it is not clear which method performs well under which circumstances. In this paper, we consider the PC hypothesis testing problem from a neuroimaging perspective. Identifying the brain regions activated by a specific cognitive task constitutes a central challenge in neuroimaging. This problem becomes complex when the objective is to evaluate whether activation patterns are consistent across different cognitive tasks or subjects. In this paper, we cast this question as a PC hypothesis testing problem, assessing, for each location in the brain, whether it is activated in at least $γ$ subjects, for a pre-specified granularity $γ$. In our comparative study, we consider three methods, namely: adaFilter, CoFilter, and a method proposed by Benjamini, Heller, and Yekutieli (BHY). In equi-correlated simulated data, the BHY procedure tends to outperform the competing methods for high values of $γ$, while CoFilter performs well for low values of $γ$. In the real-data analysis, CoFilter dominates the other methods for intermediate values of $γ$.

Figures (5)

• Figure 1: Equi-correlated data: Distribution of $\delta_1,\ldots,\delta_m$, where $\delta_j$ represents the number of subjects for which voxel $j$ is active.
• Figure 2: Equicorrelated data: FDP obtained for different correlation values $\rho$, for adaFilter, BHY, and CoFilter. Target level $\alpha=0.05$. All plots are based on $1{,}000$ repetitions. The different considered values of $\rho$ are provided above the subfigures.
• Figure 3: Equi-correlated data: power comparison. All graphs are based on $1{,}000$ repetitions. The considered values of $\rho$ are provided above the subfigures.
• Figure 4: Midnight Scan Club Data: Number of rejections by granularity $\gamma$, where a voxel $j$ is rejected if $d_j\geq\gamma$.
• Figure 5: Midnight Scan Club Data: Results $d_j$ for the three methods. Target level $\alpha=0.05$.