Optimal likelihood-ratio multiple testing with application to Alzheimer's disease and questionable dementia

Abstract

Background: Controlling the false discovery rate is important when testing multiple hypotheses. To enhance the detection capability of a false discovery rate control test, we applied the likelihood ratio-based multiple testing method in neuroimage data and compared the performance with the existing methods.

Methods: We analysed the performance of the likelihood ratio-based false discovery rate method using simulation data generated under independent assumption, and positron emission tomography data of Alzheimer's disease and questionable dementia. We investigated how well the method detects extensive hypometabolic regions and compared the results to those of the conventional Benjamini Hochberg-false discovery rate method.

Results: Our findings show that the likelihood ratio-based false discovery rate method can control the false discovery rate, giving the smallest false non-discovery rate (for a one-sided test) or the smallest expected number of false assignments (for a two-sided test). Even though we assumed independence among voxels, the likelihood ratio-based false discovery rate method detected more extensive hypometabolic regions in 22 patients with Alzheimer's disease, as compared to the 44 normal controls, than did the Benjamini Hochberg-false discovery rate method. The contingency and distribution patterns were consistent with those of previous studies. In 24 questionable dementia patients, the proposed likelihood ratio-based false discovery rate method was able to detect hypometabolism in the medial temporal region.

Conclusions: This study showed that the proposed likelihood ratio-based false discovery rate method efficiently identifies extensive hypometabolic regions owing to its increased detection capability and ability to control the false discovery rate.

Figure 1

The averaged FDR and FNDR. Within each panel, black and white bars represent the BH-FDR and LR-FDR methods, respectively. The alternative proportions of data are 80% and 60% in Simulation I (A and B) and II (C and D), respectively. In each simulation setting, depending on μ, three parameter settings are presented

Figure 2

Brain regions with significantly lower FDG uptake in probable AD compared to NC. Regions with lower FDG uptake in probable AD are displayed. The left hemisphere is shown as a 3D volume rendering. The reduction in the FDG uptake in the temporal, parietal, and posterior prefrontal regions was commonly found in the LR-FDR and BH-FDR methods. Extensive hypometabolic areas extending to posterior prefrontal were detected with the LR-FDR one-sided and two-sided tests. The color bar range from minimum to maximum significance level denotes the significance of the likelihood ratio in both LR-FDR methods and of the p-value in BH-FDR method. (AD: Alzheimer’s disease; FDR: False discovery rate; LR-FDR: Likelihood ratio false discovery rate; NC: Normal controls).

Figure 3

Brain regions with significantly lower FDG uptake in QD compared to NC. The coronal view in the left column shows hypometabolism in the medial temporal regions in QD. An anatomical map of the hippocampus is displayed in blue. Regions with a lower FDG uptake are displayed in red. The LR-FDR one-sided and two-sided tests disclosed more extensive hypometabolic areas in both temporal lobes than did the BH-FDR method. (FDR: False discovery rate; LR-FDR: Likelihood ratio false discovery rate; NC: Normal controls; QD: Questionable dementia).

Figure 4

Histograms of real and synthetic data. Histograms of of the generated synthetic data from fitted model (gray histogram) and d _v of real data (hatched histogram) (left: AD cases, right: QD cases) (AD: Alzheimer’s disease; QD: Questionable dementia).