Controlling False Disrupted Connectivities in Neuroimaging Studies

Introduction

Controlling the False Discovery Rate (FDR) is critically important for a detailed understanding of how a healthy brain differs with neurological diseases (e.g., depression), which is the fundamental requirement to the development and application of treatments for these conditions. Most of the neuroimaging research studies either do not address the issue of Multiple Testing (MT), or inadequately address MT by failing to incorporate the underlying dependency structure. Software packages often used for fMRI analysis (SPM, FSL, AFNI) can result in making false-positive rates of up to 70%, when it is fixed at 5% [1]. Inadequate use of statistical methods for MT is hindering the search for truly disrupted connectivities. Excessive false discoveries lead to wrong conclusion and may mar the importance of the study. Thus, a proper procedure to control the false discovery rate in neuro connectivity research is urgently needed.

Currently functional connectivity data are analyzed using model based methods such as cross correlation analysis or statistical parametric mapping [2-8]. Functional connectivity is also analyzed by data-driven methods such as independent component analysis, or principal component analysis [9-11]. Generally, structural connectivity data are obtained using diffusion tensor imaging, with measurements such as fractional anisotropy, relative anisotropy, mean diffusivity, or axial diffusivity [12-17]. For multimodal analysis, the existing Bayesian approach utilizes structural connectivity as a prior for functional connectivity [18-21], and frequentist statistical methods are also used with or without prior information [11,22-38]. In all neuroconnectivity studies based on either the whole brain, or any network (e.g. Salience Network, Default Mode Network), multiple testing becomes an integral part when two groups (e.g. Depression and Healthy Control) are compared. So, it is important to know the performance of different methods that are commonly used to control the false discovery rate in neuroconnectivity analysis.

Traditional approaches of large sample tests based on likelihood ratios and Wald-type statistics cannot address the issue of multiple comparison in neuroconnectivity analysis. Bonferroni correction for multiple testing becomes over conservative for a large number of comparisons. In rare cases, to control the false discovery rate, the approach by Benjamini and Hochberg (BH) [39] is used. However, the BH approach produces inflated false discovery rates in certain cases, and hence poses a problem in correctly identifying true discoveries with small samples.

The goal of this article is to develop statistical approaches to precisely detect disruptive neuroconnectivity in diseased populations and apply the findings to optimize benefits of clinical interventions. The first novelty of this article is in the development of a statistical model for neuroconnectivity data collected from neurological conditions (e.g., psychiatric, cognitive impairment etc.) and healthy control populations to identify significant changes in neuroconnectivity. For that purpose, we develop a mixed-effects model with some important characteristics in order to address within and between-subject heterogeneities, and also variabilities across links. The second novelty is in providing a simple interpretation to the q-value cut off which represents the minimum FDR at which the test can be called significant. Disrupted findings are next used to guide decisions on where to apply a neuro-modulatory intervention intended to improve behavioural disorders. The optimal approach of this article will indirectly reduce the cost of longitudinal and/or cluster neuroimaging studies, and provide the ability to study populations that are more difficult to recruit, such as minorities and traumatic brain injury patients. In summary, this article addresses modeling of neuroconnectivity data, and controlling of FDR in multiple testing for selecting the target of treatment applications.

We organize the article as follows. In Section 2, we motivate our problem with a study related to Late Life Depression (LLD) and argue that instead of controlling the type I error rate, we should control the false discovery rate for within or between group neuroconnectivity comparisons. In this section, we also discuss mixed-effects models and multiple testing procedures. In Section 3, we perform a simulation study for identifying an FDR approach that suits the best for neuroconnectivity comparisons and apply it to the LLD study for controlling the false discovery rate in section 4. We conclude the paper in Section 5.

Material and Methods

In this section, we discuss and develop some statistical methodologies intended to implement for detecting disrupted connectivities in group comparison studies. Towards that we start with a motivational example.

Motivational Example: Late Life Depression (LLD)

We motivate our research problem with a live data set from a study known as LLD recently conducted by Dr. Ajilore at University of Illinois at Chicago. LLD refers to major depressive episodes in elderly patients (usually over 50 or 60 years of age). This study recruited 23 subjects (13 healthy control (HC), and 10 LLD subjects), and collected data from 87 brain regions (i.e. a whole brain study, see Table 1) of each subject. The inclusion criteria for all subjects were over 55 years of age, medication-naive or anti-depressant free for at least two weeks (in the case of our LLD subjects) and no history of unstable cardiac or neurological diseases. The objective of this study is to detect brain regions and/or connectivity that are impaired during depression, and find out whether the identified regions can inform us about the pathophysiology of LLD Table 1.

Imaging data were collected using a Philips Achieva 3.0T scanner (Philips Medical Systems, Best, The Netherlands) with an 8-channel sensitivity encoded (SENSE) head coil. To reduce noise, headphones and foam pads were used and head movement was minimized. Subjects were instructed to stay still with their eyes closed yet awake without “thinking anything in particular” throughout the scanning process. Other sources of confounding effects such as motion artfact, white matter, and CSF were also regressed out before analysis. High resolution 3D T1-weighted images were attained by a MPRAGE (Magnetization Prepared Rapid Acquisition Gradient Echo) sequence with the following parameters: FOV = 240mm, TR/TE = 8.4/3.9 ms, flip angle = 8 degree, voxel size = 1.1 × 1.1 × 1.1 mm, and 134 contiguous axial slices. Resting-state imaging data were collected using a single-shot gradient-echo EPI sequence (EPI factor = 47, FOV = 23×23×15 cm³, TR/TE = 2000/30ms, Flip angle = 80, in-plane resolution = 3×3 mm², slice thickness/gap = 5/0 mm, slice number = 30, SENSE reduction factor = 1.8, NEX = 200, total scan time = 6: 52. The resting-state functional neuronetworks were configured using CONN [40], a Matlab toolbox. In brief, we preprocessed our raw EPI images involving four steps namely: realignment, co-registration, normalization, and smoothing.

The adjacency matrix of functional network as shown in (1), it has 87 × 86/2 = 3471 unique measures of functional connectivity. To satisfy the key assumption of normal distribution of our model, we applied the Fisher’s Z transformation to these Pearson Correlations (PC).

Modeling of Data

Mixed-effects regression models are frequently used to analyze neuroimaging data, as it can borrow strengths from multiple sources and provides reliable estimates of model parameters [4,18,41-48]. Fixed parameters of mixed-effects regression models provide population related information while random parameters provide subject specific information beyond the population mean [49-53]. Let Y_ijg/ be the fisher Z transformed pearson correlation measure of the ith link (i.e. connectivity between two regions) of the j^th subject nested within the g^th group (e.g. intervention, disease, control etc.).

where i (= 1, 2..., m) denotes the ith link (connection between two brain regions), j (= 1, 2...,N_g) denotes the j subject nested within the g^th group, x_ijg = 0, if the j^th subject is from the control group (i.e. g = control), and x_ijg= 1, if the j^th subject is from the other group (i.e. g = intervention or disease). We assume the random noise ε_ijg follows a normal distribution N (0, σ  ), in addition, random subject effect ν_jg follows a normal distribution N0, σ , and these two normal distributions are independent. The vector w_jg represents measures of additional fixed covariates such as age, race, sex etc. Thus, our decision related to significance of link connectivity will be adjusted by such fixed covariates. In this model, γ_1i differentiates the intercept of the intervention group from that of the control group at the i^th link. Note that this model allows each link to have its own mean and variance parameters, and those vary from one group to the other group. To compare two groups at the i^th link, we will test null hypotheses H₀: γ_1i = 0, i = 1, 2,…m. Thus, we have a total number of m hypotheses, which brings the notion of multiple testing.

Parameters in the model are estimated using an EM algorithm. In the E step, with the current values of the other parameters, we compute the “expected posteriori” or Empirical Bayes (EB) estimates of random effects as well as the conditional variances of random effects given data. In the M step, given the current estimated values of random effects, we obtain the Maximum Marginal Likelihood (MML) estimates of the regression coefficients, error variances, and variances of random effects. The algorithm iterates between the EB and MML estimates until convergence.

q-value based FDR Procedure

To detect disrupted connectivities in a neuroimaging study, we generally perform between group comparisons. In whole brain study, the number of Regions of Interest (ROI) in our example is 87 with a total number of 3471 connectivities. In a single hypothesis testing problem, we generally control the type I error rate at a pre-specified level (e. g. α = .05), and determine a rejection region to maximize the probability of detecting the true alternative hypothesis. When multiple hypotheses are tested simultaneously, it is important to control the expected proportion of false rejections among all rejections, and the concept of False Discovery Rate (FDR) [39] prevails there. The ingredients that we need to formally define the FDR are presented in Table 2.

By definition, FDR is the expected proportion of Type I errors among the rejected hypotheses.

Hence, FDR = E(V/(V + S) = E(V/R), where V isthe number of false rejections, R is the total number of rejections, and we define V/R=0, if R=0.

Algorithm to Control FDR

We start with the Benjamini and Hochberg [39] procedure to control the FDR. Consider a multiple testing problem consists of m hypotheses H₁, …, H_m with the corresponding p values p₁…, p_m. In the literature of FDR, [54, 55] defined a q-value as an analog of the p value that incorporates FDR-based multiple testing correction. q-value is the minimum positive FDR that can occur when rejecting a statistic with a threshold for the set of nested significance regions. The general procedure of the algorithm that controls the FDR at a threshold value of q is as follows:

1)                   Obtain p-values of all test statistics and sort those in an increasing order, i.e. p (1) ≤ p (2) ≤ … ≤ p_(m).

2)                   For a given q, find the largest k for which p_(k)≤ kq/m holds.

3)                   Declare discoveries for all H_(i), where i = 1, 2…, k.

First the BH procedure needs a cut-off q-value, then starts from the largest p value (i.e. p_(m)) and moves towards the smallest one, consequently we reject all null hypotheses with p-values less than the aforementioned threshold.

Determination of FDR Level q

In a single hypothesis testing, generally we fix the individual type I error rate α at 5%, and try to achieve 80% power. Similarly, in multiple hypothesis testing, we need to determine a q-value. However, no such standard value of the FDR level q exists in the literature, mainly because of some other factors that play crucial roles in this process. Suppose in a multiple testing scenario with 100 (out of a total of 200) hypotheses are truly null (i.e., the proportion of nulls is p₀= 0.50), we would expect 5 null rejections (out of 100) when α is individually fixed at 5%. With 80 rejections of the hypotheses that are truly non-null (i.e., 80% power), the observed theFDR level q = 5/(5+80) ≈0.059. A second scenario also conforms to multiple testing problem, with 90 of the 100 hypotheses being truly null (i.e., p₀ 0.90), and 10 of these being truly false. In this scenario, we should expect observed FDR level q close to 4/(4+8) ≈0.333.

If this procedure continues for a large value of p₀(e.g. p₀=.99), q will be close to 1 which will lead to less power and is undesirable. Thus, in a multiple testing problem, the FDR level q should be adjusted with the value of p₀, together with the individual type I error rate and power, such that q does not exceed to a desired threshold (e.g., 0.20 or 0.30). In order to better understand the interrelationship between individual type I error rate

Figure 1: mFDR level vs.

Figure 2: Adjusted type I error rate (

Table 1: Brain regions (left and right) in whole brain analysis.

1.                   Eklund A, Nichols TE, Knutson H (2016) Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates. Proceedings of the National Academy of Sciences 113: 7900.

2.                   Ogawa S, Tank DW, Menon R, Ellermann JM, Kim SG, et al. (1992) Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging Proceedings of the National Academy of Sciences 89: 5951-5955.

3.                   Cao J, Worsley K (1999) The geometry of correlation fields with an application to functional connectivity of the brain. The Annals of Applied Probability 9: 1021-1057.

4.                   Blamire AM, Ogawa S, Ugurbil K, Rothman D, McCarthy G, et al. (1992) Dynamic mapping of the human visual cortex by high-speed magnetic resonance imaging. Proceedings of the National Academy of Sciences 89: 11069-11073.

5.                   Friston KJ, Holmes AP, Worsley KJ, Poline JP, Frith CD, et al. (1994) Statistical parametric maps in functional imaging: a general linear approach. Human brain mapping 2: 189-210.

6.                   Gibbons RD, Lazar NA, Bhaumik DK, Sclove SL, Chen HY, et al. Estimation and classification of fMRI hemodynamic response patterns. NeuroImage 22: 804-814.

7.                   Kapur K, Roy A, Bhaumik DK, Gibbons RD, Lazar NA, et al. (2009) Estimation and classification of BOLD responses over multiple trials. Communications in Statistics-Theory and Methods 38: 3099-3113.

8.                   Pape TLB, Rosenow JM, Steiner M, Parrish T, Guernon A, et al. (2015) Placebo-controlled trial of familiar auditory sensory training for acute severe traumatic brain injury: a preliminary report. Neurorehabilitation and neural repair 29: 537-547.

9.                   Chuang KH, Chiu MJ, Lin CC, Chen JH (1999) Model-free functional MRI analysis using Kohonen clustering neural network and fuzzy C-means. IEEE transactions on medical imaging 18: 1117-1128.

10.                Ngan SC, Hu X (1999) Analysis of functional magnetic resonance imaging data using self-organizing mapping with spatial connectivity. Magnetic Resonance in Medicine 41: 939-946.

11.                Li K, Guo L, Nie J, Li G, Liu T (2009) Review of methods for functional brain connectivity detection using fMRI. Computerized Medical Imaging and Graphics 33: 131-139.

12.                Friston KJ, Frith CD, Frackowiak RSJ (1993) Time-dependent changes in effective connectivity measured with PET. Human Brain Mapping 1: 69-79.

13.                Friston KJ, Frith CD, Liddle P, Frackowiak R (1993) Functional connectivity: the principal-component analysis of large (PET) data sets. Journal of Cerebral Blood Flow & Metabolism 13: 5-4.

14.                Conturo TE, McKinstry RC, Akbudak E, Robinson BH (1996) Encoding of anisotropic diffusion with tetrahedral gradients: a general mathematical diffusion formalism and experimental results. Magnetic Resonance in Medicine 35: 399-412.

15.                Mori S, ZijlPC (2002)Fiber tracking: principles and strategies-a technical review. NMR in Biomedicine 15: 468-480.

16.                Lauzon CB, Crainiceanu C, Caffo BC, Landman BA (2013) Assessment of bias in experimentally measured diffusion tensor imaging parameters using SIMEX. Magnetic resonance in medicine 69: 891-902.

17.                Rykhlevskaia E, Gratton G,Fabiani M (2008) Combining structural and functional neuroimaging data for studying brain connectivity: a review. Psychophysiology 45: 173-187.

18.                Bhaumik DK, Roy A, Lazar NA, Kapur K, Aryal S, et al. (2009) Hypothesis testing, power and sample size determination for between group comparisons in fMRI experiments. Statistical methodology 6: 133-146.

19.                Patel RS, Bowman FD,Rilling JK (2006) A Bayesian approach to determining connectivity of the human brain. Human brain mapping 27: 267-276.

20.                Xue W, Bowman FD, Pileggi AV, Mayer AR (2015) A multimodal approach for determining brain networks by jointly modeling functional and structural connectivity. Frontiers in computational neuroscience 9: 22.

21.                Zhang L, Guindani M,Vannucci M (2015) Bayesian models for functional magnetic resonance imaging data analysis. Wiley Interdisciplinary Reviews: Computational Statistics 7: 21-41.

22.                Calhoun VD,Adali T (2009) Feature-based fusion of medical imaging data. IEEE Transactions on Information Technology in Biomedicine 13: 711-720.

23.                Calhoun V, Adali T, Liu J (2006) A feature-based approach to combine functional MRI, structural MRI and EEG brain imaging data. Conf Proc IEEE Eng Med Biol Soc 1: 3672-3675.

24.                Calhoun VD, Wu L, Kiehl KA, Eichele T,Pearlson GD (2010) Aberrant processing of deviant stimuli in schizophrenia revealed by fusion of fMRI and EEG data. Acta neuropsychiatrica 22: 127-138.

25.                Eichele T, Calhoun VD,Debener S (2009) Mining EEG-fMRI using independent component analysis. International Journal of Psychophysiology 73: 53-61.

26.                Franco R, Ling J, Caprihan A, Calhoun VD, Jung RE, et al. (2008) Multimodal and multi-tissue measures of connectivity revealed by joint independent component analysis. IEEE journal of selected topics in signal processing 2: 986-997.

27.                Shenton ME, Dickey CC, Frumin M, McCarley RW (2001) A review of MRI findings in schizophrenia. Schizophrenia research 49: 1-52.

28.                Teipel SJ, Bokde AL, Meindl T, Amaro E, Soldner J, et al. (2010) White matter microstructure underlying default mode network connectivity in the human brain. Neuroimage 49: 2021-2032.

29.                Lin FH, Mc-Intosh AR, Agnew JA, Eden GF, Zeffiro TA, et al. (2003) Multivariate analysis of neuronal interactions in the generalized partial least squares framework: simulations and empirical studies. NeuroImage 20: 625-642.

30.                Montes ME, Sosa PA, Miwakeichi F, Goldman RI, Cohen MS (2004) Concurrent EEG/fMRI analysis by multiway partial least squares. NeuroImage 22: 1023-1034.

31.                Mc-Intosh R,Lobaugh NJ (2004) Partial least squares analysis of neuroimaging data: applications and advances. Neuroimage 23: 250-263.

32.                Chen K, Reiman EM, Huan Z, Caselli RJ, Bandy D (2009) Linking functional and structural brain images with multivariate network analyses: a novel application of the partial least square method. Neuroimage 47: 602-610.

33.                Correa NM, Li YO, Adali T, Calhoun VD (2008) Canonical correlation analysis for feature-based fusion of biomedical imaging modalities and its application to detection of associative networks in schizophrenia. IEEE journal of selected topics in signal processing 2: 998-1007.

34.                Correa NM, Adali T, Li YO, Calhoun VD (2010) Canonical correlation analysis for data fusion and group inferences. IEEE signal processing magazine 27: 39-50.

35.                Sui J, Adali T, Li YO, Yang H, Calhoun VD (2012) A review of multivariate methods in brain imaging data fusion 15: 68-81.

36.                Sui J, Adali T, Yu Q, Chen J, Calhoun VD (2009) A review of multivariate methods for multimodal fusion of brain imaging data. Journal of neuroscience methods 204: 68-81.

37.                Xu L, Pearlson G, Calhoun VD (2009) Joint source based morphometry identifies linked gray and white matter group differences. Neuroimage 44: 777-789.

38.                Correa NM, Eichele T, Adalı T, Li YO, Calhoun VD (2010) Multi-set canonical correlation analysis for the fusion of concurrent single trial ERP and functional MRI. Neuroimage 50: 1438-1445.

39.                Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the royal statistical society Series B (Methodological) 289-300.

40.                Gabrieli SW,Castanon AN (2012) Conn: a functional connectivity toolbox for correlated and anticorrelated brain networks. Brain connectivity 2: 125-141.

41.                Li Y, Wang Y, Wu J, Gao S, Bukhari L, et al. (2005) Antidepressant effect on connectivity of the mood-regulating circuit: an FMRI study. Neuropsychopharmacology 30: 1334, 2005.

42.                Fletcher PT, Whitaker RT, Tao R, DuBray MB, Froehlich A, et al. (2010) Microstructural connectivity of the arcuate fasciculus in adolescents with high-functioning autism. Neuroimage 51: 1117-1125.

43.                Mahani NK, Zoethout RM, Beckmann CF, Baerends E, Kam ML, et al. (2012) Effects of morphine and alcohol on functional brain connectivity during resting state: A placebo-controlled crossover study in healthy young men. Human brain mapping 33: 1003-1018.

44.                Satterthwaite TD, Wolf DH, Loughead J, Ruparel K, Elliott MA, et al. (2012) Impact of in-scanner head motion on multiple measures of functional connectivity: relevance for studies of neurodevelopment in youth. Neuroimage 60: 623-632.

45.                Chen G, Saad ZS, Britton JC, Pine DS, Cox RW (2013) Linear mixed-effects modeling approach to FMRI group analysis. Neuroimage 73: 176-190.

46.                Jones BC, Nair G, Shea CD, Crainiceanu CM, Cortese IC, et al. (2013) Quantification of multiple-sclerosis-related brain atrophy in two heterogeneous MRI datasets using mixed-effects modeling. NeuroImage: Clinical 3: 171-179.

47.                Simpson SL,Laurienti PJ (2013) A two-part mixed-effects modeling framework for analyzing whole-brain network data. NeuroImage 113: 310-319.

48.                Bhaumik D, Jie F, Nordgren R, Bhaumik R, Sinha BK (2018) A mixed-effects model for detecting disrupted connectivities in heterogeneous data. IEEE Transactions on Medical Imaging.

49.                Laird NM,Slasor P (1997) Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data. Statistics in medicine 16: 2349-2380.

50.                Hedeker D, Gibbons RD (2006) Longitudinal data analysis. John Wiley & Sons.

51.                Fitzmaurice GM, Laird NM, Ware JH (2012) Applied longitudinal analysis. John Wiley & Sons.

52.                Beunckens C, Molenberghs G, Verbeke G, Mallinckrodt C (2006) Analyzing incomplete discrete longitudinal clinical trial data. Statistical Science 1: 52-69.

53.                Seltman HJ (2012) Experimental design and analysis.

54.                Storey JD (2002) A direct approach to false discovery rates. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64: 479-498.

55.                Storey JD,Tibshirani R (2003) Statistical significance for genomewide studies. Proceedings of the National Academy of Sciences 100: 9440-9445.

56.                Genovese CR, Wasserman L (2002) Operating characteristics and extensions of the false discovery rate procedure. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64: 499-517.

57.                Sun W, Cai TT (2007) Oracle and adaptive compound decision rules for false discovery rate control. Journal of the American Statistical Association 102: 901-912.

58.                Benjamini Y, Hochberg Y (2000) On the adaptive control of the false discovery rate in multiple testing with independent statistics. Journal of educational and Behavioral Statistics 25: 60-83.

59.                Tibshirani R, Storey JD,Tusher V (2001) Empirical Bayes analysis of a microarray experiment. Journal of the American statistical association 96: 1151-1160.

60.                Jin J, Cai TT (2007) Estimating the null and the proportion of nonnull effects in large-scale multiple comparisons. Journal of the American Statistical Association 102: 495-506.

61.                Hamilton JP, Etkin A, Furman DJ, Lemus MG, Johnson RF (2012) Functional neuroimaging of major depressive disorder: a meta-analysis and new integration of baseline activation and neural response data. American Journal of Psychiatry 169: 693-703.

62.                Rive M, Rooijen GV, Veltman DJ, Phillips ML, Schene AH, et al. (2013) Neural correlates of dysfunctional emotion regulation in major depressive disorder. A systematic review of neuroimaging studies. Neuroscience &Biobehavioral Reviews 37: 2529-2553.

63.                Ma Y (2015) Neuropsychological mechanism underlying antidepressant effect: a systematic meta-analysis. Molecular psychiatry 20: 311.

64.                Benjamini Y, Yekutieli D (2011) The control of the false discovery rate in multiple testing under dependency. Annals of statistics 1165-1188.

65.                Sarkar SK (2008) Some results on false discovery rate in stepwise multiple testing procedures. Annals of statistics 1: 239-257.

66.                Sarkar SK (2008) On methods controlling the false discovery rate. Sankhya: The Indian Journal of Statistics, Series A 70: 135-168.

67.                Kim KI,Wiel MA (2008) Effects of dependence in high-dimensional multiple testing problems. BMC bioinformatics 9: 114.