Evaluation of mixed effects in event-related fMRI studies: impact of first-level design and filtering M. Bianciardi, A. Cerasa, F. Patria, and G.E. Hagberg * Functional Neuroimaging Laboratory, Santa Lucia Foundation I.R.C.C.S., Rome, Italy Received 21 August 2003; revised 23 February 2004; accepted 25 February 2004 Available online 6 May 2004 With the introduction of event-related designs in fMRI, it has become crucial to optimize design efficiency and temporal filtering to detect activations at the 1st level with high sensitivity. We investigate the relevance of these issues for fMRI population studies, that is, 2nd- level analysis, for a set of event-related fMRI (er-fMRI) designs with different 1st-level efficiencies, adopting three distinct 1st-level filtering strategies as implemented in SPM99, SPM2, and FSL3.0. By theory, experiments, and simulations using physiological fMRI noise, we show that both design and filtering impact the outcome of the statistical analysis, not only at the 1st but also at the 2nd level. There are several reasons behind this finding. First, sensitivity is affected by both design and filtering, since the scan-to-scan variance, that is the fixed effect, is not negligible with respect to the between-subject variance, that is the random effect, in er-fMRI population studies. The impact of the fixed effects error on the sensitivity of the mixed effects analysis can be mitigated by an optimal choice of er-fMRI design and filtering. Moreover, the accuracy of the 1st- and 2nd-level parameter estimates also depend on design and filtering; especially, we show that inaccuracies caused by the presence of residual noise autocorrelations can be constrained by designs that have hemody- namic responses with a Gaussian distribution. In conclusion, designs with both good efficiency and decorrelating properties, for example, such as the geometric or Latin square probability distributions, combined with the ‘‘whitening’’ filters of SPM2 and FSL3.0, give the best result, both for 1st- and 2nd-level analysis of er-fMRI studies. D 2004 Elsevier Inc. All rights reserved. Keywords: er-fMRI; Mixed effects; Design efficiency; Temporal filtering Introduction The importance of optimizing design efficiency and temporal filtering in event-related fMRI (er-fMRI) is well-known to detect activations at the 1st level with high sensitivity (Birn et al., 2002; Dale, 1999; Friston et al., 1999b, 2000; Hagberg et al., 2001; Liu et al., 2001; Mechelli et al., 2003; Woolrich et al., 2001). The aim of this work is to investigate these issues for fMRI population studies, that is for 2nd-level analyses. In this context, so-called random effects analysis is extensively used in functional neuro- imaging at the population level and is based on the assumption that the between subject/session variance (random effect) is greater than the within-session variance (fixed effect) (Friston et al., 1999a; Holmes and Friston, 1998). However, in fMRI studies, a pure random effects analysis is strictly speaking at hand only if we can extend our scanning time infinitely (Worsley et al., 2002). Hence, a more appropriate term for this kind of analysis is mixed effects analysis reflecting the possibility that although the be- tween-subject variance sometimes dominates, both error terms may impact higher-order analysis. Consequently, if the assumption of dominating random effects does not hold true, then the outcome of the 2nd-level mixed effects analysis should be influenced by differences in design efficiency and filtering at the 1st level. In the present paper, we investigate whether mixed effects sensitivity varies with design efficiency and evaluate if 1st-level filtering strategies modulate such effects. Since mixed effects analysis is performed directly on 1st-level parameter estimates, attention is addressed to the 1st-level estimation process. In this context, we show that high 1st-level precision of the parameter estimation reduces the fixed effect at the 2nd level and hence plays a crucial role for inference for mixed effects sensitivity. We also show how noise-sphericity modulates the accuracy of the parameter estimates and investigate how noise and design char- acteristics may influence this factor. To start with, we derive theoretical predictions regarding the impact of design and filtering on 1st- and 2nd-level precision and accuracy of the parameter estimates. We then perform mixed effects analyses of a set of experimental event-related fMRI studies with different design efficiencies, using three distinct 1st-level filtering strategies as implemented in SPM99, SPM2, and FSL3.0. We then scrutinize 1st-level parameter estimates and evaluate their dependence on design efficiency and filtering, both by experiments and simulations. In simulations, this analysis is extended to include block design and fixed inter-event-interval (IEI) er-fMRI studies. Finally, we identify features of design and noise distributions that improve the precision and accuracy of 1st- level parameter estimates. Portions of this work have been published previously in abbreviated form (Bianciardi et al., 2003). 1053-8119/$ - see front matter D 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2004.02.039 * Corresponding author. Functional Neuroimaging Laboratory, Santa Lucia Foundation I.R.C.C.S., Via Ardeatina 306, 00179, Rome, Italy. Fax: +39-06-51501213. E-mail address: g.hagberg@hsantalucia.it (G.E. Hagberg). Available online on ScienceDirect (www.sciencedirect.com.) www.elsevier.com/locate/ynimg NeuroImage 22 (2004) 1351 – 1370