Detection Power, Estimation Efficiency, and Predictability in Event-Related fMRI

Abstract

Experimental designs for event-related functional magnetic resonance imaging can be characterized by both their detection power, a measure of the ability to detect an activation, and their estimation efficiency, a measure of the ability to estimate the shape of the hemodynamic response. Randomized designs offer maximum estimation efficiency but poor detection power, while block designs offer good detection power at the cost of minimum estimation efficiency. Periodic single-trial designs are poor by both criteria. We present here a theoretical model of the relation between estimation efficiency and detection power and show that the observed trade-off between efficiency and power is fundamental. Using the model, we explore the properties of semirandom designs that offer intermediate trade-offs between efficiency and power. These designs can simultaneously achieve the estimation efficiency of randomized designs and the detection power of block designs at the cost of increasing the length of an experiment by less than a factor of 2. Experimental designs can also be characterized by their predictability, a measure of the ability to circumvent confounds such as habituation and anticipation. We examine the relation between detection power, estimation efficiency, and predictability and show that small increases in predictability can offer significant gains in detection power with only a minor decrease in estimation efficiency.

Optimization of experimental design in fMRI: a general framework using a genetic algorithm

“…If a deconvolution approach is used, as it is in Dale's (1999) initial simulations, the efficiency reflects the power in estimating the shape of the hemodynamic response (Dale, 1999;Liu et al, 2001). If a basis set of hemodynamic response functions (HRFs) is used (Dale, 1999) or a single assumed HRF (Liu et al, 2001) is used, the efficiency statistic reflects the detection power of the design or the ability to correctly estimate the height parameter of each basis function.…”

“…If a basis set of hemodynamic response functions (HRFs) is used (Dale, 1999) or a single assumed HRF (Liu et al, 2001) is used, the efficiency statistic reflects the detection power of the design or the ability to correctly estimate the height parameter of each basis function. Liu et al (2001) demonstrated that there is an inherent trade-off between efficiency of estimating an unknown HRF shape and detection power of a signal using an assumed HRF. A single event train cannot maximize both, but pseudorandom designs whose predictors contain both high and low spectral frequencies (i.e., both blocks and isolated events) may provide a reasonable ability to estimate both the shape and the magnitude of the hemodynamic response.…”

“…Sampling at different TRs results in an equivalent scale change in the response estimates and standard errors, leaving the resulting test statistic invariant to sampling rate. However, when block design predictors (or repeated, closely spaced events) are mixed with individual events (for an example, see Liu et al, 2001, Fig. 4), the situation becomes problematic: the scaling of the block portion of the predictor relative to the individual events is arbitrary, depending on the TR, and linear convolution can yield very poor predictions of the signal response.…”

“…If X consists of a deconvolution matrix (Glover, 1999;Hinrichs et al, 2000;Menon et al, 1998), and C is the identity matrix, Eq. (7) gives the estimation efficiency for the shape of the HRF (Liu et al, 2001). If C is instead replaced by a basis set of canonical HRF vectors, then the expression evaluates the efficiency of estimating the basis set (Dale, 1999).…”

“…Event-related fMRI is a major advance in methodology because of the flexibility it allows in experimental design and the specificity with which particular mental processes may be studied; but the space of possible design choices for a given study is large and complex, and it is difficult to know which parameter values are best. The framework for optimization we present here is general and can be used to maximize statistical and nonstatistical (i.e., psychological validity) properties of fMRI designs using novel criteria or existing criteria for design fitness (e.g., Dale, 1999;Friston et al, 1999Friston et al, , 2000aJosephs and Henson, 1999;Liu et al, 2001). Previous research on optimization has considered only a narrow range of possible parameter values and design types, often excluding factors such as temporal autocorrelation of fMRI noise, nonlinearity in observed signal, the presence of multiple conditions and multiple contrasts of interest within a single experiment, experiment-related factors such as psychological probes that influence the design but are difficult to model, and factors such as counterbalancing of stimuli and repeated presentations that influence the psychological validity of the task.…”