Efficiency in Experimental Design Catherine Jones MfD2004

Overview What is efficiency? How can we maximise it?

What is efficiency? SPM uses the General Linear Model: Y = Xβ + ε The significance of the t & F statistics reflect the variance of β and the size of the error. As the variance of β decreases the statistical significance increases. There are two ways to reduce the variance of β: (1) data (2) design matrix. Efficiency is the ability to estimate β, given the design matrix (X) you have specified i.e. it reflects how well your experimental design can answer the question you are interested in. As the efficiency of the model increases, the variance of β decreases (and vice versa). Efficiency can be calculated because the variance of β is proportional to the variance of X 1=Var(X) =X T X Var(β)

Therefore… Efficiency is the process of maximising your chance of finding the experimental effect It is defined by: 1 e(c,X) c T (X T X) -1 c where e = efficiency, c = contrast, X = design matrix And is thus specific to a particular contrast

Ways to maximise efficiency… Event related vs Blocked designs Sequencing of events (i.e. the ordering) Spacing of events (i.e. the timing) Spacing of events in relation to fMRI data collection Temporal filtering Psychological validity

First… a bit of background info…

Creating a model of the neural response The stimulus model predicts the pattern of neural activity, but the BOLD response does not resemble this neat on/off pattern. Thus, the stimulus model is convolved with the Haemodynamic Response Function (HRF), a stereotyped model of the BOLD signal following an event, to give a regressor that is entered into the Design Matrix. The HRF reflects that following neural activity, there is a peak in the BOLD signal after approx. 5s, which persists for approx. 30s. Convolved design and HRF Brief Stimulus Undershoot Initial Undershoot Peak

Event related vs Blocked designs Blocked designs // PET  Types of trials are ‘blocked’ together e.g. AAAAA BBBBB AAAAA. Also described as an Epoch design. Event related designs // ERPs  Types of trials are interleaved and each trial is modelled separately as an ‘event’ e.g. AABABBAB

Advantages of efMRI Can randomise or counterbalance trial order to reduce contextual bias and minimise differences related to cognitive ‘set’ or strategy use. Some experimental designs cannot be blocked e.g. oddball designs. Can use post-hoc classification of trials e.g. separately model trials with correct or incorrect responses, following post-scanning testing or depending on subjective perception. Improves temporal resolution such that you can look at events on a shorter time scale.

Disadvantage of efMRI There is typically less efficiency in event related designs

Efficiency related to the sequencing of events Stochastic designs: at each point at which an event could occur there is a specified probability of that event occurring. The timing of when the events occur is specified. Non-occurrence = null event. Deterministic designs: the occurrence of events is pre- determined. The variable deterministic design i.e. a blocked design, is the most efficient.

But what if I want to use efMRI? When using an efMRI design, mini runs of the same stimuli may be the most efficient. You can modulate the probability of the events using a sine wave i.e. a dynamic stochastic presentation.

Joel’s example of different stimulus presentations Blocked design Fully randomised Dynamic stochastic A B C Tasks Efficiency calculation

Efficiency related to the spacing of events Stimulus Onset Asynchronies (SOAs) are the units of time between subsequent events i.e. they corresponds to the inter-stimulus interval. Generally speaking, SOAs that are small (SOA min ) and randomly distributed are the most efficient. The SOAs are generally shorter than the BOLD response, but this overlap is modelled by the HRF - successive responses are assumed to add in a linear fashion. But, very short SOAs (< 1s, Friston et al, 1999) are not advisable as the predicted additive effects upon the HRF of two closely occurring stimuli break down. +≠ (Linear Time Invariant model)

For random designs (i.e. ABBBAABAB) efficiency in detecting differential effects between event types (e.g. A-B) increases with shorter SOAs. SOA min is best! Note that it is more efficient to have relatively longer SOAs with main effect contrasts (i.e. A+B).

If you include null events (a third, unmodelled event type) then efficiency is slightly compromised for A-B but increases for contrast A+B, in which the contrast is measured relative to baseline. Now, SOA min is the most efficient for A-B and A+B. This is shift in efficiency is related to the fact that null events allow the baseline value to be lower and therefore the difference between A+B and the baseline is bigger.

Some designs require alternating presentation of stimuli (i.e. ABABABAB), in this case the most efficient SOA is approx. 8s. Some designs require a longer SOA, if the SOA needs to be >8s then it may be best to go for a permuted design (i.e. pseudorandom ABBABABAAB).

Timing of the SOAs in relation to the TR If the TR (Repetition Time of slice collection) is divisible by the SOA then data collected for each event will be from the same slices, at the same points along the HRF. Therefore, either choose a TR and SOA that are not divisible or introduce a ‘jitter’ such that the SOA is randomly shifted. Scans TR = 4s Stimulus (synchronous) SOA=8s Stimulus (asynchronous) SOA=6s Stimulus (random jitter)

Temporal Filtering: The High Pass Filter A temporal filter is used in fMRI to get rid of noise, thus increasing the efficiency of the data. Non-neuronal noise tends to be of low- frequency, including ‘scanner drift’ and physiological phenomenon. Applying a high pass filter means that parameters that occur at a slow rate are removed from the analysis. The default high pass filter in SPM is 128s, thus if you have experimental events occurring less frequently than once every 128s then the associated signal will be removed by the filter!!

Don’t forget… the tasks! A studies efficiency is only as good as the tasks that have been chosen. Typically, control tasks should control for all processes in the experimental task, bar the component of interest. i.e. There should be as few explanations for your resulting data as possible.

Summary Blocked designs are generally the most efficient, but blocked designs have restrictions. For event-related designs, dynamic stochastic presentation of stimuli is most efficient. However, the most optimal design for your data depends on the SOA that you use. The general rule is the smaller your SOA the better, but sometimes a small SOA may not be possible. Also, the most optimal design for one contrast may not be optimal for another e.g. the inclusion of null events improves the efficiency of main effects at short SOAs, at the cost of efficiency for differential effects. Finally, there is no point scanning two tasks to look for differences between them if they are too different or too similar.

A big thank you to… Joel and Lucy