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In linear combination with the task regressor, this "PPI regressor" picks up any trial-to-trial deviation from the mean task-related activation that is common between seed voxel and target voxel.
In clinical trials, deviations from protocol and losses to follow-up often lead to the exclusion of some randomised patients from the analysis.
Notably, we found that for hyperpolarizations elicited by 10 ms-duration light pulses during a λ = 100 ms Poisson train, the mean amplitude was −4.56 mV (averaged across trials and neurons), but the trial-to-trial standard deviation of this amplitude was only 400 µV (averaged across neurons, Fig 3Ci and Fig. 3Di, left side).
This resulted in on average 117 trials (±37 trials, standard deviation) remaining for further analysis, out of the available 240 trials per session.
We independently reviewed each eligible trial for deviation.
All comparisons I C k, l can be expressed in terms of basic parameters a k, P. Prior distributions need to be specified for the basic parameters, for b and for the between trial standard deviation σ α.
Each comparison of drug k versus drug l, I C k, l, can be written in terms of basic parameters d k, P. Prior distributions are required for basic parameters and between trial standard deviation σ δ.
The model calculates log odds ratios (LORs) for each study, δ i, for which random effects are assumed yielding an overall log odds ratio estimate d and a between trial standard deviation σ δ.
Between trials we assume random effects, as before and each comparison I C k, l can be written in terms of basic parameters d k, P. Prior distribution need to be defined for basic parameters and between trial standard deviation σ δ.
A uniform distribution was chosen for the between trial standard deviation parameter σ δ / α, as proposed by Gelman [ 29]. (14) σ δ / α ∼ dunif (0, 2 ) To test whether the range of the uniform prior was chosen appropriately the analysis has been rerun using wider ranges (dunif 0,5) and dunif 0,7)) and estimates did not change.
The models described above require prior distributions for the baseline treatment effect, for the effect due to MTX, for the between trial standard deviation and in the binomial models for the log odds of response in the control group and the meta-regression parameter.
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