A Bayesian perspective on sensory and cognitive integration in pain perception and placebo analgesia

Abstract

The placebo effect is a component of any response to a treatment (effective or inert), but we still ignore why it exists. We propose that placebo analgesia is a facet of pain perception, others being the modulating effects of emotions, cognition and past experience, and we suggest that a computational understanding of pain may provide a unifying explanation of these phenomena. Here we show how Bayesian decision theory can account for such features and we describe a model of pain that we tested against experimental data. Our model not only agrees with placebo analgesia, but also predicts that learning can affect pain perception in other unexpected ways, which experimental evidence supports. Finally, the model can also reflect the strategies used by pain perception, showing that modulation by disparate factors is intrinsic to the pain process.

Figure 1. Correlation between subjects’ expectation of analgesia and placebo analgesia ratings.

The expectation of analgesia / effectiveness of conditioning (parameter w) was estimated fitting the model on individual subjects’ placebo data. For Experiment 1 (A) we fitted also, on subjects’ data, the dispersion of the prior distribution of the effect of the stimuli (Eq. 5), while for Experiment 2 (B) the dispersion entered in the model was the one estimated on Experiment 1 data. The plots show a positive correlation between expectation/conditioning and the size of the placebo effect. r: Pearson’s product moment correlation coefficient, tested for positive correlation. Var_res = residual variance. (n = 24, Experiment 1; n = 31, Experiment 2).

Figure 2. Model comparison.

(A) Posterior probability and (B) Bayes factors for the three models we compared, showing a substantial evidence in favour of the full Bayesian decision model we developed. (C) Posterior probability of the three models in each subject (n = 31), showing that in most of the subjects the data support the fBD model. Models are identified by the same colors in (A) and (C). nL = no learn model; sB = simple Bayesian model; fBD = full Bayesian decision model.

Figure 3. Model predictions of pain rating.

Probability distributions before (A, B) and after (A, B, C) conditioning. (A) Posterior probability distributions of pain rating given the stimulus intensity. The color scale codes for relative probabilities (scaled so the maximum equals 1). Orange curves indicate maxima (most probable pain rating), also reported in (B). Vertical lines highlight some of the distributions shown, with same colors and line types, in (C) and in Figs. 4C and 5A. (B) Most probable rating given a stimulus, for each possible stimulus: before training (pre), and after training. Values after training are shown for stimuli paired with a cue (C_g: green cue; C_r: red cue) or not (noCue). Horizontal lines indicate the estimated pain rating for high stimuli paired with red (red dotted line, overt no-treatment) and green (green dashed line, placebo condition) cues, and for low stimuli paired with green (green dotted line, overt treatment) and red (brown dashed line, nocebo condition) cues. (C) Prior probability distribution (prior), and posterior probability distributions conditioned on the high stimulus (S_h), on the green cue (C_g), and on both the high stimulus and the green cue together (C_gS_h, placebo).

Figure 4. Placebo effect.

(A, B) Experimental placebo effect after conditioning, observed in the two samples of participants recruited for Experiment 1 (left columns) and Experiment 2 (right columns). (A) Mean pain scoring, rated through a visual analogical scale (VAS), for high electrical stimuli paired with red (C_rS_h, overt no-treatment) or green (C_gS_h, placebo condition) cues. (B) Mean placebo analgesic effect, as percent difference relative to pain rating with overt no-treatment. (C) Model predictions: box-plot and 100 random draws (top) from the posterior probability distributions (bottom) for high stimuli paired with red (C_rS_h, no-treatment) or green (C_gS_h, placebo) cues. The posterior probability distribution for the low stimulus paired with the green cue is also plotted (C_gS_l, overt treatment). Δ = observed placebo analgesia; $\widehat{\Delta }$ = predicted placebo analgesia (difference between the means (◊) of the no-treatment and placebo samples). ***P < 0.001 (Experiment 1: P = 5.96 × 10⁻⁸, n = 24; Experiment 2: P = 2.00 × 10⁻⁸, n = 31; (one tail Wilcoxon signed-rank test); all error bars represent s.d.

Figure 5. Model predictions of pain rating with and without cues, after conditioning.

(A) 100 random draws (top) from posterior probability distributions (bottom) for high (noCS_h), low (noCS_l) and intermediate (noCS_m) stimulus intensities, paired with no cue. (B) Probability distributions of pain rating obtained with different effectiveness of conditioning (w = weight factor attributed to conditioning), and 20 random draws from each probability distribution. Predictions for intermediate stimuli paired with no cue (mid_blue stimuli, left) are displayed aside those for high stimuli (right) paired with green (green circles and curves, placebo condition) and red (red circles and curves, overt no-treatment condition) cues. ◊ = means of each sample.

Figure 6. Ratings of pain induced by intermediate intensity electrical stimuli paired with no cue.

(A) 31 subjects’ pain rating (y axis) scaled, for each subject, to the mean of pain ratings for high intensity stimuli in the same stimulation block); subjects are ordered according to the magnitude of the placebo effect (x axis, the magnitude is relative to the mean of pain ratings for high intensity stimuli paired with red cues). Each subject rated 8 stimuli and is represented with a different color and symbol. The square box delimits subjects with no significant placebo effect (tested at P < 0.05; n = 8; one tail Mann-Whitney rank-sum test). (B) Correlation between individual clustering measures of pain rating (cluster distance, first column; cluster separation index, second column; probability that the data followed a bimodal distribution, third column) and the magnitude of the placebo effect (first row); or the expectation of analgesia (parameter w) estimated by the model on placebo data (second row). Cluster analysis: K-means method for 2 clusters; test of bimodal distribution vs unimodal: Bayesian hypothesis comparison; correlation analysis: Pearson’s product moment correlation coefficient, tested for positive correlation. (n = 31). (See also Table 1).