A Bayesian elicitation of veterinary beliefs regarding systemic dry cow therapy: variation and importance for clinical trial design

Abstract

The two key aims of this research were: (i) to conduct a probabilistic elicitation to quantify the variation in veterinarians' beliefs regarding the efficacy of systemic antibiotics when used as an adjunct to intra-mammary dry cow therapy and (ii) to investigate (in a Bayesian statistical framework) the strength of future research evidence required (in theory) to change the beliefs of practising veterinary surgeons regarding the efficacy of systemic antibiotics, given their current clinical beliefs. The beliefs of 24 veterinarians in 5 practices in England were quantified as probability density functions. Classic multidimensional scaling revealed major variations in beliefs both within and between veterinary practices which included: confident optimism, confident pessimism and considerable uncertainty. Of the 9 veterinarians interviewed holding further cattle qualifications, 6 shared a confidently pessimistic belief in the efficacy of systemic therapy and whilst 2 were more optimistic, they were also more uncertain. A Bayesian model based on a synthetic dataset from a randomised clinical trial (showing no benefit with systemic therapy) predicted how each of the 24 veterinarians' prior beliefs would alter as the size of the clinical trial increased, assuming that practitioners would update their beliefs rationally in accordance with Bayes' theorem. The study demonstrated the usefulness of probabilistic elicitation for evaluating the diversity and strength of practitioners' beliefs. The major variation in beliefs observed raises interest in the veterinary profession's approach to prescribing essential medicines. Results illustrate the importance of eliciting prior beliefs when designing clinical trials in order to increase the chance that trial data are of sufficient strength to alter the clinical beliefs of practitioners and do not merely serve to satisfy researchers.

Fig. 1

Map of England showing all 13 veterinary practices (clusters) within the sample area; clusters visited are marked in black (red, colour version). Nottingham is marked in light grey (green, colour version).

Fig. 2

Joint probability distributions (θ₁, θ₂) for each individual veterinarian displayed as contour plots and grouped by veterinary practice (cluster). Treatment 1 = intra-mammary dry cow therapy (IDCT) alone. Treatment 2 = systemic antibiotics plus IDCT. θ₁ = the probability of cure with treatment 1 and refers to commercial dairy cows at calving, who at the point of drying-off received treatment 1 and had chronic (somatic cell count ≥400,000 cells per ml) intra-mammary infections (≥1 quarters) due to (unknown) major pathogens; and similarly, θ₂ = the probability of cure with treatment 2. The black diagonal line denotes θ₁ = θ₂.

Fig. 3

Classical scaling of the data. Each number represents an individual veterinarian, with those from the same practice sharing the same first digit (e.g. 11, 12, 13, 14 all worked for the same practice, labelled “1”). A square box highlights those holding extra qualifications. “A” and “B” represent the clinical academics from the University of Nottingham. Theta 3 = θ₃ = the probability of cure with treatment 2, given treatment 1 has failed.

Fig. 4

The prior beliefs (column 1) and posterior beliefs (columns 2–4) 95% credible intervals for the odds ratio for the 24 veterinarians. The likelihood was based on synthetic data from a single clinical trial that showed no difference between treatment 1 and 2 and total trial size = 100, 500 and 1000 infected cows. An odds ratio ≥ 1.5 was the threshold used for a “clinically worthwhile benefit” with treatment 2 compared to treatment 1 (i.e. the adjunct use of systemic antibiotics for dry cow therapy). Note: The choice of x-axis scale truncates 8 of the prior credible intervals at their upper range, but this choice facilitates comparison with the posterior predicted beliefs.