‘1-IN-X' RATIOS LEAD TO MEDICAL PROBABILITY OVERESTIMATION

Purpose: Recent evidence showed that ‘1-in-X’ ratios (e.g., 1 in 12) triggered higher subjective probability than ‘N-in-X*N’ ratios (e.g., 3 in 36) when interpreting health-related risks on a verbal probability scale (hereafter, ‘1-in-X’ effect), however it is not clear whether the ‘1-in-X’ formats overestimate or the ‘N-in-X*N’ formats underestimate the objective probabilities. Therefore, we aimed to establish which format lead to more accurate probability perception.

Method(s): In five parallel-designed experiments, 975 participants from a general adult population (54.7% women, M = 35.0, SD=11.2 years old) were randomly allocated to one of five experiments. Each experiment followed a 2(format) × 4(scenario) mixed design. In each experiment, participants read the risk of contracting a disease during their trip abroad. The risk was presented either in a ‘1-in-X’ or ‘N-in-X*N’ format in four scenarios randomly presented: malaria, Ebola, flu, Lyme disease. Participants assessed the risk on either a verbal probability scale (Exp. 1), a numerical probability scale (0-100%, Exp. 2), an arbitrary frequency scale (X out of 286, Exp. 3), a numerical probability scale with a delayed presentation (Exp. 4) or an arbitrary frequency scale with a delayed presentation (Exp. 5). Participants also made decision whether to cancel the trip to respective countries.

Result(s): We replicated the ‘1-in-X’ effect when probability perception was measured with a verbal probability scale (Exp. 1, Hedges’ g = 0.63, 95% CI[0.35, 0.91]). In the remaining numerical scale experiments (Exp. 2-5), we found that both ratio formats led to probability over-estimation (on average by 5.2%, 95% CI[2.1%, 8.4%], estimated in a multilevel meta-analysis). The ‘1-in-X’ formats triggered consistently higher subjective probability than ‘N-in-X*N’ formats: multi-level meta-analytical effect was g = 0.18, 95% CI[0.05, 0.32]. The ‘1-in-X’ ratio formats affected participants’ decision-making as they led to a higher willingness to cancel the trip abroad, aggregated effect across scenarios in Exp. 1-5, g= 0.17, 95% CI[0.04, 0.29].

Conclusion(s): Participants overestimated actual objective probabilities in both ratio formats. Since the ‘1-in-X’ effect was observed in all numerical scales (Exp. 2-5), bigger overestimation occurred in the ‘1-in-X’ format conditions. Health professionals should use ‘1-in-X’ formats with caution, because they make medical probabilities look bigger than they really are and, in turn, affect related decision-making.