Biostatistics calculations from a psychiatry abstract (MEQ)

(i) Rates and NNT. CER (placebo response) = 34/100 = 0.34. EER = 52/100 = 0.52. Absolute benefit = 0.52 − 0.34 = 0.18. RR = 0.52/0.34 ≈ 1.53. RRR for non-response framing is less natural here; for response, relative increase = 0.18/0.34 ≈ 53% of the control response rate — note this is not "53% of patients improved." NNT = 1/0.18 ≈ 5.6 → about 6 patients treated for 8 weeks for one extra responder.^[1][6]

(ii) Odds vs risk. Odds drug = 52/48; odds placebo = 34/66; OR = (52/48)/(34/66) ≈ 2.1, which can be spun as roughly a doubling of odds — different from RR ≈ 1.53 and from a 53% relative risk increase. OR ≈ RR only when the outcome is uncommon; at 34–52% response, OR is not a safe substitute for RR.^[2]

(iii) p-value. p = 0.01 means that if H0 of no difference in response proportions (and model assumptions) were true, data this extreme or more would occur about 1% of the time. It is not the probability Drug X does not work, nor proof of clinical importance.^[3]

(iv) Mean difference CI. −2.8 points (95% CI −4.9 to −0.7) excludes zero → statistically significant mean benefit; magnitude is modest and may or may not exceed an MCID depending on scale and context — separate statistical from clinical importance; continuous outcomes do not give NNT without dichotomisation.^[4]

(v) Base rates. PPV depends on prevalence. A sample of trial enrolees with known MDD is not a screening population; exporting clinic PPV to 3% prevalence primary care without Bayes/recalculation is base-rate neglect and will overstate the chance a positive screen is true disease.^[5]