Methods to convert continuous outcomes into odds ratios of treatment response and numbers needed to treat: meta-epidemiological study

Int J Epidemiol. 2012 Oct;41(5):1445-59. doi: 10.1093/ije/dys124.


Background: Clinicians find standardized mean differences (SMDs) calculated from continuous outcomes difficult to interpret. Our objective was to determine the performance of methods in converting SMDs or means to odds ratios of treatment response and numbers needed to treat (NNTs) as more intuitive measures of treatment effect.

Methods: Meta-epidemiological study of large-scale trials (≥ 100 patients per group) comparing active treatment with placebo, sham or non-intervention control. Trials had to use pain or global symptoms as continuous outcomes and report both the percentage of patients with treatment response and mean pain or symptom scores per group. For each trial, we calculated odds ratios of observed treatment response and NNTs and approximated these estimates from SMDs or means using all five currently available conversion methods by Hasselblad and Hedges (HH), Cox and Snell (CS), Furukawa (FU), Suissa (SU) and Kraemer and Kupfer (KK). We compared observed and approximated values within trials by deriving pooled ratios of odds ratios (RORs) and differences in NNTs. ROR <1 and positive differences in NNTs imply that approximations are more conservative than estimates calculated from observed treatment response. As measures of agreement, we calculated intraclass correlation coefficients.

Results: A total of 29 trials in 13 654 patients were included. Four out of five methods were suitable (HH, CS, FU, SU), with RORs between 0.92 for SU [95% confidence interval (95% CI), 0.86-0.99] and 0.97 for HH (95% CI, 0.91-1.04) and differences in NNTs between 0.5 (95% CI, -0.1 to -1.6) and 1.3 (95% CI, 0.4-2.1). Intraclass correlation coefficients were ≥ 0.90 for these four methods, but ≤ 0.76 for the fifth method by KK (P for differences ≤ 0.027).

Conclusions: The methods by HH, CS, FU and SU are suitable to convert summary treatment effects calculated from continuous outcomes into odds ratios of treatment response and NNTs, whereas the method by KK is unsuitable.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Clinical Trials as Topic / methods*
  • Clinical Trials as Topic / statistics & numerical data*
  • Data Interpretation, Statistical*
  • Humans
  • Numbers Needed To Treat
  • Odds Ratio
  • Pain Management / methods
  • Pain Management / statistics & numerical data
  • Research Design / statistics & numerical data*