Pharmacy & Therapeutics - December 2008 - (Page 702)

Interpreting Estimates of Treatment Effects When SMDs of similar studies have CIs that do not overlap, this suggests that the SMDs probably represent true differences between the studies. SMDs that have overlapping CIs suggest that the difference in magnitude of the SMDs might not be statistically significant. Cohen5 offered the following guidelines for interpreting the magnitude of the SMD in the social sciences: small, SMD = 0.2; medium, SMD = 0.5; and large, SMD = 0.8. 1.0 .9 .8 .7 .6 .5 0 1 2 3 Standardized mean difference 4 Probability of Benefit The probability-of-benefit (POB) statistic was originally proposed by McGraw and Wong.6 They called it the common language effect size statistic, which they defined as the probability that a randomly selected score from one population would be greater than a randomly selected score from another. For treatment research, this becomes the probability that a randomly selected treated patient would show a level of improvement exceeding that of a randomly selected placebo patient. To calculate the POB for continuous data, we first compute: Z SMD 2 Figure 1 Comparison of the standardized mean difference and the probability of benefit. (2) Number needed to treat This Z statistic is normally expressed as a standard normal distribution, and the POB is computed as the probability that a randomly selected standard normal variable is less than Z. The POB is equivalent to the area under the receiver operating characteristic curve and is also proportional to the Mann– Whitney statistic comparing drug and placebo outcome scores.7,8 Further details and prior applications of the method are available elsewhere.9–15 For binary variables, the POB statistic can be computed from the absolute difference (AD) in treatment response as follows: POB = 0.5(AD+1). AD is computed by subtracting the percentage of patients who improved with placebo from the percentage who improved with treatment. Using the formula in Equation 2, we can show how the POB corresponds to varying values of the SMD. Stata Corporation’s statistical software was used to make the computations.16 Figure 1 presents the results. When the SMD equals zero, the probability that treatment outperforms placebo is 0.5, which is no better than the flip of a coin. When the SMD equals 1, the probability that treatment outperforms placebo is 0.76. The incremental change in the probability of benefit is small for SMDs greater than two. In Equation 3, the denominator of the NNT is the absolute difference, which is also used to compute the POB for binary variables. As Kraemer and Kupfer showed, NNT can be defined for continuous variables if we assume that a treated patient has a successful outcome if the outcome is better than a randomly selected nontreated patient.10 We can then compute: NNT = 1 2 (POB 1) Probability of benefit (4) Using these formulas in Equations 2 and 4, we can show how the POB corresponds to varying values of the NNT. Stata’s software was used to make the computations.16 Figure 2 presents the results. As the SMD approaches zero, the NNT becomes very large. When the SMD = 1, the NNT = 2. As with the POB, the incremental change in the NNT is small for SMDs greater than two. Ideally, the NNT would be very small. For example, when NNT = 2, for every two patients who are treated, one will have a good outcome. The NNT exceeds one for effective therapies 20 15 10 Number Needed to Treat Another statistic that has a straightforward interpretation is the number needed to treat (NNT), or the number of patients who must be treated to prevent one adverse outcome. The poor outcome would be not showing improvement in symptoms. The NNT is computed as follows: 100 percent improved with treatment percent improved with placebo 5 0 0 1 2 3 4 Standardized mean difference NNT = (3) Figure 2 Comparison of the standardized mean difference and the number needed to treat. 702 P&T® • December 2008 • Vol. 33 No. 12

Table of Contents Feed for the Digital Edition of Pharmacy & Therapeutics - December 2008

Pharmacy & Therapeutics - December 2008 Contents Editorial Medication Errors Prescription: Washington New Drugs/Drug News/ New Medical Devices Drug Forecast Interpreting Estimates of Treatment Effects Chemotherapy Foundation Symposium XXVI: Innovative Cancer Therapy for Tomorrow Third Annual Onmark National Payor/Provider Forum Fourth Annual Ophthalmic Drug Development and Delivery Summit Classification and Pharmacological Management Of Obesity CE Test and Forms Season’s Greetings: Thanks to Our Readers and Reviewers

Pharmacy & Therapeutics - December 2008

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