Re: The number needed to treat: a clinically useful measure of treatment effect
This 1995 article by Cook and Sackett [1] is one of continuing significance at least because it underlies the assumption in the guidance for adjusting for baseline risk in the calculation of number needed to treat provided by the Clinical Evidence Glossary that an observed relative risk reduction (RRR) effected by an intervention will commonly be constant across different baseline risks.[2] The article may also underlie the statement in the Glossary’s guidance for calculating risks that “RRR is usually constant across a range of absolute risks.”[3]
I suspect that such empirical basis that may exist for the assumption of a constant RRR lies in a common failure to find statistically significant evidence that the RRR varies across different baselines risk, even though most studies lack power to provide such evidence save when differences in RRRs for different baseline risks are extremely large. In any case, the assumption is unsound. A factor that reduces different baseline rates equal proportionate amounts must necessarily increase the opposite outcome rates different proportionate amounts. And since there is no more reason to expect that a factor will cause equal proportionate reductions in rates of experiencing an outcome than there is to expect it to cause equal proportionate increases in the opposite outcome, there is no reason to expect equal proportionate changes in either of the outcomes. In fact, features of normal risk distributions provide reason to expect that a factor that similarly affects groups with different baseline rates will tend to cause larger proportionate changes for groups with lower baseline rates while causing larger proportionate changes in the opposite outcome for other groups.[4-7]
The most defensible method for using the reduction of a baseline risk observed in a study to estimate the absolute risk reduction and number needed to treat for other baseline risks is to derive from the study’s rates for treated and controls the difference between means of underlying risk distributions. That difference between means can then be used to estimate the absolute risk reduction for any baseline rate, as reflected in Table 3 of reference 7, as well as the corresponding number needed to treat.
References:
1. Cook RJ, Sackett DL. The number needed to treat: a clinically useful measure of treatment effect. BMJ 1995;310:452-454.
6. Scanlan JP. Interpreting Differential Effects in Light of Fundamental Statistical Tendencies, presented at 2009 Joint Statistical Meetings of the American Statistical Association, International Biometric Society, Institute for Mathematical Statistics, and Canadian Statistical Society, Washington, DC, Aug. 1-6, 2009: http://www.jpscanlan.com/images/JSM_2009_ORAL.pdf
Rapid Response:
Re: The number needed to treat: a clinically useful measure of treatment effect
This 1995 article by Cook and Sackett [1] is one of continuing significance at least because it underlies the assumption in the guidance for adjusting for baseline risk in the calculation of number needed to treat provided by the Clinical Evidence Glossary that an observed relative risk reduction (RRR) effected by an intervention will commonly be constant across different baseline risks.[2] The article may also underlie the statement in the Glossary’s guidance for calculating risks that “RRR is usually constant across a range of absolute risks.”[3]
I suspect that such empirical basis that may exist for the assumption of a constant RRR lies in a common failure to find statistically significant evidence that the RRR varies across different baselines risk, even though most studies lack power to provide such evidence save when differences in RRRs for different baseline risks are extremely large. In any case, the assumption is unsound. A factor that reduces different baseline rates equal proportionate amounts must necessarily increase the opposite outcome rates different proportionate amounts. And since there is no more reason to expect that a factor will cause equal proportionate reductions in rates of experiencing an outcome than there is to expect it to cause equal proportionate increases in the opposite outcome, there is no reason to expect equal proportionate changes in either of the outcomes. In fact, features of normal risk distributions provide reason to expect that a factor that similarly affects groups with different baseline rates will tend to cause larger proportionate changes for groups with lower baseline rates while causing larger proportionate changes in the opposite outcome for other groups.[4-7]
The most defensible method for using the reduction of a baseline risk observed in a study to estimate the absolute risk reduction and number needed to treat for other baseline risks is to derive from the study’s rates for treated and controls the difference between means of underlying risk distributions. That difference between means can then be used to estimate the absolute risk reduction for any baseline rate, as reflected in Table 3 of reference 7, as well as the corresponding number needed to treat.
References:
1. Cook RJ, Sackett DL. The number needed to treat: a clinically useful measure of treatment effect. BMJ 1995;310:452-454.
2. http://clinicalevidence.bmj.com/ceweb/resources/adjusting_baseline_risk.jsp
3. http://clinicalevidence.bmj.com/ceweb/resources/calculate_risk.jsp
4. Scanlan JP. Race and mortality. Society 2000;37(2):19-35: http://www.jpscanlan.com/images/Race_and_Mortality.pdf
5. Scanlan JP. Divining difference. Chance 1994;7(4):38-9,48: http://jpscanlan.com/images/Divining_Difference.pdf
6. Scanlan JP. Interpreting Differential Effects in Light of Fundamental Statistical Tendencies, presented at 2009 Joint Statistical Meetings of the American Statistical Association, International Biometric Society, Institute for Mathematical Statistics, and Canadian Statistical Society, Washington, DC, Aug. 1-6, 2009: http://www.jpscanlan.com/images/JSM_2009_ORAL.pdf
7. Subgroup Effects sub-page of Scanlan’s Rule page of jpscanlan.com: http://www.jpscanlan.com/scanlansrule/subgroupeffects.html
Competing interests: No competing interests