Category: Measuring benefit/risk. There are many measures of risk or benefit. I describe some of these (the odds ratio, the relative risk, the number needed to treat) and explain the advantages and disadvantages of particular measures. Articles are arranged by date with the most recent entries at the top. You can find the theme and closely related categories and other resources at the bottom of this page.

Stats: Calculating NNT for observational studies (March 3, 2008). Recent discussion at the Evidence Based health list centered on the calculation of NNT in a case-control study. While it is indeed possible to do so, I have always been a bit curious why NNT and NNH are computed almost exclusively for randomized studies and why they are rarely used for observational studies. No one says this explicitly, but I suspect that the reason is that the NNT and NNH lead to problematic interpretations in observational studies.

Stats: Analyzing data under an Intention to Treat model (December 19, 2007). Dear Professor Mean, I need to know how to analyze a data set using the intention to treat principle.

Stats: Handling dropouts in NNT/NNH calculations (January 16, 2006). Someone asked a question on the Evidence-Based Health email discussion group about how to handle dropouts in an NNT/NNH calculation. There is no standard way of handling this, but a little bit of common sense goes a long way.

Stats: Fractions are funny (December 13, 2005). On my web page about odds ratios, I point out the fractions are funny and cite some well known examples of how fractions behave in a counter intuitive fashion.

Stats: Converting an odds ratio to a relative risk (August 3, 2005). The odds ratio and the relative risk do not always agree, especially when the baseline risk level in the control group is large. I have a simple Excel spreadsheet that will calculate the relative risk from the odds ratio and the control risk, ConvertORtoRR.xls.

Stats: The difference between absolute risks and relative risks (July 15, 2005). There are two general ways to compare a treatment and a control group, relative comparisons and absolute comparisons. For a relative comparison, the basic computation is division. When the ratio A/B is larger than one, that implies that A is superior to B. For an absolute comparison, the basic computation is subtraction. When the difference A-B is greater than zero, that implies that A is superior to B.

Stats: What does a 60% drop mean? (June 20, 2005). A friend sent me an email quoting the following statistic: "A woman's chances of getting married dropped 60% for every rise of 15 points in her IQ, according to an English study reported in The Atlantic." reported in June 2005 Touchstone. I do not have easy access to either The Atlantic or Touchstone magazine. But the number seemed too large to be credible. so I ran a few simple calculations.

Stats: Incidence density ratio (April 19, 2005). Someone asked me about a technical term, incidence density ratio, that was used in an article: Comprehensive discharge planning and home follow-up of hospitalized elders: a randomized clinical trial. Naylor MD, Brooten D, Campbell R, Jacobsen BS, Mezey MD, Pauly MV, Schwartz JS. Jama 1999: 281(7); 613-20.. Looking at the article, they only mention the term once and in context with another term, rate ratio, that you are probably familiar with.

Stats: Side effects of Cox-2 inhibitors (February 15, 2005). There has been so much published about side effects of Cox-2 inhibitors that it is hard to keep up with the evolving story. Here are a few recently released articles.

Stats: Small relative risks (January 13, 2005). I found a quote on the Skeptic's Dictionary web site that is worth commenting on. The author, Robert Todd Carroll was describing the Vioxx controversy and the lawyers who are now aggressively recruiting people for a lawsuit against Merck, the manufacturer of Vioxx. In it, he repeats a common misconception about relative risk (RR): According to mathematician John Brignell, "In observational studies, [scientists] will not normally accept an RR of less than 3 as significant and never an RR of less than 2."

Stats: Odds ratios less than one (January 6, 2005). Someone sent me an email asking how to interpret an odds ratio less than 1.

Stats: Testing for side effects (December 29, 2004). Today's USA Today has a nice summary of the recent controversies over drugs that are being removed from the market because of an unacceptable increased risk of side effects. Under special scrutiny these days are a class of drugs known as COX-2 inhibitors.

Stats: Neyman bias (December 15, 2004). Selection of controls in a case-control study is difficult enough, but you also have to worry about the selection of the cases. Do you select incident cases (for example all breast cancer patients newly diagnosed during a given time frame) or prevalent cases (for example, all breast cancer patients who are alive during a given time frame). These can lead to very different answers, because the probability of finding a case in a given time frame is related to mortality risk.

Stats: Number Needed to Harm Examples (February 18, 2004). I was trying to track down a reference on the NNH (number needed to harm) for antibiotic use, but noticed instead the large number of good examples of NNH calculations in journal articles with full text on the web.

Stats: Odds ratio versus relative risk (January 9, 2001). Dear Professor Mean:  There is some confusion about the use of the odds ratio versus the relative risk. Can you explain the difference between these two numbers?

Stats: Intention to treat (January 27, 2000). Dear Professor Mean: I'm confused by medical journal articles that talk about the use of "Intention to Treat" analysis. What does this term mean?

Stats: Number needed to treat (January 27, 2000). Dear Professor Mean: How are patients and their doctors supposed to decide whether a research finding has practical significance? Why don't the medical journals make things clearer?

Theme and closely related categories:

• Theme: Data analysis
• Category: Logistic regression
• Category: Measuring agreement

Other resources:

• 3M APR-DRG Severity-of-Illness Software Excerpt: Grouping, validating, and pricing claims data will never be the same. The State of Maryland is leading the move toward a more equitable and accurate way to pay for health care: A severity-based payment system. Supported by years of research, Maryland is acting on the fact that patients with a higher level of severity require more healthcare resources and that there are significant variances in patient severity in the existing payment system. As the State of Maryland moves toward its implementation of having hospitals set payment rates based on the 3M™ APR-DRG™ Classification System’s severity scoring, hospitals might feel overwhelmed with the requirements for change. But, this change doesn’t have to be complex. In fact, it can be easy and simple, thanks to 3M APR-DRG Severity-of-Illness Software.
• Absolute and relative truth in clinical trials. Description: This article criticizes a recent publication for failing to present risk in absolute rather than relative terms.
• Applying evidence to the individual patient Description: This paper provides practical guidance on the NNT/NNH tradeoffs.
• The “Arms Race” on American Roads: The Effect of SUV’s and Pickup Trucks on Traffic Safety [pdf] Description: This web publication paper calculates expected deaths if a million drivers switched from light trucks to cars. It could easily be adapted to NNT and NNH calculations.

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This webpage was written by Steve Simon on 2007-06-26, edited by Steve Simon, and was last modified on 2008-07-14. Send feedback to ssimon at cmh dot edu or click on the email link at the top of the page.