# Numeric Presentation of Results

Data from observational and randomized clinical trials can be presented as odds ratios, relative risks and absolute risks. When the absolute risk of an event is low and the 95% confidence level is narrow, relative risk and odds ratios are similar. If the baseline event rate is small, a large relative risk reduction may have a relatively small impact on the population. For example, although the relative risk reduction of complications may be constant for each 10% reduction of A1C, the absolute risk reduction will be greater for older individuals with higher baseline A1C.

Relative risk, relative rate, rate ratios, and odds ratios are all examples of relative differences.

It is also important for the clinician to evaluate the absolute risk of both benefits and harms. Unfortunately, these are not always explicitly stated in the literature. For example, the incidence of severe hypoglycemia in intensively treated persons with type 2 diabetes may differ in populations with different characteristics. Thus, clinicians must rely upon judgment in deciding what is best for the individual patient.

**Odds ratios**

Primer on Probability, Odds and Interpreting their Ratios Effective Clinical Practice, May/June 2000, American College of Physicians/American Society for Internal Medicine. For complete information go to www.acponline.org/clinical_information/journals_publications/ecp/ecp.primer.2.pdf

**Absolute versus relative risks**

*Primer on Absolute vs. Relative Differences*

Quoted directly from Effective Clinical Practice, January/February 2000, American College of Physicians/American Society for Internal Medicine. For complete information go to: www.acponline.org/clinical_information/journals_publications/ecp/janfeb00/primer.htm- The challenges of communicating with patients about risk. www.acpinternist.org/archives/2008/02/risks.htm

When presenting data that compare two or more groups, researchers (and reporters)
naturally focus on differences. Compared to others, one group may cost more, have
longer hospital stays or have higher complication rates. These relationships may
be expressed as either absolute or relative differences. An absolute difference
is a subtraction; a relative difference is a ratio. Because this choice may influence
how big a difference "feels," readers need to be alert to the distinction.

When the units are counts, such as dollars, the distinction between absolute and
relative differences is obvious: group 1 costs $30,000 more vs. group 1 had 40%
higher costs. But when the units are percentages (frequently used to describe rates,
probabilities, and proportions), it can be very difficult to determine whether a
stated difference is absolute or relative.

Consider the risk of blindness in patients with diabetes over a 5-year period. If
the risk of blindness is 2 in 100 (2%) in a group of patients treated conventionally
and 1 in 100 (1%) in patients treated intensively, the absolute difference is simply
the subtraction of the two risks:

2% - 1% = 1%

Expressed as an absolute difference, the benefit of intensive therapy is to reduce
the 5-year risk of blindness by 1%.

The relative difference is the ratio of the two risks. (NB: Relative risk, relative rate, rate ratios, and odds ratios are all examples of relative differences.) Given the data above, the relative difference is:

1% / 2% = 50%

Expressed as a relative difference, the benefit of intensive therapy is to reduce
the risk of blindness by half.

Both expressions have their place. Without any qualification, both statements ("reduced
the risk by 1%" and "reduced the risk by 50%") could be construed as representing
either an absolute or relative difference. But most importantly, notice the difference
in "feel." A statement of "reduced the risk by 1%" does feel like a smaller effect
than "reduced the risk by 50%."

**Number needed to treat (NNT)**

For clinical decision-making it may be meaningful to use the measure "number needed to treat." This measure is calculated on the inverse of the absolute risk reduction. It has the advantage that it conveys both statistical and clinical significance to the health care provider.

*Primer on 95% Confidence Intervals for the Number Needed To Treat*

Quoted directly from Effective Clinical Practice, May/June 1999, American College of Physicians/American Society for Internal Medicine. For complete information go to www.vaoutcomes.org/downloads/95CIforNNT.pdf.

Few, if any, therapeutic interventions benefit every patient. One way to gauge the likelihood that one patient will benefit is to calculate the number needed to treat (NNT) -- that is, the number of patients who must be treated for one to benefit. The general approach is as follows:

% with outcome (standard treatment) - % with outcome (new treatment) = absolute risk reduction

100 / absolute risk reduction = number needed to treat

For example, consider a randomized trial in which 50% of the participants die in the control group and 40% die in the intervention group. The absolute risk reduction for death is thus 10%, and the NNT to avoid a death is 10 (100/10). This treatment would be preferred over a competing treatment whose NNT to avoid death was 20.

**Number needed to harm (NNH)**

NNH is calculated in the same way as for NNT, but used to describe adverse events. For NNH, large numbers are good, because they mean that adverse events are rare. Small values for NNH are bad, because they mean adverse events are common.

For example, in a “large, international, randomized trial involving adults in the ICU, we found that intensive glucose control, as compared with conventional glucose control, increased the absolute risk of death at 90 days by 2.6 percentage points; this represents a number needed to harm of 38. The difference in mortality remained significant after adjustment for potential confounders... In conclusion, our trial showed that a blood glucose target of less than 180 mg per deciliter resulted in lower mortality than a target of 81 to 108 mg per deciliter. On the basis of our results, we do not recommend use of the lower target in critically ill adults...” [1]