ACP American College of Physicians - Internal Medicine - Doctors for Adults

Effective Clinical Practice

Primer on Absolute vs. Relative Differences

January/February 2000

When presenting data comparing two or more groups, researchers (and reporters) naturally focus on differences. Compared to others, one group may (pick one): 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-patient 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%".

The most frequent problem readers will face is the reporting of an isolated relative difference. Research abstracts, medical review articles, or general circulation newspapers and magazines are filled with statements like "60% decrease in costs", "twice as many days in the hospital" or "20% decrease in mortality". These statements provide no information about the starting point. The statement "the risk of disease X was cut in half", for example, provides no information about where you started. As shown in the table below, there is a wide range of risks that can be cut in half.

Risk of disease Absolute Difference Relative Difference
Group A Group B [A - B] [B/A]
20% (2/10) 10% (1/10) 10% 50%
2% (2/100) 1% (1/100) 1% 50%
0.2% (2/1000) 0.1% (1/1000) 0.1% 50%

Consequently, when you really want to get a complete picture of what's going on - when presented with a relative difference ("60% more") make sure you ask the question: "from what?". If the goal is clarity, the actual data (the dollars, the hospital days, and the mortality rates) for each group is tough to beat.