Basic Statistics for Clinicians

MEASURES OF ASSOCIATION

Relative risk or risk ratio (RR)

The relative risk of the event after the experimental treatment, expressed as a percentage of the risk without such treatment. (Post-experiment risk divided by pre-experiment risk, expressed as a percentage).

Relative risk reduction (RRR)

The relative risk reduction is an estimate of the percentage of the baseline risk (the risk of an event in the control patients) removed as a result of therapy. The simplest way to derive it is to subtract the RR from 1.

Absolute risk reduction (ARR)

The absolute risk reduction (ARR) is the difference in the risk of an event between the groups. The difference in the risk of the outcome between patients who have undergone one therapy and those who have undergone another is called the absolute or attributable risk reduction or the risk difference. (It's a simple subtraction)

Odds ratio (OR)

The odds ratio, which is the measure of choice in case-control studies, gives the ratio of odds of an event in the experimental group to (divided by) those in the control group. The OR has certain optimal statistical properties that make it the fundamental measure of association in many types of studies. These statistical advantages may be particularly important when data from several studies are combined, as they are in a meta-analysis. Among such advantages, the comparison of risk represented by the OR does not depend on whether the investigator chose to determine the risk of an event occurring or not occurring. This is not true for RR. In some situations the OR and the RR will be close - e.g. in case-control studies of a rare disease.

Number needed to treat (NNT)

The number needed to treat tells the clinician how many patients need to be treated to prevent one event. One can arrive at this number by taking the reciprocal of the ARR (1/ARR). The NNT is directly related to the proportion of patients in the control group who suffer an adverse event. In general the NNT changes inversely in relation to the baseline risk - if the number of adverse events doubles, we need only treat half as many patients to prevent the same number of adverse events. In addition to calculating the NNT, one could also consider resources expended to prevent an event.

The OR and the RR provide limited information in reporting the results of prospective trials because they do not reflect changes in the baseline risk. The ARR and the NNT reflect both the baseline risk and the RRR. If the timing of events is important - to determine whether treatment extends for life, for example - survival curves are used to show when events occur over time.

Confidence intervals can be calculated for each of these measures of association.

Prospective randomized controlled trials

In such trials we start with an experiments group of patients who are subject to an intervention and a control group of patients who are not. The investigators follow the patients over time and record the incidence of events.

Prospective cohort studies

The process is similar, but patients are sampled according to whether they were or were not exposed to the treatment or risk factor, rather than being assigned to an intervention.

Case-control studies

Participants are sampled on the basis of whether they have experienced an event. Patients start the study with/without the event rather than with/without the exposure or intervention. Patients with the adverse outcome are compared with controls who have not suffered the outcome - a number chosen by the investigators Therefore the RR is not available because we do not know the population at risk.

The only measure of association that makes sense in a case-control study is the OR.

Acknowledgement

This article is based on Basic statistics for clinicians: Basic statistics for clinicians: 3. Assessing the effects of treatment: measures of association. G. Guyatt, R. Jaeschke, N. Heddle, D. Cook, H. Shannon, and S. Walter
Can. Med. Assoc. J., Feb 1995; 152: 351 - 357