# 9. Analysing and interpreting results

Once the eligible studies are selected and quality appraised, the magnitude of the intervention effect should be estimated. The best way to do this is by performing a meta-analysis (i.e. the statistical combination of results from two or more separate studies), although this is not always feasible. An interesting tool for doing a limited meta-analysis is the free Review Manager software of the Cochrane Collaboration.

The starting point of the analysis and interpretation of the study results involves the identification of the data type for the outcome measurements. Five different types of outcome data can be considered:

• dichotomous data: two possible categorical response;
• continuous data
• ordinal data: several ordered categories;
• counts and rates calculated from counting the numbers of events that each individual experiences;
• time-to-event data

Only dichotomous data will be addressed here. Dichotomous outcome data arise when the outcome for every study participant is one of two possibilities, for example, dead or alive. These data can be summarised in a 2x2 table:

 Outcome YES NO Intervention a b a + b Control c d c + d a + c b + d

The most commonly encountered effect measures used in clinical trials with dichotomous data are:

• Relative risk (RR): the ratio of the risk (i.e. the probability with which the outcome will occur) of the outcome in the two groups, or [a/(a+b)]/[c/(c+d)]. For example, a RR of 3 implies that the outcome with treatment is three times more likely to occur than without treatment;
• Absolute risk reduction (ARR): the absolute difference of the risk of the outcome in the two groups, or [a/(a+b)]-[c/(c+d)];
• Number needed to treat (NNT): the number of persons that need to be treated with the intervention in order to prevent one additional outcome, or 1/ARR.
• For diagnostic accuracy studies, the results will be expressed as
• Sensitivity: the proportion of true positives correctly identified by the test: Sens=a/a+c
• Specificity: the proportion of true negatives correctly identified by the test: Spec=d/b+d
• Positive predictive value: the proportion of patients with a positive test result correctly diagnosed: PPV=a/a+b
• Negative predictive value: the proportion of patients with a negative test result correctly diagnosed: NPV=d/c+d
• Likelihood ratio: likelihood that a given test result would be expected in a patient with the target disorder compared to the likelihood that that same result would be expected in a patient without the target disorder LR+=(a/a+c)/(b/b+d); LR-=(c/a+c)/(d/b+d)
• Diagnostic odds ratio: ratio of the odds of having a positive index test result in a patient with the target condition over the odds of having this test result in a patient without the target condition: OR=ad/bc
 Target conditionPositive Target conditionNegative Index test positive a b Index test negative c d

As discussed above, other types than dichotomous data are possible, each with their own outcome measures and statistics. It is beyond the scope of this document to describe and discuss all these types. Interested readers are referred to textbooks such as Practical statistics for medical research (Altman 1991) Modern Epidemiology (Rothman and Greenland 1998) and Clinical epidemiology : a basic science for clinical medicine (Sackett 1991) .