What are continuous outcome data?

The strict definition of a continuous outcome is one measured on a scale that is continuously variable, i.e. for any two valid continuous measurements there is always one in between. Thus the number of hairs on one's head is not strictly continuous since it can only be a whole number, but the length of a hair is continuous since it can have any number of decimal places. However, such subtle differences do not really matter in practice and we often treat outcomes that don't quite meet this strict definition as if they were continuous. This includes outcomes that are:

• numerical
• made up of many ordered categories

This covers a lot of potential outcomes, including things like weight loss, dimensions (e.g. length of a hospital visit, area of scar, or volume of a tumour), concentrations, costs, and scores on psychometric scales. That doesn't mean that we can automatically enter results for all such outcomes as continuous data in RevMan. We shall see that there are several issues to think about before we do so.

Can I analyse this outcome as a continuous outcome?

Here are two things to consider if you have an outcome that you think may be treated as a continuous variable.

Is an increase in 1 unit in one region equivalent to an increase of 1 unit in another region?

There is an implicit assumption that the answer is "yes" when we analyse continuous data in RevMan. Consider weight as a simple outcome. Is an increase in weight of 1kg from 50kg to 51kg the same as an increase from 80kg to 81kg? One might question whether these are clinically equivalent, but there is general consensus that we are talking about the same quantity.

Now consider a pain scale. Is a change from 5 (maximum pain) to 4 the same as a change from 1 to 0? It's impossible to say: maybe the reduction at the more severe end of the scale is greater than a change from 1 to 0, maybe not.

Many health measurement scales are constructed by counting the number of positive responses to a set of questions or criteria. So, in terms of their psychometric properties they meet this criterion, although it may be difficult to argue that an increase in one unit has the same clinical meaning at all points on the scale.

As a general rule, short scales (those with not many categories) such as the pain scale tend to be unsuitable for the methods described in this module, and are usually analysed as dichotomous data, as discussed at the beginning of Module 11.

Is it reasonable to summarize a group of people using a mean and standard deviation?

Methods for meta-analysis of continuous data are derived assuming the data have a Normal distribution, and revolve around means and standard deviations. A mean is the 'average' (i.e. sum of the observations divided by the number of observations). The standard deviation is a measure of how variable the observations are around the mean. A small standard deviation indicates that the observations are all near the mean; a large standard deviation indicates that the observations vary a lot.

A key fact about means is that they can be sensitive to extreme values. For example, the mean of the numbers 1, 2 and 3 is 2, which is a fair single summary of the three numbers. The mean of 1, 2, 3 and 50 is 14, which seems a rather less satisfactory summary. When the mean is influenced by an extreme value, we have skew, and the observations have an asymmetrical distribution. When outcomes have an asymmetrical or skewed distribution, the mean (and hence the standard deviation) are not very useful ways to summarize the data. This may lead to analyses reaching spurious conclusions, especially when sample sizes are small. In practice it is not essential that the data have a perfect Normal distribution, but analyses may become misleading if the distribution of data is severely skewed.

Summary

We can treat outcomes as continuous data if they have an approximately symmetrical distribution and if realistic differences in the outcome can be interpreted similarly from different starting points. This may be the case for dimensions, counts of common events, and scales with many categories. It is less likely to be the case for costs, concentrations and counts of rare events (which all tend to be skewed) or short scales.

Skewed data are not bad data, they are just more difficult to analyse. We will look at ways you might make use of them later in the module.