Preferred method for handling continuous
variables
The data required to enter into RevMan to calculate the weighted mean
difference (WMD) or pooled effect estimate for continuous outcomes are:
1. the mean change in variable x from baseline to follow up
2. the standard deviation (SD) of the mean difference in variable x
3. the number in each comparison group (n) at follow up.
Sometimes these values have not been calculated in the source papers. To
calculate the mean change in a variable from baseline to follow up is straight
forward. This is illustrated in the dataset below:
Worked example:
Total blood cholesterol (mmol/L) in an exercise only rehabilitation group
compared to a usual care group, follow up period of 5 years.
Intervention
Control
Baseline (mean, SD, n)
7.01, 0.99, 47
7.19, 1.25, 51
Follow up (mean, SD, n)
6.58, 0.9, 47
7.14, 0.94, 51
To calculate the net mean change in total cholesterol:
Mean difference = mean at follow up minus mean at baseline
In the intervention group the mean difference in total cholesterol is
6.58 minus 7.01 = - 0.43 mmol/L
The same process is used to calculate the mean difference in the control group.
More often than not we find that the SD difference has not been calculated in the
source papers. We can contact the authors to find out more information, or we
can impute or estimate the variance from the information available. The formula
below is often used where we can calculate the SD difference when we have the
SD (or standard error, confidence intervals etc to then convert to SD) for the
comparison groups at baseline and follow up.
Where:
To calculate the SD difference from the SE difference:
so:
Using the above example for total cholesterol, the SD difference in the
intervention group is:
The same process is used to calculate the SD difference in the control group.
Whilst this approach is reasonable as it allows the pooling of the variance from
baseline and follow up values, it makes no allowance for the correlation between
baseline and follow up within individuals. Essentially, we can think of the data for
baseline and follow up as paired comparisons providing that the follow up group
is representative of the baseline group. This can be checked by looking at the
standard deviations at baseline and follow up, as long as there is not a high loss
to follow up, and the methods of measurement do not differ, these should be
similar. By using the formula below (which is the same as the one above with the
extra term 1 minus the correlation coefficient for the correlation between baseline
and follow up (1-r)) we make allowance for within-individual correlation. The
value of r will depend on the outcome of interest, and the period of follow up. We
recommend that you obtain the value of r from empirical data from large
epidemiological studies or clinical studies. For the worked example below, the r
value for total blood cholesterol was obtained from the Caerphilly study for follow
up periods of 5 years for over 2000 men (correlation between phase 1 and phase
2 of Caerphilly, r=0.687).
so:
Using the above example:
If the outcome of interest is something where there is little evidence available to
be able to assign a correlation coefficient, it is suggested that a value of 0.5 be
assumed (Follmann 1992).
Once we have calculated the adjusted SD difference for each outcome in the
comparison groups, we enter this value in the SD difference column in RevMan.
The n number that is entered into RevMan is self-evident. However, where we
have missing data, for example in 163 patients with measurements at baseline,
and only 144 patients with measurements at follow up, we should always use the
lower number, in this case 144, in any calculations, and this should be the n
number entered into RevMan. By using this approach, not only are we being
consistent, but we are producing a more conservative estimate of effect, and
guarding against introducing bias associated with selecting out those participants
who died or who were lost to follow up.
Conversions:
To convert SEM to SD:
To convert 95% confidence intervals (CI) to SD:
References:
Follmann D, Elliot P, Suh I, Cutler J. Variance imputation for overviews of clinical
trials with continuous response. J Clin Epidemiol 1992;45(7):769-773