Graphical representations and data interpretation
Content
Simple (symmetrical, skewed) distributions
Scatter diagrams
Box and whisker plots
Forest plots
Funnel plots
Statistical process control charts
Cates diagrams
Decision aids
The Normal Distribution
Standard Deviation is measure of the spread of results above (e.g. +1 SD) and below (e.g. − 1 SD) the arithmetic mean
SD = √ VARIANCE
Assuming x is a set with a range of values within a normally distributed population,
− 1 SD ≤ x ≤ + 1 SD 68% of population will have the same range of values as x
− 2 SD ≤ x ≤ + 2 SD 95% of population will have the same range of values as x
− 3 SD ≤ x ≤ + 3 SD 99.7% of population will have the same range of values as x
The further the patient’s result lies from the mean, in terms of standard deviations, the more likely that result is ‘abnormal’ or pathological.
Normal ranges are commonly set 2 SDs above and below the mean for a ‘normal’ population.
By definition, 34% of results will lie between − 1 SD and the mean (green shaded area on the graph)
By definition, 50% of results will lie above the mean (blue shaded area on the graph).
Hence, overall, 84% (50%+34%) of results will lie above − 1 SD (green shaded + blue shaded)
Funnel Plot and homo/heterogeneity of included studies
Funnel plots are used in meta-analysis to assess for homo/heterogeneity of studies and possible bias.
A funnel plot is a scatter plot of treatment effect (horizontal axis) reported by individual studies against the size of the individual study (plotted as standard error on the vertical axis). The treatment effect from smaller studies should scatter more widely at the bottom, with the spread narrowing among larger studies.
Statistical heterogeneity refers to differences between study results beyond those attributable to chance, such as differences in study population or differences in study methodology.
If the studies included are homogenous and there is no bias, the scatter will be due to sampling variation alone and the plot resembles a symmetrical inverted funnel with the triangle incorporating 95% of studies.
Significant heterogeneity or reporting bias (often a propensity to include studies reporting positive results as those are most likely to be published and accessible by the meta-analysis authors) changes the symmetry, shape or spread of the plot.
FOREST PLOT
A pictorial representation of the studies included in a meta-analysis.
The results of individual studies are shown as squares centred on the point estimate of the result of each study. The size of the square relates to the size and weighting of the study. A horizontal line runs through the square to show its 95% confidence interval.
The overall estimate from the meta-analysis and its confidence interval are put at the bottom, represented as a diamond. The horizontal tips of the diamond represent the confidence interval. Significance of the overall effect is achieved if the diamond is clear of the line of no effect (shown as s vertical line at 1)
Meta-analysis will also report a measure of study heterogeneity .
Ideally, included studies should be as similar as possible and any difference in effect should be due to sampling error alone.
Using Higgins I2, a value of 0% indicates statistical homogeneity.
if I2 >50%, this suggests significant statistical heterogeneity