Analysis of continuous outcomes when a large proportion of the data are zeroes
Continuous outcomes are not straightforward to analyse if there are a large proportion of zeroes, as frequently occurs with outcomes such as volume of blood transfused for conditions where blood transfusion is not always necessary. Should we analyse volume per person randomised (PPR) or per person transfused (PPT)?
If numbers randomised and transfused are both known, we can convert between PPR and PPT using the relationship between sums of squares familiar from ANOVA but several statistical and practical issues arise.
Standard methods of analysis for continuous outcomes rely on the Central Limit Theorem. When the underlying distribution is extreme due to a large proportion of zeroes in the data, an intention-to-treat analysis (PPR) may require sample sizes of many hundreds or even thousands before the sampling distribution of the mean is closely approximated by the normal distribution. A PPT analysis will converge with smaller sample sizes but, if only a small proportion required transfusion, this still requires a large number randomised.
Some trials report the mean volume transfused without reporting the number receiving a transfusion and so would be excluded from a PPT analysis.
It is sometimes unclear whether a trial has reported PPR or PPT. Converting between PPR and PPT may produce impossible values (negative sums of squares), helping to clarify this. This may also highlight cases where a standard error has been mislabelled as a standard deviation.
Conclusions: When extracting these sorts of outcomes it is important to be sure which value (PPR or PPT) was reported and to ensure that pooled results are all based on the same denominator. Extracted data should be carefully assessed for unusual or impossible values. There is no clear answer as to which analysis is best under any given circumstance; it may be useful to present both and note where the sample sizes available may not be sufficient to meet the underlying assumptions. We have produced a spreadsheet (available on request) to convert between PPR and PPT, including error flags and plots to help diagnose issues with the data extracted.
Patient, public and/or healthcare consumer involvement: none