# How to deal with 0 values in the treatment data during calculation of log-transformed response ratios of meta-analysis?

Suppose I have this type of data in meta-analysis (example):

AbundanceTreat<-c(0,0,50,1,0.25,500)
AbundanceContr<-c(5000,1,0,1,0.5,1500)


I want to calculate RR of plants abundance as the log-transformed ratio of treatment/control. Assuming it is ok for my study to remove observation that have 0 values in the control, you still get infinite estimates in the observations that have 0 values in the control when using log-transformed ratios.

Is any of the two following option accepted in meta-analysis?

1) Make a continuity correction of +1 in both treatment and control to avoid this issue. However, I have data measuring the change in plant abundance but with different units (i.e. % of cover, biomass, number of shoots) which in the end makes the data out of proportion with values in some observations extremely higher/lower compared to others. Isn't a problem to add the same +1 factor in each observation in my case? Shouldn't you apply a continuity correction factor in proportion to the values reported to account for these differences?

2) (best option to me so far) I can just avoid to log-transform the response ratio so to have an effect size = 0 in case of 0 values in the treatment and exclude observations with 0 values in the control. However to not logtransform the response ratios is really not ok in meta-analysis apparently...

• Two comments (a) do you have the corresponding sizes of the studies, perhaps the area concerned? (b) I think you are going to be struggling to combine this with the other sorts of outcome you mention. – mdewey Jun 18 '17 at 15:17
• Yes @mdewey I am using variance to do a weighted meta-analysis – Gabriele Midolo Jun 19 '17 at 13:57
• From Koricheva, Handbook of Meta-analysis: "A consequence of using log-transformed ratios, however, is that the ratio must be positive […] In this case, the response ratio is an inappropriate measure and Hedges’ d is instead recommended. One should also not use a ratio as an effect size measure when either the numerator or denominator would be equal to zero; the transform is undefined and trying to adjust the values by adding a tiny fraction to the numerator and denominator usually results in abnormally large estimates of effect size" – Valentin Feb 6 '18 at 13:15
• @Valentin why not convert your comment into an answer since comments are not deemed permanent on these sites? – mdewey Aug 24 '18 at 15:16
• Hi @mdewey. Now I realize that I might have actually created a duplicate by asking a similar question some time ago here. – Valentin Aug 26 '18 at 18:15