It sounds like the effect you are want to use is a response ratio (RR). See the attached paper for how you calculate the variance for the log(RR) using dependent samples.

I would like to be clear with your question? Is the mean fold change continuous outcome? If yes, are the scales of measurement for the outcome similar across studies? Are you dealing with randomised controlled trials in your meta-analysis?

I also think that some further clarification is required regarding the type of outcome

Also are trying to use change from baseline? You would need to adjust for the within patient correlation 

Hi Mihiretu and Nikolas

Thescales of measurement (for baseline and peak) is a continuous variable in the unit of pM, consistent across all studies.

For example, baseline = 1.2pM; peak = 2.4pM, calculated fold change = 2.0

All the studies to be included are randomised controlled trials. However, the control intervention is not consistent across the studies, therefore it is not the Odds Ratio kind of analysis. The primary aim is to investigate the fold change of hormones after (any) diet intervention, and subgroup analysis will be done based on diet characteristics (such as macronutrient composition).

If you have let's say 2 arms in the prospective trial you can get the mean difference between the before and after measurements within groups and the standard deviation of the difference

Then you can use the 2 calculated differences for the two arms in the meta analysis

A possible issue is the calculation of the sd of the difference because the sd of the difference should be adjusted downwards due to the fact that the before/after measurements are within the same patient. If you have raw data you can calculate it, if you don't perhaps you can see if in any papers the sd of the difference is reported and from there you can calculate backwards the correlation coefficient which you will use to adjust the sd of the difference of your included studies

the formula is sd diff= square root(sd before^2+sd after^2 - 2*sd before*sd after*r)

r=correlation coefficient you need to calculate 

Another approach would be to make assumptions about r like .25, .50, .75 and do sensitivity analyses to see if conclusions change

I hope this helps but if something is unclear please post again

which meta analysis software are you using? I can help you further  if you use Stata or revman

Nick

Hello Nikolas, thank you for your information. I believe what you have provided is the estimation of std error of mean difference (before and after), which works on absolute values, ie. difference = after treatment - before treatment.

However, if I would like it to do it in terms of fold change, rather than absolute change, what is your opinion. For your information, the peak of some hormones is 5 to 10 times as higher than the baseline, absolute difference would not seem to be reflective of the response. ie, a change from 1pM to 2pM (2 fold) is thought to be more responsive to the intervention than 5pM to 6pM (1.2 fold).

I am using Comprehensive Meta-Analysis, but I am open to the suggestion of any software to use as long as the software can do the work.

Prof Gordon, may I know what software can be used to work out the Response Ratio? To be honest, I only understood the Introduction section, but it seems like it is what I would like to do. Do you have any "idiot-proof" guidelines on Response Ratio? I have never done a Response Ratio before, I only know Odds Ratio, Hazards Ratio, Risks Ratio, which clearly those ratio is not my desired outcomes.

The Comprehensive Meta-Analysis software can handle it but you will need to manually calculate the response ratio and its variance for each study. Do you have the Intro to Meta-Analysis book by Borenstein et al. They discuss calculation of the response ratio and its variance, though the variance is that assuming independent samples. That is why I provided the Lajeunesse (2011) paper because it discusses the case using dependent samples. I have used the response ratio before but not with dependent samples like you have. I am sorry I can't be of more help.

In this case, I think Gordon's suggestion and paper make sense

I believe you can use the same formula for RR on the log scale to calculate the corr coefficient 

Comprehensive meta analysis should be able to handle this and in fact you may directly email Michael Borenstein since you use his software to see if he can provide any guidance in solving your problem

Dear Jia Jiet Lim,

I am sorry I didn't receive notification from RG. I was not aware that you have already responded to my question. I am also currently working on a meta-analysis of continuous outcome and I have recently raised such question on RG. I would like to share you some helpful materials to deal with a continuous outcome. 

I would also like to raise some practical issues which others might respond. Please check my question at the very end of this answer. .

Analyzing continuous outcome is relatively sophisticated. If the measurement is similar across studies due to the inherent nature of the measurement (outcomes such as blood glucose level, blood pressure, hormone levels,, etc), then standardized mean difference is not a good effect size estimator, rather mean difference is appropriate effect estimator. Practically, mean difference can be calculated mainly in three ways.

1.      Simple analysis of final values estimated by Mean difference = (Follow-up  mean among intervention group – Follow-up mean among control group)

2.      Simple analysis of Change scores estimated by: Mean difference = (mean change among the intervention group)-(mean change among the control group)

Where mean change among the control group = follow up mean C group - baseline mean Control group,

Mean change among the intervention group = follow-up mean Int. group – baseline mean Int. group

3.      Using ANCOVA estimator

The first two are biased estimators. The third one is relatively unbiased and a more conservative effect size estimator. The value of the ANCOVA estimator lies in between the first two.  It accounts for baseline imbalance and pre-post correlation within the two groups.  The bad news, practically you may find only a few RCT report using ANCOVA effect size estimator. I have experienced that and methodology papers say so.  The good news: You can calculate it if the studies report necessary information. if the studies report: (1) means and SDs at baseline and follow-up for both intervention and control groups, (2) means and SDs of change for both intervention and control groups, and (3) sample size of both intervention and control groups.

In some cases, you may have p values or confidence intervals. From p values, it is possible to calculate z scores and t scores using Excel functions eg. tinv(p,df), normsinv(1- pvalue/2). This will calculate either Z or t scores which will be helpful to impute SD, and from CI it is easy to calculate SD or SE.

Do yourself a favor, create a long excel data extraction format to extract everything. It is not feasible to do more than one outcome. If you planned more than one outcome in your meta-analysis, focus only one of them.  

If you have all of this, you can easily calculate the correlation in both control and experimental groups.

Finally, you need this two equations to calculate the ANCOVA effect size estimator. ANCOVA effect size estimator = (Follow up mean among the intervention group- Follow up mean among the intervention group) – b (Baseline mean among the int group - Baseline mean among the control group)

Equation 2: b=r(sy/sx)

To calculate r: please check the included references. If it is not possible by any means to impute r. Take an assumption of 0.5

Where b is regression coefficient to adjust for baseline correlation and baseline imbalance, r is pre-post correlation

As you have two correlation values, you need to average them.

Sx: standard deviation for the change score among the intervention group

Sy: Standard deviation for the change score among the control group.

These links will help you a lot

https://www.ncbi.nlm.nih.gov/books/NBK154408/

http://onlinelibrary.wiley.com/doi/10.1002/sim.5726/abstract;jsessionid=A1BD6C92A078821BEB5FB68ED3EB620E.f02t04

http://methods.cochrane.org/sites/methods.cochrane.org.statistics/files/public/uploads/SMG_training_course_cardiff/2010_SMG_training_cardiff_day1_session1_mckenzie.pdf

Cochrane handbook chapter 16.1, missing data

http://handbook-5-1.cochrane.org/

https://www.ncbi.nlm.nih.gov/pubmed/26715122

https://www.ncbi.nlm.nih.gov/pubmed/25927135

Finally, I would like to raise one important question for those who are following this question.

Q. For some studies, we may be able to compute the ANCOVA effect size estimator while for the others we may not due to missing data. The questions is it reasonable to combine different effect size estimators in one meta-analysis? I have seen conflicting evidence. Please share your experience.

I would like to raise one important question for those who are following this question.

Q. For some studies, we may be able to compute the ANCOVA effect size estimator while for the others we may not due to missing data. The questions is: is it reasonable to combine different effect size estimators in one meta-analysis? I have seen conflicting evidence. Please share your experience.

Thanks,

Mihiretu

Hi Miheretu,

Thank you for your response. I understood the rationale of your question but I am not very experienced in effect size statistics, I am not able to answer your question, unfortunately.

HI, the potential problem for the change fold may be non-normal distribution, so pooling approach to obtain summarry effect size. what I recommand is to take logarithm tranformation of change fold,you get a difference of logarithm scale, when you get summary effect size, then tranform bank to original scale.