When doing meta-analysis of continuous outcome such as glycated haemoglobin (which the scale of measurement is similar across studies), mean difference is the preferred effect size estimator. There are three ways of measuring effect size estimate for continious outcomes with similar scale of measurement. Simple analysis final values, Change scores and ANCOVA effect size estimator. It is well recognized that ANCOVA estimator is the best effect size estimator as it adjusts for baseline imbalance and correlation.

To do meta-analysis using ANCOVA etsimator, we need to have ANCOVA estimator from each RCTs. However, many RCTs don't report this value.

In many papers, it is described that ANCOVA effect size estimator can possibly be calculated:   " When a study does not report ANCOVA estimates, it is possible to calculate them if the studies report: (1) means and SDs at baseline and followup 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.". Randomized Control Trials, unfortunately, don’t report with such level of detail.

From the available literature, I have been trying to find out the formula how to calculate the ANCOVA effect size estimator for continuous outcome(in my case glycated hemoglobin level measured as A1c%). Some of the papers I have read reported that it is possible to calculate it given that necessary information is reported from individual studies.  https://www.ncbi.nlm.nih.gov/books/NBK154408/.

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

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

My questions regarding calculating the ANCOVA effect size estimate:

1.      How can we calculate ANCOVA estimate while we don't have individual participant data?  Jo McKenzie described a formula how to calculate it

Equation 1: 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)

Where b is regression coefficient to adjust for baseline coorelation and baseline imbalance, r is correlation

The coefficient (b) can be calculated from correlation and the SD of y and x as described in the second equation above.

2.      When we calculate b (coefficient), which correlation should we use (Note that: there are two correlation results as both for control and intervention groups)? In addition, there are SD in Y and SD in X mentioned as numerator and denominator in the second equation. We have 4 SD for Follow up mean among the int group, Follow up mean among the control group, Baseline mean among the int group, Baseline mean among the control group. Which SD among the intervention and the control group should I use to calculate the Beta coefficient?

I really appreciate if you help me on these issues. Thank you very much in advance.

Kind regards,

Mihiretu Kebede