Hi Heba, 

The Cochrane Handbook provides a really useful guide to how to analyse binary data. http://handbook.cochrane.org/ - 

Dichotomous (binary) outcome data arise when the outcome for every participant is one of two possibilities, for example, dead or alive, or clinical improvement or no clinical improvement. This section considers the possible summary statistics when the outcome of interest has such a binary form. The most commonly encountered effect measures used in clinical trials with dichotomous data are:

the risk ratio (RR) (also called the relative risk);

the odds ratio (OR);

the risk difference (RD) (also called the absolute risk reduction); and

the number needed to treat (NNT).

Details of the calculations of the first three of these measures are given in Box 9.2.a. Numbers needed to treat are discussed in detail in Chapter 12 (Section 12.5).

Aside: As events may occasionally be desirable rather than undesirable, it would be preferable to use a more neutral term than risk (such as probability), but for the sake of convention we use the terms risk ratio and risk difference throughout. We also use the term ‘risk ratio’ in preference to ‘relative risk’ for consistency with other terminology. The two are interchangeable and both conveniently abbreviate to ‘RR’. Note also that we have been careful with the use of the words ‘risk’ and ‘rates’. These words are often treated synonymously. However, we have tried to reserve use of the word ‘rate’ for the data type ‘counts and rates’ where it describes the frequency of events in a measured period of time.

I would write the authors of the article you need additional data from. Most often your peers are happy to help :)

Highly appreciate your help! Your ideas are different but all helpful

Heba, meta-analysis is, by definition, a quantitative synthesis. It calculates weighted average of summary statistics from each study. Without numerical data you cannot calculate this. For binary outcomes, you need ratio (RR or OR) or difference of risks and their 95% confidence interval (CI). 

Another reason you need numerical data is that the main condition for meta-analysis is that the results of the included studies should be similar to each other (no significant heterogeneity). If the study reports only "increase/decrease", and doesn't not report the numerical data, you can't compare the results (can't determine heterogeneity).  You can contact the the authors to request the numerical values.

Mine

Just pasting few points from the Cochrane Handbook for Systematic Reviews of Interventions on missing data.

The principal options for dealing with missing data are.

1. analysing only the available data (i.e. ignoring the missing data);

2. imputing the missing data with replacement values, and treating these as if they were observed (e.g. last observation carried forward, imputing an assumed outcome such as assuming all were poor outcomes, imputing the mean, imputing based on predicted values from a regression analysis);

3. imputing the missing data and accounting for the fact that these were imputed with uncertainty (e.g. multiple imputation, simple imputation methods (as point 2) with adjustment to the standard error);

4. using statistical models to allow for missing data, making assumptions about their relationships with the available data.

Option 1 may be appropriate when data can be assumed to be missing at random. Options 2 to 4 are attempts to address data not missing at random. Option 2 is practical in most circumstances and very commonly used in systematic reviews. However, it fails to acknowledge uncertainty in the imputed values and results, typically, in confidence intervals that are too narrow. Options 3 and 4 would require involvement of a knowledgeable statistician.

Four general recommendations for dealing with missing data in Cochrane reviews are as follows.

Whenever possible, contact the original investigators to request missing data.

Make explicit the assumptions of any methods used to cope with missing data: for example, that the data are assumed missing at random, or that missing values were assumed to have a particular value such as a poor outcome.

Perform sensitivity analyses to assess how sensitive results are to reasonable changes in the assumptions that are made (see Chapter 9, Section 9.7).

Address the potential impact of missing data on the findings of the review in the Discussion section.

The preferred option is to contact/write the author(s) of the study and request missing data. But in my case, I am just unlucky to get the missing data from the study author, even after couple of requests ...!

http://handbook.cochrane.org/chapter_16/16_1_2_general_principles_for_dealing_with_missing_data.htm

Yes you can, but the problem will be that you always end up with Null Hypothesis. Moreover, the study measures like tau^2, H^2, I^2 shows you either zero or one (if your data is binary in nature) and it is highly unlikely that you get any valid value for R^2. But you may get  a meaningful forest and funnel plots I guess. So better to avoid binary data only to remain in favor of the purpose of Meta Analysis.  You can take dummy data sets and try in R or for that matter Spreadsheets also useful.