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    meta analysis of many regression studies




    Ive searched the forum for answers to this but no joy yet so please help if you can.

    I have about 30 published studies looking at the dependence of arsenic in urine on arsenic in drinking water. All the studies find significant positive relationships as demonstrated by regression analysis. The studies cover a range of drinking water concentrations.

    I want to do a meta analysis of all these studies by taking the mean drinking water arsenic and mean urine arsenic from each study, plotting them in a scatterplot and then fitting a linear regression model to the data. This model will allow me to predict the water arsenic levels a person has been drinking by measuring the arsenic in their urine, based on all these 30 studies.

    However there are problems such as some studies report medians instead of means, some studies report ranges of water concentration rather than means etc.

    In order to research how to overcome these problems I need to understand what technique I am using. Is it meta regression? Is there a way that I can model the separate study regression equations into one equation? Can I change the data into frequency distributions and get a more probabilistic model?

    Tearing my hair out trying to find methodologies for this on the internet. Please help

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    Re: meta analysis of many regression studies

    Of the 30 studies, can you present a table of what each one presented? Perhaps if you can't unify how the units are presented, you may have to throw some out or contact the authors. You may also want to think about how you are going to weight each of these measurements, since I am guesing each study did not have the same sample size.

    What was predicted in all of the regression models, and did they control for the same covariates. Please provide much more information.
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    Re: meta analysis of many regression studies

    All the separate studies linked drinking water arsenic to urine arsenic concentration. The 30 studies I have are the result of a whittling down process making sure they all have same units, same analysis methodology, controlled for arsenic consumed in seafood etc. yes they all have different sample sizes, and they are from different countries and different ethnicities so there is bound to be intra study varation and I will need to weight studies appropriately. But I just need to know what it is im trying to do so I can look into it.

    I have found one way of going about it called a random effects model of meta analysis but that requires regression equations and SDs from each study which then narrows it down to only 6 studies. I was hoping to just analyse the average water/average urine data.

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    Re: meta analysis of many regression studies

    I believe if you can't unify units, you are out of luck and have to parcel down the eligible studies. Yes, if you want to find overall weighted effect you will need to run a meta-analysis.
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    Re: meta analysis of many regression studies

    Quote Originally Posted by hlsmith View Post
    you may have to throw some out or contact the authors.
    Yes, try contacting the authors to get the type of data you need. Let them know where you plan to publish your research, that may entice them to share since their data will be further referenced.

    Can you do a meta analysis without contacting the authors of the individual analyses?
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    Re: meta analysis of many regression studies

    OK
    Here is some dummy data to try and explain what I mean.



    So basically I have data on the average of variable X against the average of variable Y from several studies, sometimes with more than one data from the same study i.e. say the study measured the variables in different towns.
    So I want to look at how all of theses studies combined can provide a model of how variable Y varies with variable X for the general population which each of the studies provides an estimate of via a study population.

    My questions are:
    Is this actually a robust analysis without considering weights of the studies (for example considering sample sizes and standard errors from each study)? If not then how can I consider the weights? Every book I have read only explains how to do it for correlation r, odds ratios and differences in means (students t tests)

    Is including the multiple values from one study just introducing bias, even though all the studies used the exact same methodology to derive the values of X and Y?

    Some studies have included regression equations to model variable Ys response to variable X. Can I somehow do a meta analysis of the regression equation Beta values from these studies? Again, textbooks have zero info on this.

    There must be someone out there who knows what to do in this situation?

    Thanks

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    Re: meta analysis of many regression studies

    Beta values include intercepts?

    Can you plot all of the slopes for the studies to get a feel for if you may need to control for random slopes and/or effects?
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    Re: meta analysis of many regression studies

    I want to do a meta analysis of all these studies by taking the mean drinking water arsenic and mean urine arsenic from each study, plotting them in a scatterplot and then fitting a linear regression model to the data.
    I have never seen such a thing, and it is not a meta-analysis.
    Why don't you combine the the 30 regression coefficients, using
    real meta-analytic techniques (weighting by sample size etc.)?

    With kind regards

    K.

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    Re: meta analysis of many regression studies

    Yeah, and the listed contact probably also did not do the analytics. But in theory this should work

    I know you would reply, vic.
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    Re: meta analysis of many regression studies


    Great thanks for the tips.

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