meta regression

[Shripada Rao]

Hi,
We conducted a meta-analysis to find if hyperglycaemia is associated with increased risk of mortality. We included 12 studies that had given adjusted odds ratios and pooled them together. The pooled odds ratio was 2.416 (95% CI:1.364; 4.279). Heterogeneity was high (I²=60%).
We explored heterogeneity by conducting a meta regression wherein the covariate was the cut-off value of blood glucose that was used to define hyperglycaemia in individual studies. Two studies had used blood glucose threshold of 6.6 mmol/L, three studies used 8.3, four studies used 10, one used 11.1, one used 12 and one used 16.6 mol/L.
The meta-regression output was as below. I would be grateful for help with interpretation of this output.

meta regress hyperglycemia_definition

Effect-size label: Effect Size
Effect size: mortality_log_or_adj
Std. Err.: mortality_se_adj

Random-effects meta-regression Number of obs = 12
Method: REML Residual heterogeneity:
tau2 = .6156
I2 (%) = 62.48
H2 = 2.67
R-squared (%) = 0.00
Wald chi2(1) = 0.19
Prob > chi2 = 0.6661
-----------------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------------+----------------------------------------------------------------
hperglycemia_definition | .0543421 .1259339 0.43 0.666 -.1924838 .301168
_cons | .3701254 1.22663 0.30 0.763 -2.034024 2.774275
-----------------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(10) = 23.66 Prob > Q_res = 0.0085

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[Tiago Pereira]

Hi, Shripada.

To have a better understanding on how much your explanatory variable (blood glucose threshold) explains the between-study variance, I would suggest to fit the random-effects model for the summary log-odds ratio with the REML estimator of between-study variance. That model will be more comparable to the estimates from the meta-regression model. In other words, both estimates (univariate meta-analysis and meta-regression model) should be based on the REML estimator to facilitate the comparison. If your initial random-effects model was based on the methods-of-moments (MM), it is more complicated to compare it to the REML estimator from the meta-regression model. MM and REML estimates often differ in magnitude, with REML being a better estimator (in general).

Apparently, there is no association between blood glucose threshold and the magnitude of the log-odds ratio (P = 0.67).

The model did not explain the between-study variance (R² = 0), and the residual statistical heterogeneity is still significant (P = 0.0085).

However, it is unclear whether you have created a meta-regression model with categorical variables (0 = 6.6 mmol/L,1 = 8.3 mmol/L, 2 = 10 mmol/L, etc) and tested the linear trend, or whether you assumed that the explanatory variable was continuous. Have you considered it as a factor variable?

Check the following link:
https://journals.sagepub.com/doi/pdf...867X0800800403

It provides details on how to interpret meta-regression in Stata. Although it uses -metareg-, the interpretation is the same.
Hope this help.

Tiago

[Shripada Rao]

Hi Tiago, thanks so much the interpretation of the stata output and for your advice. I will go through the article that you have suggested. I had fitted the random-effects model for the summary log-odds ratio with the REML estimator of between-study variance. For meta-regression, I had assumed that the explanatory variable was continuous. Regards, Shripada Rao

[Shripada Rao]

Now I converted them into categorical variables: 0= less than 8; 1= 8-9.9; 2=10 to 11.9; 3= 12 or more.
Still found no association between hyperglycemia and mortality



Random-effects meta-regression Number of obs = 12
Method: REML Residual heterogeneity:
tau2 = .6091
I2 (%) = 63.40
H2 = 2.73
R-squared (%) = 0.00
Wald chi2(3) = 2.01
Prob > chi2 = 0.5709
--------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
hypergly_group |
1 | .0960165 .8883006 0.11 0.914 -1.645021 1.837054
2 | .9046921 .7902218 1.14 0.252 -.6441141 2.453498
3 | .894328 1.022329 0.87 0.382 -1.1094 2.898056
|
_cons | .3734486 .6307528 0.59 0.554 -.8628041 1.609701
--------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 20.97 Prob > Q_res = 0.0072

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[Tiago Pereira]

Yes, Shripada, there is no evidence that that variable is associated with the magnitude of the log-odds ratio in your meta-analysis. Low statistical power cannot be ruled out, though.

[Shripada Rao]

Thank you Tiago