1. What is heterogeneity?
Broad: Describes differences and diversity in measurements across participants, interventions, and a series of studies, or variation in inherent realism within those studies.
Narrow sense: Statistical heterogeneity, used to describe the degree of variation in effect sizes in a series of studies, and also used to indicate the existence of excess between studies except for mere foreseeable chance.
2. How to perform heterogeneity analysis?
(1) Heterogeneity test
Heterogeneity tests can be used for heterogeneity analysis, and the conclusions are more objective, including: Q test, I2 value judgment, H value judgment, etc. Usually, the p value in Q test is >0.1, which means there is no heterogeneity (i.e., homogeneity); the I2 index measures the proportion of heterogeneity between groups. Usually, when I2 is greater than 50%, the heterogeneity is considered to be high. , when I2 is greater than 75%, the heterogeneity is considered to be too high; usually, an H value greater than 1.5 indicates the existence of heterogeneity, and an H value less than 1.2 indicates that there is no heterogeneity problem. If H is between 1.2 ~ 1.5, if 95 If the % interval includes 1, it means there is no heterogeneity, otherwise it means there is heterogeneity.
(2) Visual graphics
You can also use graphics for analysis, such as forest plots, Galbraith diagrams, L’Abbe diagrams, etc. For example, an example of a forest diagram is as follows:
The left side of the forest plot shows the study name, heterogeneity test and combined effect statistical test and other information; the middle part of the forest plot shows the effect size and confidence interval, the square rectangle is the weight size, which indicates the contribution of the study, and the middle dotted line is the reference comparison. The line corresponds to the combined effect value, and the diamond represents the combined effect size result; the right side of the forest plot displays the specific data of the effect and its confidence interval, and displays the weight information of each study; if there is a subgroup, the effect size of each subgroup will be displayed and inspection information, etc.
3. How to calculate heterogeneity analysis indicators?
How to calculate Q value, I2, etc. in heterogeneity analysis? Heterogeneity analysis is implemented in many methods. For example, in meta-analysis, the SPSSAU results are as follows (taking fixed effects as an example):
The uploaded data is as follows:
The effect size results are as follows:
And so on.
You can also use excel to calculate, the results are as follows:
The results of the heterogeneity test are as follows:
So the Q value is calculated as follows:
250×（0.2-0.2814）^2+136.5333×（0.375-0.2814）^2+……+443.7333×（0.375-0.2814）^2=8.9022；
（2） I2
I2=100%×(Q-df)/Q, where Q is the Q value and df is the number of documents-1. The calculation is as follows:
100%×(8.9022-5)/8.9022=43.83％
The analysis of heterogeneity test is as follows:
When performing the heterogeneity Q test in this analysis, the p value = 0.113>=0.1, which means that there is no heterogeneity problem and the fixed effects model can be considered.
I2 represents the proportion of heterogeneity. As can be seen from the table above: The I2 value is 0.438<=50%, which means that there is no heterogeneity problem in the study, and the fixed effects model can be considered.
H2 represents the ratio of the total variation to the variation within the group. The larger H2 is, the greater the variation between groups, that is, the greater the heterogeneity. In substantive research, the H value (the root of H2) is generally used for analysis. At the time of this study: the H value is 1.334, which is between 1.2 and 1.5, and its 95% confidence interval does not include 1, which means that this study has certain heterogeneity and the random effects model can be considered.
[PS: Heterogeneity analysis usually combines multiple indicators to make a comprehensive decision. If there are conflicting results between indicators, it is recommended to use the Q test or I2 value as the criterion. In addition, the tau2 value in the random effect represents the degree of dispersion of the effect size, which is the estimated value in the random effect. The larger the value, the stronger the heterogeneity]
4. How to deal with heterogeneity?
(1) Indicators that change the outcome variable
Fleiss points out that simply changing the indicator of the outcome variable may be sufficient to remove heterogeneity. For a dichotomous variable, changing the index of the outcome variable from an absolute measurement scale (such as risk difference RD) to a relative measurement scale (such as odds ratio OR) can reduce the degree of heterogeneity. For continuous variables, transforming them into logarithmic form is also a common method, although this method may lead to a trade-off between statistical homogeneity and clinical interpretability.
(2) Select random effects to combine effect sizes
In meta-analysis, statistical methods generally include fixed effects and random effects. The fixed effect is a calculation model of combined effect size in which all observed variations are caused by chance. The random effect also takes into account the within-study sampling error and the random effect. When the included studies have heterogeneity other than chance, the random effects model will give a wider confidence interval than the fixed effects model. (PS: If the heterogeneity is small, you can choose the fixed effects model. If the heterogeneity is large, you can choose the random effects model, but other analysis is required)
(3) Explain heterogeneity
When heterogeneity occurs, it is necessary to explore the source of heterogeneity, which can be viewed through subgroup analysis, meta-regression, and sensitivity analysis.
(4) Ignore heterogeneity
[1] Wang Dan, Zhai Junxia, Mou Zhenyun, etc. Heterogeneity and its processing methods in meta-analysis [J]. Chinese Journal of Evidence-Based Medicine, 2009, 9(10): 1115-1118.