Incidence Rate Meta-analysis


Menu location: Analysis_Meta-Analysis_Incidence Rate.


Cohort studies are often used to reveal incidence rates of a condition under different environmental conditions or exposures. This function helps you to compare incidence rates from several studies by meta-analysis (Sahai and Kurshid, 1996; Ioannidis et al., 1995; Rothman and Monson 1983). Meta-analysis may be used to investigate the combination or interaction of a group of independent studies, for example, a series of incidence rates from similar studies conducted at different centres.


You can also use incidence rate difference to provide a better estimate of the effects of treatment in groups of trials that have different lengths of follow up.


Person time for a group is the sum total of times that each of the subjects in that group have been studied for:


  Exposed Not exposed
Group Cases Person-time Cases Person-time
stratum 1: a1 pte1 b1 ptn1
. . . . .
stratum k: ak ptek bk ptnk


For each stratum:

Incidence rate difference = IRD = [a/pte] - [b/ptn]

Incidence rate ratio = IRR = [a/pte] / [b/ptn]


StatsDirect gives you the option of IRD or IRR based meta-analysis. For each stratum (e.g. trial) you are given either IRD (with approximate confidence interval) or IRR (with exact confidence interval). Pooled estimates for IRD or IRR are given for both fixed and random effects models.


An exact conditional likelihood method is optionally used to evaluate the pooled rate ratio (Martin and Austin, 2000). The exact method may take an appreciable time to compute with large numbers. The exact results should be used in preference to the approximation, especially if some categories involve few observations (less than 15 or so).


The inconsistency of results across studies is summarised in the I² statistic, which is the percentage of variation across studies that is due to heterogeneity rather than chance – see the heterogeneity section for more information.



You may enter the number of cases occurring in an exposed and a non-exposed group where subjects are possibly followed up for different times. Person time for a group is the sum total of times that each of the subjects in that group have been studied for.


Technical Validation

Pooled incidence rate difference for fixed effects is estimated as follows:

- where the weight, Wi, is the inverse of the estimated variance.


Pooled incidence rate ratio for fixed effects is estimated as follows:

- where the weight, Wi, is the inverse of the estimated variance for the log transformed statistic.



The example looks at mortality by sex and age for patients with trigeminal neuralgia (Rothman et al., 1973). The person-time data are person-years.


  Exposed Not exposed
Group: Cases Person-time Cases Person-time
Age < 65: 14 1516 10 1701
Age ³ 65: 76 949 121 2245


To analyse these data in StatsDirect first prepare them in four workbook columns and label these columns appropriately. Alternatively, open the test workbook using the file open function of the file menu. Then select incidence rate difference from the meta-analysis section of the analysis menu. Select the columns marked "Exposed cases", "Exposed person-time", "Non-exposed cases" and "Non-exposed person-time" when prompted for data. Note that "exposed" and "experimental" groups are the same.


For this example:


Incidence rate difference (IRD) meta-analysis


Study Table (a, person-time exposed, b, person-time not exposed)
1 14 1516 10 1701   age <65
2 76 949 121 2245   age >=65


Study IRD 95% CI (approximate) % Weights (fixed, random)
1 0.0034 -0.0026 0.0093 91.9048 59.4819
2 0.0262 0.0073 0.045 8.0952 40.5181


Fixed effects (inverse variance)

Pooled IRD = 0.005204 (95% CI = -0.000602 to 0.01101)

Z (test IRD differs from 0) = 1.756825 P = 0.0789


Non-combinability of studies

Cohran Q = 4.419452 (df = 1) P = 0.0355

Moment-based estimate of between studies variance = 0.000202

I² (inconsistency) = *% (95% CI = *% to *%)


Random effects (DerSimonian-Laird)

Pooled IRD = 0.012607 (95% CI = -0.009361 to 0.034574)

Z (test IRD differs from 0) = 1.124754 P = 0.2607


Here we infer with 95% confidence, assuming a fixed effects model, that the true size of the difference between incidence rates was somewhere between -0.0006 and 0.01 person-years for the exposed group compared with the non-exposed group; i.e. not statistically significant.


P values

confidence intervals



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