Figure describes the evolution of the OR (first row), Q (second row) and I2 (third row) for each of the five interventions. We performed cumulative meta-analyses in the order in which studies were published. As expected, Q is non-decreasing over the entire period. Moreover, the average changes in Q are equally inconsistently reflected in the changes in the OR. For instance, the OR for nicotine replacement using patches changes only by 12% from 1996 to 2000 while Q changes by more than 130%. Note the difficulty of comparing Q across studies because of the different ranges as exemplified by the varying ordinates.
Figure 1 Cumulative meta-analytic estimates of the odds ratio (OR) for clonidine, nicotine replacement therapy (gum and patch), physician advice and acupuncture as smoking cessation interventions across time are shown in the first row of graphs. The second row (more ...)
The utility of I2 is immediately apparent. First, the use of standard limits from 0 to 1 allows comparisons to be made between different meta-analysis. Second, the absolute level of I2 may be interpreted in a meaningful way. For instance, we see that between-study variance (τ2) played a minimal role in comparison to within-study variance (σ2) prior to 1993 for clonidine while essentially disappearing after this time. In contrast, the results for physician advice and acupuncture showed that τ2 was proportionally large in earlier cumulations. While there was a decrease in the overall level over time, the absolute amounts remained above 35%.
Third, changes in I2 correlate well with changes in the OR, but plateauing of the OR does not necessarily mean a plateauing of I2. The dips and rises in the OR are reflected in the rise or fall of I2. This can be seen quite clearly in the early and middle periods in the cumulations of both gum and patch. The slight perturbations in the OR are magnified in trends and absolute levels of I2. However, a steady level of the OR does not necessarily mean that the I2 value stabilises, too. This is seen in the different behaviour of I2 during the later periods of the cumulations for gum and patch.
Since I2 and H2 are related arithmetically by equation (5), we would expect to see similarities in their graphical representations. This is borne out in Figure in which I2 and H values are plotted across time for the cumulative meta-analyses of the five interventions.
A comparison between trends in I2 (first row) and H (second row) across time for smoking cessation interventions.
Note that I2 is limited by [0, 1] and trends that approach these limits will be compressed. On the other hand, while H has a lower limit of 1, it has no theoretical upper limit. However, since very little heterogeneity is expected in such high values, the scale is wasted, producing a compression effect in the lower portion of the ordinate range. This effect is much more pronounced than the trends seen in the I2 curves, resulting in poorer resolution.
The evolution of measurable heterogeneity in relation to time was considered previously. When plotted in this manner, periods of increased or decreased heterogeneity may be identified for further study. For instance, I2
was about twice its final value in the mid-1980's for nicotine replacement therapy using gum (Figure , column 1). Following this period, I2
values hovered around 20% until 2000. The increase in heterogeneity may be due to the differences in the components of the intervention [17
] or quality of the research [20
] in those studies that were conducted at the time. For instance, one of the studies in 1983 [17
] assigned participants into one of four groups, only one of which included the intervention of interest (nicotine gum). In the meta-analysis, the results for the other three groups were collapsed to provide a "control" group against which the effect of nicotine gum could be compared.
Trends in the summary odds ratio (OR) and I2 for nicotine replacement therapy using gum. The first column shows trends by year of publication, the second by control event rate, and the last by cumulative sample size.
By cumulatively performing a meta-analysis by ascending (or descending) control event rates, additional information may be gained in the assessment of heterogeneity especially with regard to the severity of the condition in the study population. Note that small control event rates were associated with smaller values of I2 in nicotine replacement therapy using gum (Figure , column 2). In studies in which the control event rate of smoking cessation was at least 10%, the proportional contribution of between-study variance to the total variance was about 20%.
Meta-analyses may be performed cumulatively over the studies arranged in order of increasing sample size (Figure , column 3). The smaller number of endpoints associated with smaller studies impacts on their variability. In the case of nicotine replacement therapy using gum, the variability seemed to arise from within-study sources rather than between-study sources. It was not until more than 3,500 patients were studied cumulatively in 28 studies that appreciable heterogeneity as measured by I2 was detected.
Results for the meta-analyses performed according to year, control event rate and sample size for patches, physician advice and acupuncture are available in Additional File 1