Deliverable D 1.3 RESULTS OF META-ANALYSIS ... - cast-eu.org

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Campaigns and awareness raising strategies in traffic safety — Deliverable D-1.1In meta-analysis, then, the odds ratio is treated in two ways: (i) it istransformed to its natural logarithm, and (ii) it assigned a weight. A weight iscalculated for each individual effect using the formula 29 :1/(1/[n before campaign] + 1/[n after campaign] + 1/[control n before campaign] + 1/[control nafter campaign])Thus the greater the number of accident counts the effect is based on, thegreater the weight assigned to the effect. A final weighted effect is thenobtained by simply multiplying the ln odds ratio by the weight.Once a weighted effect has been obtained for each individual effect in a set ofeffects, an overall effect for the set is calculated by dividing the sum of theindividual weighted effects by the sum of the individual weights, and theninversing the natural logarithm to obtain the overall effect in terms of theoriginal odds ratio, which can then be converted to a percentage effect, asdescribed above.In this way, we calculated that the overall weighted effect of road safetycampaigns on accident counts according to the effects extracted from thestudies retrieved is a statistically significant reduction of 10%. The result ispresented in Table 7.17.Table 7.17 Overall effect of road safety campaigns on road accidents according to the effects extractedfrom the studies identified.Groupeffect(%)95%confidenceinterval (%)Significant?(p < 0.05)All accident effects (n = 115) - 10 (- 11 -10) yesStep 2 & 3. Publication biasThe overall effect reported is dependent on the effects extracted from thestudies retrieved. It is a valid concern that these studies do not represent thetrue overall effect. Although we have tried to obtain unpublished studies wherepossible, most of the studies included in the database are published. Theconcern is therefore that our overall effects are influenced by publication bias,a tendency for authors to publish only favourable effects and not to publishunfavourable ones. If there is publication bias, the magnitude of the overalleffects reported here may be too great.One way to observe publication bias is to plot the weight of each effect, whichas we have seen can be considered as the relative number of participants orcounts in that study, against the effect size, as shown in Figure 7.1. It isreasonable to assume that the individual effects in such a plot should be29 The reader might appreciate the anomaly that where there are no control data, greaterweight is assigned. However, an adjustment is made for this by doubling the weightdenominators for non-controlled effects.66
Campaigns and awareness raising strategies in traffic safety — Deliverable D-1.1normally distributed about the true effect size, which should be approachedwith greater proximity by those studies with greater weight. There is said to bepublication bias where this normal distribution is skewed in the direction of‘favourable’ effect.Figure 7.1 indicates that there is indeed publication bias for the set of effectsbased on accident counts included in the CAST database (bias can be seenin normal distribution of the solid diamonds). However, it is possible to correctfor this bias using a statistical method called trim-and-fill. This methodattempts to represent the true distribution of effects by adding in the ‘missing’or unfavourable data points. A computer algorithm is used to generate twoestimates of the number of studies that should be added to the ‘depleted’ sideof the distribution in order to make it normal. The two estimators are called Rand L.R is generated by first modifying the effect set by subtracting the average ofall effects from each individual effect. The mathematical sign of the modifiedeffects is then disregarded while they are ranked in order of size. Sign isreallocated to the resulting rank values, in order to find the number of effectsalong an uninterrupted sequence of one mathematical sign, beginning withthe largest effect value going down. The number 1 is subtracted from thenumber of effects in this uninterrupted sequence to obtain R.For the accident data in Figure 7.1 it is estimated that there are no missingstudies using R. This can be explained in simpler terms by referring to theextreme negative and positive ln effect values in Figure 7.1. Independent ofsign, the data point with the highest value is (-)1.31, but the next highest is(+)1.25, and so the number of ranks of one particular sign in the highestvalued sequence is 1. Thus according to the R estimator there are no missingstudies because 1-1=0.L estimates not the number of extreme values missing on the depleted side ofthe distribution, but the number of values missing across the depleted side ofthe effects. To begin with, the effects are again ranked according to size,independent of sign, and the signs of the original effects reattributed to theirrank values. The rank values are then divided into two sets, according to sign.Then the following equation is used 30 :L = (4T n – n[n+1]) / (2n-1)where T n is the sum of rank values in the largest rank set, and n is the totalnumber of effects in the group being analysed for bias . For the accident datain Figure 6.1, the estimator of missing effects L = 26. We can see by lookingat Figure 6.1 that, relative to the left, a number of effects are indeed missingacross the right hand side.Consultation of the two estimators R and L together is recommended by Duvaland Tweedie (2000). In our conservative approach, we simply use whicheverestimator gives the largest value.Trim-and-fill generates compensatory effects to fill the distribution by copyingthe most extreme values on the favoured side and ‘pasting’ them into the30 This is actually used in reiterative rounds of testing of the data set in order to achieve anoptimal solution, using a computer algorithm.67
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