Optimising the Analysis of vascular Prevention trials (OA-Prevention)

Statistical analysis of vascular eventsPrevention trials typically count outcomes as dichotomous events (e.g. stroke-no stroke) although this is inefficient statistically and gives no indication on the severity of recurrent events. It is hypothesised that vascular events may be polychotomised with ordering determined by severity, e.g. stroke categorised as fatal-severe-mild-TIA-no stroke. In the OA-P pilot study using published summary trial data, ordinal analysis of these ordered categorical outcomes was more efficient statistically than current binary approaches. It is planned to further test this concept using individual patient data from the same trials, not least because many publications do not provide sufficient granular data. Relevant trials will be identified and ordered vascular outcomes will be generated. Binary and ordinal statistical methods of analysis will be then compared, both unadjusted and adjusted, then compared sample size estimates and number-needed-to-treat for these trials using published binary and ordinal methods. If these ordinal approaches are superior, future trials should consider using stroke and other vascular outcomes as ordered categories, and should be analysed using ordinal (or even linear) statistical tests. Using this approach, future trials could potentially be smaller (thereby reducing trial costs and competition for patient recruitment) and provide extra information on the effect of treatment on the severity, as well as frequency of vascular events. This information will be vital for patients, carers, healthcare professionals, and Government. It is hypothesised that vascular events may be polychotomised with ordering determined by severity: -   3 stroke levels: Fatal / non-fatal / no stroke-   4 stroke levels: Fatal / severe (dependent) / mild (independent) / no stroke-   4 stroke/TIA levels: Fatal / severe / TIA / no stroke-TIA-   5 stroke/TIA levels: Fatal / severe / mild / TIA / no stroke-TIA-   5 stroke/TIA levels: Fatal / severe (mRS 2-5) / mild (mRS 0,1) / TIA / no stroke-TIA [This is the primary outcome in the on-going BHF TARDIS trial; PB is CI.]-   6 stroke/TIA levels: Fatal / severe (mRS 4,5) / moderate (mRS 2,3) / mild (mRS 0,1) / TIA / no stroke-TIA-   9 stroke/TIA levels: fatal / mRS=5 / mRS=4 / mRS=3 / mRS=2 / mRS=1 / mRS=0 / TIA / no stroke-TIA-   3 MI levels: Fatal / non-fatal / no event-   4 MI levels: Fatal / non-fatal / angina / no event-   6 MI levels: Fatal / MI + heart failure / STEMI + no heart failure / NSTEMI / unstable angina / none-   3 vascular levels: Fatal stroke or MI / non-fatal stroke or MI / no event-   4 vascular levels: Fatal stroke or MI / non-fatal stroke or MI / TIA or angina / no event-   4 renal failure levels: Fatal / dialysis / no dialysis / no event-   4 venous thromboembolism (VTE) levels: Fatal / non-fatal pulmonary embolism (PE) / deep vein thrombosis (DVT) / no event-   3 serious adverse event levels: Fatal / non-fatal serious / no event-   4 serious adverse event levels: Fatal / severe / moderate-mild / no event-   5 serious adverse event levels: Fatal / severe / moderate / mild / no event-   3 bleeding levels: Fatal / non-fatal major / no bleeding-   4 bleeding levels: Fatal / major / moderate-mild / no bleeding-   5 bleeding levels: Fatal / major / moderate / mild / no bleedingThe choice of ordinal scale will depend, in part, on its reliability and ease of measurement. Statistically, 5-9 levels will be more efficient than having fewer; clinically, it will be difficult to differentiate more than 9 levels. The underlying assumption in using such ordered outcomes is that treatments will have benefit across the range of event severity, i.e. the intervention will reduce the number of severe strokes by making them less severe, and reduce the number of mild strokes by preventing them all together; when present, this delivers the assumption of ‘proportionality of odds', as seen for the majority of trials in OAST-A and the OA-P pilot. A number of advantages are likely to accrue with ordinal analysis of ordered outcome scales as compared with conventional binary analysis of dichotomous outcomes:-   Ordinal analysis is more efficient (powerful) statistically, i.e. confidence intervals are narrower and p-values smaller (as it was showed in acute stroke).-   Ordinal analyses may be more efficient than time to event analyses (e.g. log rank test) since these offer little advantage over dichotomous approaches when event rates are low (e.g. <14%).-   Calculated sample sizes for ordinal scales are smaller, as showed in acute stroke.-   Calculated numbers needed to treat (NNT) are smaller, i.e. more subjects will be seen to benefit, as it was showed in acute stroke and in one secondary prevention trial (ESPS-2).-   Ordered outcomes convey to patients, carers, healthcare practitioners and Government that interventions alter both severity and frequency of outcomes. Reductions in stroke severity are important economically since healthcare costs are much higher with severe non-fatal events.-   Hazardous interventions are easier to identify if ordered outcomes are assessed, as seen with HRT (stroke) and chronic antiplatelets (bleeding).It has been argued that ordinal scales with sufficient numbers of levels, e.g. 7 or more, should be analysed using continuous (parametric) approaches, particularly if the dataset is large (so that large-sample normal approximations become valid). Nevertheless, ordinal data is often skewed and kurtotic which will reduce the power advantage of parametric over non-parametric approaches.Statistical approachesUnivariate analyses - compare ordinal, nominal and dichotomous approaches Statistical approaches for analysing dichotomous, nominal and ordered data will be compared: (i)   Fisher's Exact test/Chi-square - binary data. (ii)   Fisher-Freeman-Halton test/Chi-square - unordered multi-level data; [this will provide a ‘negative' control for ordered tests.] (iii)   Cochran-Armitage trend test.(iv)   MWU two-sample test. (v)   Robust Ranks Test [34]. (vi)   t test (pooled). (vii)   t test (unpooled/Welsh). (viii)   Bootstrap of difference in mean rank (3 x 3000 cycles [35, 36]). Chi-square and MWU tests will be corrected for continuity, a conservative approach; MWU will also be adjusted for ties. Each data set will be analysed using each test and the z score obtained (as in OAST-A). [Other non-parametric tests will not be used since they have assumptions which will not be appropriate (e.g. Wald-Wolfowitz runs test is inappropriate if multiple ties are present).]Multiple variable analyses - compare ordinal and dichotomous approaches Where relevant, statistical approaches relating to the analysis of dichotomous and ordinal data with and without adjustment for baseline covariates will be performed. These approaches will parallel and be compared with the above univariate tests: (i)   logistic regression (binary events); (ii)   ordinal logistic regression; (iii)   Cochran-Mantel-Haenszel test; (iv)   multiple linear regression; (v)   Cox regression (binary time to event data).Comparison of statistical testsEach data set will be analysed using each statistical approach. These results will then be ordered within each trial and given a rank, with the lowest rank given to the test which produced the most significant result, i.e. the largest z score, within that trial. A 2-way analysis of variance test will then be used to see on average which statistical test had produced the lowest ranks. The statistical tests will be then ordered in terms of their efficiency in identifying treatment effects. The number of statistically significant (at 5%) results each test found will be also assessed.To assess the validity and reliability of the results, a number of supplementary analyses will be carried out:1.   Comparison of statistical tests within subgroups of trials sharing similar characteristics (although there may not be enough trials to allow this for all subgroups)2.   Assessment of statistical assumptions underlying the tests3.   Assessment of the sensitivity of the tests to ensure that treatment effects are only detected when they truly existed (the type 1 error rate).Analyses will be carried out in SAS (version 9.3 or later) and significance will be taken at P<0.05.