Calculation of sample size for stroke trials assessing functional outcome: comparison of binary and ordinal approaches

Background Many acute stroke trials have given neutral results. Sub-optimal statistical analyses may be failing to detect efficacy. Methods which take account of the ordinal nature of functional outcome data are more efficient. We compare sample size calculations for dichotomous and ordinal outcomes for use in stroke trials. Methods Data from stroke trials studying the effects of interventions known to positively or negatively alter functional outcome – Rankin Scale and Barthel Index – were assessed. Sample size was calculated using comparisons of proportions, means, medians (according to Payne), and ordinal data (according to Whitehead). The sample sizes gained from each method were compared using Friedman 2 way ANOVA. Results Fifty-five comparisons (54 173 patients) of active vs. control treatment were assessed. Estimated sample sizes differed significantly depending on the method of calculation (Po00001). The ordering of the methods showed that the ordinal method of Whitehead and comparison of means produced significantly lower sample sizes than the other methods. The ordinal data method on average reduced sample size by 28% (inter-quartile range 14–53%) compared with the comparison of proportions; however, a 22% increase in sample size was seen with the ordinal method for trials assessing thrombolysis. The comparison of medians method of Payne gave the largest sample sizes. Conclusions Choosing an ordinal rather than binary method of analysis allows most trials to be, on average, smaller by approximately 28% for a given statistical power. Smaller trial sample sizes may help by reducing time to completion, complexity, and financial expense. However, ordinal methods may not be optimal for interventions which both improve functional outcome

The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Döring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

Granulocyte-colony stimulating factor in experimental stroke and its effects on infarct size and functional outcome: a systematic review

Background Granulocyte-colony stimulating factor (G-CSF) shows promise as a treatment for stroke. This systematic review assesses G-CSF in experimental ischaemic stroke. Methods Relevant studies were identified with searches of Medline, Embase and PubMed. Data were extracted on stroke lesion size, neurological outcome and quality, and analysed using Cochrane Review Manager using random effects models; results are expressed as standardised mean difference (SMD) and odds ratio (OR). Results Data were included from 19 publications incorporating 666 animals. G-CSF reduced lesion size significantly in transient (SMD -1.63, p<0.00001) but not permanent (SMD -1.56, p=0.11) focal models of ischaemia. Lesion size was reduced at all doses and with treatment commenced within 4 hours of transient ischaemia. Neurological deficit (SMD -1.37, p=0.0004) and limb placement (SMD -1.88, p=0.003) improved with G-CSF; however, locomotor activity (>4 weeks post ischaemia) was not (SMD 0.76, p=0.35). Death (OR 0.27, p<0.0001) was reduced with G-CSF. Median study quality was 4 (range 0-7/8); Egger’s test suggested significant publication bias (p=0.001). Conclusions G-CSF significantly reduced lesion size in transient but not permanent models of ischaemic stroke. Motor impairment and death were also reduced. Further studies assessing dose-response, administration time, length of ischaemia and long-term functional recovery are needed.