Allocation of subjects to test null relative risks smaller than one

Comparative poisson clinical trials of multiple experimental treatments vs a single control using the negative multinomial distribution

This paper introduces a method which conditions on the number of events that occur in the control group to determine rejection regions and power for comparative Poisson trials with multiple experimental treatment arms that are each compared to one control arm. This leads to the negative multinomial as the statistical distribution used for testing. For one experimental treatment and one control with curtailed sampling, this is equivalent to Gail's (1974) approach. We provide formulas to calculate exact one-sided overall Type I error and pointwise power for tests of treatment superiority and inferiority (vs the control). Tables of trial design parameters for combinations of one-sided overall Type I error = 0.05, 0.01 and pointwise power = 0.90, 0.80 are provided. Curtailment approaches are presented to stop follow-up of experimental treatment arms or to stop the study entirely once the final outcomes for each arm are known.

Why add anything to nothing? The arcsine difference as a measure of treatment effect in meta-analysis with zero cells

For clinical trials with binary endpoints there are a variety of effect measures, for example risk difference, risk ratio and odds ratio (OR). The choice of metric is not always straightforward and should reflect the clinical question. Additional issues arise if the event of interest is rare. In systematic reviews, trials with zero events in both arms are encountered and often excluded from the meta-analysis.The arcsine difference (AS) is a measure which is rarely considered in the medical literature. It appears to have considerable promise, because it handles zeros naturally, and its asymptotic variance does not depend on the event probability.This paper investigates the pros and cons of using the AS as a measure of intervention effect. We give a pictorial representation of its meaning and explore its properties in relation to other measures. Based on analytical calculation of the variance of the arcsine transformation, a more conservative variance estimate for the rare event setting is proposed. Motivated by a published meta-analysis in cardiac surgery, we examine the statistical properties of the various metrics in the rare event setting.We find the variance estimate of the AS to be more stable than that of the log-OR, even if events are rare. However, parameter estimation is biased if the groups are markedly unbalanced. Though, from a theoretical viewpoint, the AS is a natural choice, its practical use is likely to continue to be limited by its less direct interpretation.

Successful multi-site measurement of antisaccade performance deficits in schizophrenia

The antisaccade task is a promising schizophrenia endophenotype; it is stable over time and reflects neurophysiological deficits present in both schizophrenia subjects and their first-degree relatives. Meaningful genetic research requires large sample sizes that are best ascertained using multi-site study designs. To establish the criterion validity of the antisaccade task in a multi-site design, the Consortium on the Genetics of Schizophrenia (COGS) examined whether seven sites could detect previously reported antisaccade deficits in schizophrenia subjects. Investigators presented 3 blocks of 20 antisaccade stimuli to 143 schizophrenia subjects and 195 comparison subjects. Frequent collaborator communication, standardized training, and ongoing quality assurance optimized testing uniformity. Data were discarded from only 1.2% of subjects due to poor quality, reflecting the high fidelity of data collection and scoring methods. All sites detected a significant difference in the proportion of correct antisaccades between schizophrenia and comparison subjects (p<.02 at all sites); group differences in gain and latency were less robust. Regression analyses to adjust for the effects of group, site, age, gender, smoking, and parental education on the proportion of correct antisaccades revealed a significant effect of group, site, and age but no effect of gender, smoking, or parental education, and no group-by-site interactions. Intraclass correlations between proportion of correct antisaccades across the blocks of stimuli ranged from 0.87 to 0.93, demonstrating good within-session reliability at sites. These results confirm previous findings of antisaccade deficits in schizophrenia subjects and support the use of the antisaccade task as a potential schizophrenia endophenotype in multi-site genetic studies.

Subject allocation and study curtailment for fixed event comparative poisson trials

Comparative Poisson trials of prophylactic interventions, such as vaccines, can be lengthy and costly. We evaluate two easily implemented approaches to reduce numbers of disease cases and person years of follow up (N(u+t)) for comparative Poisson trials with fixed numbers of cases (T); (i) altering k the portion of N(u+t) allocated to treatment and (ii) curtailed stopping before T cases if numbers of cases in the treatment or control group indicate that H(0) has already been rejected or will not be rejected at T cases. Normal and arcsine approximations as well as discrete exact tests are evaluated. For studies not stopped early, allocating about 1/(1+\sqrt r_a) of person years to treatment roughly minimizes T needed for given size and power (where r(a) is the alternative hypothesized relative disease incidence in treated subjects used to power the study). This reduces T moderately vs equal allocation (k=0.5) by 2-3 cases in our examples with exact tests. However, the common practice of allocating k=0.5 of the person years to treatment may be the overall best strategy to minimize N(u+t) for studies that are not stopped early. For studies analysed by exact test and planned with a one-sided alpha ranging from 0.005 to 0.025, beta from 0.1 to 0.2 and r(a) from 0.2 to 0.5, curtailed stopping reduces both the number of disease cases and N(u+t) by 6-40 per cent depending on true treatment benefit. With curtailed stopping, allocating k=0.5 person years to treatment approximately minimizes the numbers of cases and person years under most conditions, although k as large as 0.6 often performs comparably well. If a specific localized k is selected to minimize disease cases for a study analysed by exact test, the study may be underpowered should the final allocation deviate even slightly from that k when it is conducted.