Use of unequal allocation in survival trials

Optimal allocations for two treatment comparisons within the proportional odds cumulative logits model

This paper studies optimal treatment allocations for two treatment comparisons when the outcome is ordinal and analyzed by a proportional odds cumulative logits model. The variance of the treatment effect estimator is used as optimality criterion. The optimal design is sought so that this variance is minimal for a given total sample size or a given budget, meaning that the power for the test on treatment effect is maximal, or it is sought so that a required power level is achieved at a minimal total sample size or budget. Results are presented for three, five and seven ordered response categories, three treatment effect sizes and a skewed, bell-shaped or polarized distribution of the response probabilities. The optimal proportion subjects in the intervention condition decreases with the number of response categories and the costs for the intervention relative to those for the control. The relation between the optimal proportion and effect size depends on the distribution of the response probabilities. The widely used balanced design is not always the most efficient; its efficiency as compared to the optimal design decreases with increasing cost ratio. The optimal design is highly robust to misspecification of the response probabilities and treatment effect size. The optimal design methodology is illustrated using two pharmaceutical examples. A Shiny app is available to find the optimal treatment allocation, to evaluate the efficiency of the balanced design and to study the relation between budget or sample size and power.

Cost-efficient clinical studies with continuous time survival outcomes

Time-to-event outcomes are common in clinical studies. For example, the time to a first major adverse cardiovascular event (MACE, defined as CVD death, nonfatal myocardial infarction, or stroke) is a commonly used outcome in cardiovascular outcome trials. Owing to the lengthy time frame and other factors, the high costs of conducting such studies has been identified as one of the major obstacles in conducting clinical trials in the United States. However, typical approaches for designing clinical trials with time-to-event outcomes do not consider study costs. For a given effect size (eg, hazard ratio), the power to detect differences between two groups is typically a function of the total number of events observed in the study. Therefore, the same level of power will be achieved based on various combinations of the total number of participants, length of enrollment and total follow-up times, and group allocation probability. Herein, we provide a general framework for designing cost-efficient studies comparing treatments with respect to continuous time-to-event outcomes. Among the various designs that achieve the desired level of power to detect a given effect size for a fixed type-I error level, the optimal cost-efficient design is the design that minimizes the expected total study cost. The method is general and can be used for Cox proportional hazards models or Aalen additive models, and under various recruitment and censoring assumptions. The proposed approach for designing cost-efficient studies is illustrated for a Weibull time-to-event outcome with uniform recruitment and exponentially distributed censoring time. The case of an additive hazards model is also described. A Shiny web application implementation of the proposed methods is presented.

The Impact of Community Service Learning Upon the Expected Political Voice of Participating College Students

This study considered the impact of the SERVE Program at Ignatius University upon participating students’ expected political involvement. The SERVE Program is a community service learning program sponsored jointly by Ignatius University’s philosophy and theology departments. Through a mixed methods research design, the authors found that Ignatius University students participating in the SERVE Program demonstrated statistically significant increases in their expected political voice in comparison with peers in a control group. Qualitative interviews with SERVE participants revealed that the program increased students’ awareness of political and social issues; heightened their commitment to philanthropy; fostered their interest in pursuing socially responsible work; and strengthened their commitment to working for social change.

Sequential boundaries approach in clinical trials with unequal allocation ratios

Background

In clinical trials, both unequal randomization design and sequential analyses have ethical and economic advantages. In the single-stage-design (SSD), however, if the sample size is not adjusted based on unequal randomization, the power of the trial will decrease, whereas with sequential analysis the power will always remain constant. Our aim was to compare sequential boundaries approach with the SSD when the allocation ratio (R) was not equal.

Methods

We evaluated the influence of R, the ratio of the patients in experimental group to the standard group, on the statistical properties of two-sided tests, including the two-sided single triangular test (TT), double triangular test (DTT) and SSD by multiple simulations. The average sample size numbers (ASNs) and power (1-β) were evaluated for all tests.

Results

Our simulation study showed that choosing R = 2 instead of R = 1 increases the sample size of SSD by 12% and the ASN of the TT and DTT by the same proportion. Moreover, when R = 2, compared to the adjusted SSD, using the TT or DTT allows to retrieve the well known reductions of ASN observed when R = 1, compared to SSD. In addition, when R = 2, compared to SSD, using the TT and DTT allows to obtain smaller reductions of ASN than when R = 1, but maintains the power of the test to its planned value.

Conclusion

This study indicates that when the allocation ratio is not equal among the treatment groups, sequential analysis could indeed serve as a compromise between ethicists, economists and statisticians.

Ethics and practice: alternative designs for phase III randomized clinical trials

For decades, biostatisticians have developed and refined the methodology for clinical trials with the intent of giving trial participants a better representation than traditional, equal-allocation, fixed sample-size designs. Despite these methodologic advances and ethical advantages, alternative or data-dependent designs for phase III clinical trials, including sequential designs, Bayesian methods, and adaptive designs, have not been widely adopted in practice. We attempt to characterize situations under which these designs are feasible and desirable from ethical and logistical standpoints. In particular, we describe the role of individual and collective ethics in designing clinical trials and argue that greater attention should be paid to the former. We give examples of those alternative designs that have been used in practice, including discussion of their strengths and shortcomings. We conclude that alternative designs are applicable in limited classes of trials and that investigators should consider them more often when planning clinical trials.

Adaptive survival trials

We present a design for adaptive survival trials, where the probability of randomization to one of two treatments is skewed away from 0.5 according to the current value of the logrank statistic. A formula mapping the logrank statistic onto [0,1] is given, which is then used to bias a coin used for randomization. Simulation evidence shows that the allocation scheme works well and offers a more ethical alternative when lifetime data are available from other patients during the recruitment period. Power is not adversely affected by the resulting unequal allocation. The usual test statistic appears to be standard normal under the proposed allocation scheme.

Dynamic balanced randomization for clinical trials

Common methods of treatment allocation for multi-centre and/or stratified randomized clinical trials can result in substantial differences between the number of patients allocated to each treatment arm. This can occur in the overall trial for a permuted block design or within individual institutions/strata when using a minimization scheme. This may lead to a bias in the result. Also, these procedures can be predictable, with the possibility of an investigator-introduced selection bias. An easily implemented method of randomization is proposed which attempts to overcome these problems by balancing treatment allocations both within strata and across the trial as a whole. The method keeps a running tally on total treatment allocation numbers at all stratification levels. When a patient accrues a hierarchical decision rule is applied, and the allocation is deterministic if certain pre-defined limits are exceeded, and random otherwise. The method is an extension of the big stick design of Soares and Wu, and is related to both Zelen's key number randomization methods and the schemes of Nordle and Brantmark. Simulation studies are used to demonstrate that major imbalances possible with other schemes do not occur using this method, and that the potential for selection bias is much reduced.

A decade of progress in statistical methodology for clinical trials

Clinical trials played a dominant and expanding role in the evaluation of new treatments during the decade of the 1980s. There were major improvements in the quality of clinical trials in many medical fields. There were also important developments in the methodology of designing, monitoring, conducting, analysing, reporting and interpreting clinical trials. This paper attempts to review some of these developments. A comprehensive review is beyond the abilities of any one individual. Consequently, this paper attempts to offer a broad stroke description of this area and to highlight specific topics of importance based on my particular experience. An extensive, but non-comprehensive bibliography is included to provide entry points to the literature of methodologic developments for clinical trials in the 1980s.