Selecting a randomization method for a multi-center clinical trial with stochastic recruitment considerations.

BACKGROUND: The design of a multi-center randomized controlled trial (RCT) involves multiple considerations, such as the choice of the sample size, the number of centers and their geographic location, the strategy for recruitment of study participants, amongst others. There are plenty of methods to sequentially randomize patients in a multi-center RCT, with or without considering stratification factors. The goal of this paper is to perform a systematic assessment of such randomization methods for a multi-center 1:1 RCT assuming a competitive policy for the patient recruitment process. METHODS: We considered a Poisson-gamma model for the patient recruitment process with a uniform distribution of center activation times. We investigated 16 randomization methods (4 unstratified, 4 region-stratified, 4 center-stratified, 3 dynamic balancing randomization (DBR), and a complete randomization design) to sequentially randomize n = 500 patients. Statistical properties of the recruitment process and the randomization procedures were assessed using Monte Carlo simulations. The operating characteristics included time to complete recruitment, number of centers that recruited a given number of patients, several measures of treatment imbalance and estimation efficiency under a linear model for the response, the expected proportions of correct guesses under two different guessing strategies, and the expected proportion of deterministic assignments in the allocation sequence. RESULTS: Maximum tolerated imbalance (MTI) randomization methods such as big stick design, Ehrenfest urn design, and block urn design result in a better balance-randomness tradeoff than the conventional permuted block design (PBD) with or without stratification. Unstratified randomization, region-stratified randomization, and center-stratified randomization provide control of imbalance at a chosen level (trial, region, or center) but may fail to achieve balance at the other two levels. By contrast, DBR does a very good job controlling imbalance at all 3 levels while maintaining the randomized nature of treatment allocation. Adding more centers into the study helps accelerate the recruitment process but at the expense of increasing the number of centers that recruit very few (or no) patients-which may increase center-level imbalances for center-stratified and DBR procedures. Increasing the block size or the MTI threshold(s) may help obtain designs with improved randomness-balance tradeoff. CONCLUSIONS: The choice of a randomization method is an important component of planning a multi-center RCT. Dynamic balancing randomization with carefully chosen MTI thresholds could be a very good strategy for trials with the competitive policy for patient recruitment.

Sphingolipid Metabolism in Tumor Cells.

Sphingolipids are a diverse family of complex lipids typically composed of a sphingoid base bound to a fatty acid via amide bond. The metabolism of sphingolipids has long remained out of focus of biochemical studies. Recently, it has been attracting an increasing interest of researchers because of different and often multidirectional effects demonstrated by sphingolipids with a similar chemical structure. Sphingosine, ceramides (N-acylsphingosines), and their phosphorylated derivatives (sphingosine-1-phosphate and ceramide-1-phosphates) act as signaling molecules. Ceramides induce apoptosis and regulate stability of cell membranes and cell response to stress. Ceramides and sphingoid bases slow down anabolic and accelerate catabolic reactions, thus suppressing cell proliferation. On the contrary, their phosphorylated derivatives (ceramide-1-phosphate and sphingosine-1-phosphate) stimulate cell proliferation. Involvement of sphingolipids in the regulation of apoptosis and cell proliferation makes them critically important in tumor progression. Sphingolipid metabolism enzymes and sphingolipid receptors can be potential targets for antitumor therapy. This review describes the main pathways of sphingolipid metabolism in human cells, with special emphasis on the properties of this metabolism in tumor cells.

Approaches to expanding the two-arm biased coin randomization to unequal allocation while preserving the unconditional allocation ratio.

The paper discusses three methods for expanding the biased coin randomization (BCR) to unequal allocation while preserving the unconditional allocation ratio at every step. The first method originally proposed in the contexts of BCR and minimization is based on mapping from an equal allocation multi-arm BCR. Despite the improvement proposed in this paper to ensure tighter adherence to the targeted unequal allocation, this method still distributes the probability mass at least as wide as the permuted block randomization (PBR). This works for smaller block sizes, but for larger block sizes, a tighter control of the imbalance in the treatment assignments is desired. The second method, which has two versions, allows to tighten the distribution of the imbalance compared with that achieved with the PBR. However, the distribution of the imbalance remains considerably wider than that of the brick tunnel randomization - the unequal allocation procedure with the tightest possible imbalance distribution among all allocation ratio preserving procedures with the same allocation ratio. Finally, the third method, the BCR with a preset proportion of maximal forcing, mimics the properties of the equal allocation BCR. With maximum forcing, it approaches the brick tunnel randomization, similar to how 1:1 BCR approaches 1:1 PBR with the permuted block size of 2 (the equal allocation procedure with the lowest possible imbalance) when the bias approaches 1. With minimum forcing, the BCR with a preset proportion of maximal forcing approaches complete randomization (similar to 1:1 BCR). Copyright © 2017 John Wiley & Sons, Ltd.

Brick tunnel randomization and the momentum of the probability mass.

The allocation space of an unequal-allocation permuted block randomization can be quite wide. The development of unequal-allocation procedures with a narrower allocation space, however, is complicated by the need to preserve the unconditional allocation ratio at every step (the allocation ratio preserving (ARP) property). When the allocation paths are depicted on the K-dimensional unitary grid, where allocation to the l-th treatment is represented by a step along the l-th axis, l = 1 to K, the ARP property can be expressed in terms of the center of the probability mass after i allocations. Specifically, for an ARP allocation procedure that randomizes subjects to K treatment groups in w1 :⋯:wK ratio, w1 +⋯+wK =1, the coordinates of the center of the mass are (w1 i,…,wK i). In this paper, the momentum with respect to the center of the probability mass (expected imbalance in treatment assignments) is used to compare ARP procedures in how closely they approximate the target allocation ratio. It is shown that the two-arm and three-arm brick tunnel randomizations (BTR) are the ARP allocation procedures with the tightest allocation space among all allocation procedures with the same allocation ratio; the two-arm BTR is the minimum-momentum two-arm ARP allocation procedure. Resident probabilities of two-arm and three-arm BTR are analytically derived from the coordinates of the center of the probability mass; the existence of the respective transition probabilities is proven. Probability of deterministic assignments with BTR is found generally acceptable. Copyright © 2015 John Wiley & Sons, Ltd.

Hierarchical dynamic allocation procedures based on modified Zelen's approach in multiregional studies with unequal allocation.

Morrissey, McEntegart, and Lang (2010) showed that in multicenter studies with equal allocation to several treatment arms, the modified Zelen's approach provides excellent within-center and across-study balance in treatment assignments. In this article, hierarchical balancing procedures for equal allocation to more than two arms (with some elements different from earlier versions) and their unequal allocation expansions that incorporate modified Zelen's approach at the center level are described. The balancing properties of the described procedures for a case study of a multiregional clinical trial with 1:2 allocation where balance within regions as well as in other covariates is required are examined through simulations.

Wide brick tunnel randomization - an unequal allocation procedure that limits the imbalance in treatment totals.

In open-label studies, partial predictability of permuted block randomization provides potential for selection bias. To lessen the selection bias in two-arm studies with equal allocation, a number of allocation procedures that limit the imbalance in treatment totals at a pre-specified level but do not require the exact balance at the ends of the blocks were developed. In studies with unequal allocation, however, the task of designing a randomization procedure that sets a pre-specified limit on imbalance in group totals is not resolved. Existing allocation procedures either do not preserve the allocation ratio at every allocation or do not include all allocation sequences that comply with the pre-specified imbalance threshold. Kuznetsova and Tymofyeyev described the brick tunnel randomization for studies with unequal allocation that preserves the allocation ratio at every step and, in the two-arm case, includes all sequences that satisfy the smallest possible imbalance threshold. This article introduces wide brick tunnel randomization for studies with unequal allocation that allows all allocation sequences with imbalance not exceeding any pre-specified threshold while preserving the allocation ratio at every step. In open-label studies, allowing a larger imbalance in treatment totals lowers selection bias because of the predictability of treatment assignments. The applications of the technique in two-arm and multi-arm open-label studies with unequal allocation are described.

Shift in re-randomization distribution with conditional randomization test.

Proschan, Brittain, and Kammerman made a very interesting observation that for some examples of the unequal allocation minimization, the mean of the unconditional randomization distribution is shifted away from 0. Kuznetsova and Tymofyeyev linked this phenomenon to the variations in the allocation ratio from allocation to allocation in the examples considered in the paper by Proschan et al. and advocated the use of unequal allocation procedures that preserve the allocation ratio at every step. In this paper, we show that the shift phenomenon extends to very common settings: using conditional randomization test in a study with equal allocation. This phenomenon has the same cause: variations in the allocation ratio among the allocation sequences in the conditional reference set, not previously noted. We consider two kinds of conditional randomization tests. The first kind is the often used randomization test that conditions on the treatment group totals; we describe the variations in the conditional allocation ratio with this test on examples of permuted block randomization and biased coin randomization. The second kind is the randomization test proposed by Zheng and Zelen for a multicenter trial with permuted block central allocation that conditions on the within-center treatment totals. On the basis of the sequence of conditional allocation ratios, we derive the value of the shift in the conditional randomization distribution for specific vector of responses and the expected value of the shift when responses are independent identically distributed random variables. We discuss the asymptotic behavior of the shift for the two types of tests.

Preserving the allocation ratio at every allocation with biased coin randomization and minimization in studies with unequal allocation.

The demand for unequal allocation in clinical trials is growing. Most commonly, the unequal allocation is achieved through permuted block randomization. However, other allocation procedures might be required to better approximate the allocation ratio in small samples, reduce the selection bias in open-label studies, or balance on baseline covariates. When these allocation procedures are generalized to unequal allocation, special care is to be taken to preserve the allocation ratio at every allocation step. This paper offers a way to expand the biased coin randomization to unequal allocation that preserves the allocation ratio at every allocation. The suggested expansion works with biased coin randomization that balances only on treatment group totals and with covariate-adaptive procedures that use a random biased coin element at every allocation. Balancing properties of the allocation ratio preserving biased coin randomization and minimization are described through simulations. It is demonstrated that these procedures are asymptotically protected against the shift in the rerandomization distribution identified for some examples of minimization with 1:2 allocation. The asymptotic shift in the rerandomization distribution of the difference in treatment means for an arbitrary unequal allocation procedure is explicitly derived in the paper.

Brick tunnel randomization for unequal allocation to two or more treatment groups.

Studies with unequal allocation to two or more treatment groups often require a large block size for permuted block allocation. This could present a problem in small studies, multi-center studies, or adaptive design dose-finding studies. In this paper, an allocation procedure, which generalizes the maximal procedure by Berger, Ivanova, and Knoll to the case of K≥2 treatment groups and any allocation ratio, is offered. Brick tunnel (BT) randomization requires the allocation path drawn in the k-dimensional space to stay close to the allocation ray that corresponds to the targeted allocation ratio. Specifically, it requires the allocation path to be confined to the set of the k-dimensional unitary cubes that are pierced by the allocation ray (the 'brick tunnel'). The important property of the BT randomization is that the transition probabilities at each node within the tunnel are defined in such a way that the unconditional allocation ratio is the same for every allocation step. This property is not necessarily met by other allocation procedures that implement unequal allocation.

On the second role of the random element in minimization.

Although the main reason for adding a random element at every step of minimization procedure is to reduce predictability of the upcoming treatment assignments in single-center open-label trials, there is another reason for its use, applicable to double-blind trials. Adding the random element at every allocation step allows one to avoid a fully deterministic sequence of treatment assignments for sequences of covariates for which at every allocation step one of the treatments leads to a better balance in covariates than all other treatments. An example of such a sequence is provided in this communication.