Data-dependent Allocation Rules Research Articles

An Efficient Allocation in Group Sequential Tests for the Linear Mixed Effects Model

In the context of linear mixed effects models, we derive an asymptotically efficient group sequential testing procedure fitted with a data dependent allocation rule for comparing the effects of two treatments. The allocation is designed so as to favor procedures that stop early while allocating less patients to the inferior treatment. A simulation study is used to compare the performance of the proposed procedure to those of four standard procedures.

Corrected confidence intervals following a sequential adaptive clinical trial with binary responses

A sequential clinical trial model is considered in which two treatments are compared and the responses are binary. One of the properties of the model is that, for a given stopping boundary, the error probability is insensitive to the allocation rule. It is shown how a corrected confidence interval may be determined for the log odds ratio at the end of the trial. Simulation is used to assess the accuracy of the method for a selection of stopping boundaries and data-dependent allocation rules.

Approximate confidence intervals after a sequential clinical trial comparing two exponential survival curves with censoring

A sequential test is considered for comparing two exponential survival curves with unknown failure rates θ 1, θ 2 > 0. The survival times are censored by both real time and an independent censoring variable. It is shown how very weak expansions for the bivariate version of the signed root transformation may be used to construct an approximate confidence interval for δ = log( θ 1 θ 2 ) following the test. The accuracy of the method is illustrated by simulation results for several sequential tests and data-dependent allocation rules.

Efficient allocations in group sequential tests

We derive asymptotically efficient data dependent allocation rules for three group sequential testing procedures: Pocock (1977), O'Brien and Fleming (1979) and Falissard and Lellouch (1992). Sampling costs are defined such that the costs of observing the next group are higher than the cumulative costs of the previous groups. This formulation is used in an attempt to favor procedures that stop early while allocating less patients to the inferior treatment, We use a simulation study to compare the performances of these procedures when the efficient and the pairwise allocations are used. An example of applications on data is presented.

Data-dependent allocation rules a comparative study of some for bernoulli data

A clinical trial setting is considered in which two treatments are available for a particular ailment. The response to treatment is Bernoulli with “success” or “failure” as the outcome. Several allocation rules which are designed to reduce the number of patients who receive the inferior treatment are compared with random allocation using simulation. Particular attention is paid to the bias and variance for estimation of the true treatment difference. The effect of time trends in the data is examined.

Adaptive sequential procedures for selecting the best of several normal populations†

There are k(≧2) competing normal populations with common known variance and unknown means . Let denote the ordered values of the {z i}. Nothing is known concerning the pairing of the {z.Θ i} and the {z.Θ [i]}. In the location invariant identification problem, the differences are given and it is desired to select the population associated with {z.Θ [k]}. Of particular interest is the slippage configuration where δ *>0 is given. We restrict attention to procedures that guarantee that the population with the largest mean is correctly selected with probability at least P * where is preassigned. Essentially, this requirement is satisfied by the stopping rule of Bechhofer, Kiefer and Sobel (Sequential Identification and Ranking Procedures, Univ. of Chicago Press 1968, Chap. 3) independently of the sampling rule and thus data dependent allocation rules can be considered. Unlike the case k=2 (see Robbins and Siegmund ( 1974) J. Am. Statist. Assoc. 69, 132-139), when k≧3,substantial savings in expected tot...

Optimal allocation in sequential tests comparing the means of two Gaussian populations

SUMMARY The invariant sequential probability ratio test used in testing for a difference between the means of two Gaussian populations is set up. The error probabilities for this test are effectively constant over a rich class of data-dependent allocation rules. The additional risk, average sample number plus (y - 1) times the expected number of observations to the inferior population, for y > 1, is introduced and the optimal allocation rule is found for the continuous-time analogue to this problem. Analytical results show this rule to be asymptotically optimal in discrete time, and simulations indicate its near optimal per- formance for the finite case. The problem of two-population hypothesis testing with data-dependent allocation of observations has been treated by several authors. Also, the applications of this decision model, especially to clinical testing, have been well documented. Recent results show that when the test is sequential and the termination rule is of the sequential probability ratio test type, the probability of correct hypothesis selection is constant, ignoring overshoot, for a rich class of data-dependent allocation rules; see Flehinger, Louis, Robbins & Singer (1972) and an as yet unpublished paper of mine. This constancy permits one to search the class for a rule which performs well with respect to some additional cost structure, one usually based on the number of observations taken on the superior and inferior populations. Flehinger & Louis (1972) and Robbins & Siegmund (1974) give simulations showing that a substantial reduction in the expected number of observations on the inferior popu- lation is possible using data-dependent allocation rules, as opposed to equal assignment, for the case of comparing two Gaussian populations with known variances. The simulation results of Flehinger & Louis (1971) show the same reduction for the exponential distri- bution. In the present paper the risk function formed from the average sample number plus (y - 1) x the expected number of observations allocated to the inferior population, for y > 1, is introduced into the Gaussian testing model. Here y is the relative cost of taking an observation from the inferior as opposed to the superior population, and varying y allows one to balance the two components of risk. In ? 2 first the Gaussian allocation and testing problem is set up and previous results are summarized. Using the above risk function, in Appendix A the optimal allocation and its risk are obtained for the continuous-time idealization, that of comparing the drifts of two Brownian motions. Back in ? 2 this optimal rule is related to the discrete testing situation.

Reducing the Number of Inferior Treatments in Clinical Trials

In clinical trials comparing two treatments, one would often like to control the probability of erroneous decision while minimizing not the total sample size but the number of patients given the inferior treatment. To do this obviously requires that one use a datadependent allocation rule for the two treatments rather than the conventional equal sample size scheme, whether fixed or sequential. We show here how this may be done in the case of deciding which of two normally distributed treatment effects has the greater mean, when the variances are assumed to be equal and known. Similar methods can be used under other hypotheses on the underlying probability distributions, and will provide a considerable increase in flexibility in the design of sequential clinical trials.