Sequential allocation rules for multi-armed clinical trials

Woodroofe

1998

Sequential Analysis

Key words and Phrases: adapttve normal h e a r model; autoregresstv~ model; fundanenta: dentaty of seqtieiitzal analysts; m a z z m u n !tkelthood estzmator: zlrlhozun zrarzabtlzty; very weak erpanszon. ABSTRACT A linear model is considered in which the design variables may be functions of previous responses and /or auxiliary randomisation. T h e model is observed t successive times, where t is a stopping time, and interest lies in estimating the parameters of the model. Approximations are derived for the bias and variance of the maximum likelihood estimators of the parameters a t time t . T h e derivations involve differentiating the fundamental identity of sequential analysis. The accuracy of the approximations is assessed by simulation for a multi-armed clinical trial model proposed by Coad (1995), two autoregressive models and the sequential des~gn of Ford and Silvey (1980). Very weak expansions are used t o justify the approximations. Downloaded by [Columbia University] at 15:

“…Thus, model (1) holds with p = 3. Coad (1995) proposed several sequential allocation rules for t h e above problem.…”

Section: Formulae For the Bias And Variancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Approximate bias calculations for sequentially designed experiments

Woodroofe

1998

Sequential Analysis

“…Coad [5] proposed three sequential procedures for the comparison of K ≥ 3 treatments. However, only two of these will be considered here.…”

Section: Procedures Based On the Range Statisticmentioning

confidence: 99%

“…Bather and Coad [4] considered sequential procedures for comparing K ≥ 3 treatments with binary responses. Coad [5] proposed several sequential procedures for comparing K ≥ 3 treatments with normal responses when the variances are known or unknown. Betensky [6] extended the earlier work to compare three treatment groups yielding censored survival data.…”

Section: Introductionmentioning

confidence: 99%

Sequential procedures for comparing several normal means

Journal of Statistical Computation and Simulation

Halimeh²

2006

Self Cite

A sequential clinical trial model is considered in which K ≥ 3 treatments with normally distributed responses and unknown means are compared. For the case of equal variances, four sequential elimination procedures are studied -two based on the between treatments sum-of-squares statistic and two on the range statistic. Simulation indicates that the procedures based on the former statistic are slightly more efficient at determining the treatment with the highest mean. Approximations are also given for the bias of the sample mean vector following the designs and their accuracy is assessed using simulation. A generalisation of the procedures based on the between treatments sum-of-squares statistic to the unequal variances case is then considered. Some possible extensions to the work are briefly discussed.

Sequential urn designs with elimination for comparingK3 treatments

Ivanova

2005

Statist. Med.

A fully sequential procedure is proposed for comparing K > or =3 treatments with immediate binary responses. The procedure uses an adaptive urn design to randomize patients to the treatments and stopping rules are incorporated for eliminating less promising treatments. Simulation is used to assess the performance of the procedure for several adaptive urn designs, in terms of expected numbers of treatment failures and allocation proportions, and the effect on estimation at the end of the trial is also addressed. It is concluded that the drop-the-loser rule is more effective than equal allocation and all of the other designs considered. The practical benefits of the procedure are illustrated using the results of a three-treatment lung cancer study. It is then shown how the sequential elimination procedure may be used in dose-finding studies and its performance is compared with a recently proposed method. Several possible extensions to the work are briefly indicated.