Biased Coin Design Research Articles

Minimum Effective Volume of Lidocaine for Double-Injection Ultrasound-Guided Axillary Block

The aim of this study was to determine the minimum effective volume of lidocaine 1.5% with epinephrine 5 μg/mL in 90% of patients (MEV90) for double-injection ultrasound-guided axillary block (AXB). All subjects received a double-injection ultrasound-guided AXB with lidocaine 1.5% and epinephrine 5 μg/mL. A 17-gauge, 8-cm Tuohy needle was initially advanced until its tip was positioned next to the musculocutaneous nerve. Volume assignment was carried out using a biased coin design up-and-down sequential method, where the volume of local anesthetic administered to each patient depended on the response of the previous one. In case of failure, the next subject received a higher volume (defined as the previous volume with an increment of 1.0 mL). If the previous patient had a successful block, the next subject was randomized to a lower volume (defined as the previous volume with a decrement of 1.0 mL), with a probability of b = 0.11, or the same volume, with a probability of 1 - b = 0.89. After injection of the musculocutaneous nerve, the needle was redirected toward the dorsal aspect of the axillary artery. For this second injection, volume assignment was carried out in a similar fashion; however, volume increments/decrements were 3.0 instead of 1.0 mL. Using a composite scale encompassing sensory and motor block, success was defined, at 30 minutes, as a composite score of 4 points (out of 4 points), and 10 points (out of 12 points) for the musculocutaneous and perivascular injection, respectively. Patients undergoing surgery of the forearm, wrist, or hand were prospectively enrolled until 45 successful musculocutaneous blocks or 45 successful perivascular injections were obtained. Fifty patients were included in the study. Using isotonic regression and bootstrap confidence interval (CI), the MEV90 was estimated to be 5.5 mL (95% CI, 3.0-6.7 mL) and 23.5 mL (95% CI, 23.1-23.9 mL) for the musculocutaneous and perivascular injection, respectively. For double-injection ultrasound-guided AXB, the MEV90 of lidocaine 1.5% with epinephrine 5 μg/mL is 5.5 and 23.5 mL for the musculocutaneous nerve and perivascular injection, respectively. Further dose-finding studies are required for other concentrations of lidocaine, other local anesthetic agents, and other techniques for ultrasound-guided AXB.

Exact statistical power for response adaptive designs

This paper develops a unified method to compute the exact statistical power for a general class of response adaptive designs including the randomized play-the-winner design, the drop-the-loser design, and the doubly biased coin design. The adaptation of treatment allocation in response adaptive designs is formulated as a Markov chain. The exact statistical power is computed based on the transition probability of the formulated Markov chain. The proposed approach is demonstrated through the ECMO trial example. The difference between the asymptotic and exact statistical power is also explored for large sample sizes.

Bias and loss: the two sides of a biased coin

The paper assesses biased-coin designs for sequential treatment allocation in clinical trials. Comparisons emphasise the importance of considering randomness, as well as treatment balance, which are calculated as bias and loss. In the numerical examples, the responses are assumed normally distributed, perhaps after transformation, and balance is required over a set of covariates. The effect of covariate distribution on the properties of five allocation rules is investigated, with an emphasis on methods of comparison, which also apply to other forms of response. The concept of admissibility shows that the widely used minimisation rule is outperformed by Atkinson's rule derived from the theory of optimum experimental design. We present a simplified form of this rule. For this rule, the ability to guess the next treatment allocation decreases with study size. For the other rules, it is constant.

Multi-objective optimal designs in comparative clinical trials with covariates: The reinforced doubly adaptive biased coin design

The present paper deals with the problem of allocating patients to two competing treatments in the presence of covariates or prognostic factors in order to achieve a good trade-off among ethical concerns, inferential precision and randomness in the treatment allocations. In particular we suggest a multipurpose design methodology that combines efficiency and ethical gain when the linear homoscedastic model with both treatment/covariate interactions and interactions among covariates is adopted. The ensuing compound optimal allocations of the treatments depend on the covariates and their distribution on the population of interest, as well as on the unknown parameters of the model. Therefore, we introduce the reinforced doubly adaptive biased coin design, namely a general class of covariate-adjusted response-adaptive procedures that includes both continuous and discontinuous randomization functions, aimed to target any desired allocation proportion. The properties of this proposal are described both theoretically and through simulations.

The Effect of Obesity on the ED95 of Propofol for Loss of Consciousness in Children and Adolescents

Anesthesiologists face a dilemma in determining appropriate dosing of anesthetic drugs in obese children. In this study we determined the dose of propofol that caused loss of consciousness in 95% (ED(95)) of obese and nonobese children as determined by loss of eye lash reflex. Forty obese (body mass index [BMI] > 95th percentile for age and gender) and 40 normal weight (BMI 25th to 84th percentile) healthy ASA 1 to 2 children ages 3 to 17 years presenting for surgical procedures were studied using a biased coin design. The primary endpoint was loss of lash reflex at 20 seconds after propofol administration. The first patient in each group received 1.0 mg/kg of IV propofol, and subsequent patients received predetermined propofol doses based on the lash reflex response in the previous patient. If the lash reflex was present, the next patient received a dose increment of 0.25 mg/kg. If the lash reflex was absent, the next patient was randomized to receive either the same dose (95% probability) or a dose decrement of 0.25 mg/kg (5% probability). The ED(95) and 95% confidence intervals (CI) were calculated using isotonic regression and bootstrapping methods respectively. The ED(95) of propofol for loss of lash reflex was significantly lower in obese pediatric patients (2.0 mg/kg, approximate 95% CI, 1.8 to 2.2 mg/kg) in comparison with nonobese patients (3.2 mg/kg, approximate 95% CI, 2.7 to 3.2 mg/kg), P ≤ 0.05. A simple approach to deciding what dose of propofol should be used for induction of anesthesia in children ages 3 to 17 years is to first establish the child's BMI on readily available gender-specific charts. Obese children (BMI >95th percentile for age and gender) require a lower weight-based dose of propofol for induction of anesthesia, than do normal-weight children.

Sequential monitoring with conditional randomization tests

Sequential monitoring in clinical trials is often employed to allow for early stopping and other interim decisions, while maintaining the type I error rate. However, sequential monitoring is typically described only in the context of a population model. We describe a computational method to implement sequential monitoring in a randomization-based context. In particular, we discuss a new technique for the computation of approximate conditional tests following restricted randomization procedures and then apply this technique to approximate the joint distribution of sequentially computed conditional randomization tests. We also describe the computation of a randomization-based analog of the information fraction. We apply these techniques to a restricted randomization procedure, Efron's [Biometrika 58 (1971) 403--417] biased coin design. These techniques require derivation of certain conditional probabilities and conditional covariances of the randomization procedure. We employ combinatoric techniques to derive these for the biased coin design.

Doubly adaptive biased coin designs for balancing competing objectives in time-to-event trials

Doubly adaptive biased coin designs for balancing competing objectives in time-to-event trials

The adaptive accelerated biased coin design for phase I clinical trials

Phase I clinical trials are designed to study several doses of the same drug in a small group of patients to determine the maximum tolerated dose (MTD), which is defined as the dose that is associated with dose-limiting toxicity (DLT) in a desired fraction Γ of patients. Durham and Flournoy [5] proposed the biased coin design (BCD), which is an up-and-down design that assigns a new patient to a dose depending upon whether or not the current patient experienced a DLT. However, the BCD in its standard form requires the complete follow-up of the current patient before the new patient can be assigned a dose. In situations where patients’ follow-up times are relatively long compared to patient inter-arrival times, the BCD will result in an impractically long trial and cause patients to either have delayed entry into the trial or refusal of entry altogether. We propose an adaptive accelerated BCD (aaBCD) that generalizes the traditional BCD design algorithm by incorporating an adaptive weight function based upon the amount of follow-up of each enrolled patient. By doing so, the dose assignment for each eligible patient can be determined immediately with no delay, leading to a shorter trial overall. We show, via simulation, that the frequency of correctly identifying the MTD at the end of the study with the aaBCD, as well as the number of patients assigned to the MTD, are comparable to that of the traditional BCD design. We also compare the performance of the aaBCD with the accelerated BCD (ABCD) of Stylianou and Follman [19], as well as the time-to-event continual reassessment method (TITE-CRM) of Cheung and Chappell [4].

Minimum Effective Volume of Lidocaine for Ultrasound-Guided Supraclavicular Block

The aim of this study was to determine the minimum effective volume of lidocaine 1.5% with epinephrine 5 μg/mL in 90% of patients (MEV90) for double-injection ultrasound-guided supraclavicular block (SCB). Using an in-plane technique and a lateral to medial direction, a double-injection ultrasound-guided SCB was performed. A 17-gauge, 8-cm Tuohy needle was initially advanced until its tip was positioned at the intersection of the first rib and subclavian artery ("corner pocket"). Half the volume of lidocaine was injected in this location. Subsequently, the needle was redirected toward the neural cluster formed by the trunks and divisions of the brachial plexus. The remaining volume of lidocaine was deposited in this location. Volume assignment was carried out using a biased coin design up-and-down sequential method, where the total volume of local anesthetic administered to each patient depended on the response of the previous one. In case of failure, the next subject received a higher volume (defined as the previous volume with an increment of 2.5 mL). If the previous patient had a successful block, the next subject was randomized to a lower volume (defined as the previous volume with a decrement of 2.5 mL), with a probability of b = 0.11, or the same volume, with a probability of 1 - b = 0.89. Each increment or decrement was evenly distributed between the "corner pocket" (1.25 mL) and neural cluster (1.25 mL). Lidocaine 1.5% with epinephrine 5 μg/mL was used in all subjects. Success was defined, at 30 minutes, as a minimal score of 14 of 16 points using a composite scale encompassing sensory and motor block. Patients undergoing surgery of the elbow, forearm, wrist, or hand were prospectively enrolled until 45 successful blocks were obtained. Fifty-four patients were included in the study. Using isotonic regression and bootstrap confidence interval, the MEV90 for double-injection ultrasound-guided SCB was estimated to be 32 mL (95% confidence interval, 30-34 mL). All patients with a minimal composite score of 14 points at 30 minutes achieved surgical anesthesia intraoperatively. For double-injection ultrasound-guided SCB, the MEV90 of lidocaine 1.5% with epinephrine 5 μg/mL is 32 mL. Further dose finding studies are required for other concentrations of lidocaine, other local anesthetic agents and single-injection techniques.

Block urn design — A new randomization algorithm for sequential trials with two or more treatments and balanced or unbalanced allocation

Permuted block design is the most popular randomization method used in clinical trials, especially for trials with more than two treatments and unbalanced allocation, because of its consistent imbalance control and simplicity in implementation. However, the risk of selection biases caused by high proportion of deterministic assignments is a cause of concern. Efron's biased coin design and Wei's urn design provide better allocation randomness without deterministic assignments, but they do not consistently control treatment imbalances. Alternative randomization designs with improved performances have been proposed over the past few decades, including Soares and Wu's big stick design, which has high allocation randomness, but is limited to two-treatment balanced allocation scenarios only, and Berger's maximal procedure design which has a high allocation randomness and a potential for more general trial scenarios, but lacks the explicit function for the conditional allocation probability and is more complex to implement than most other designs. The block urn design proposed in this paper combines the advantages of existing randomization designs while overcoming their limitations. Statistical properties of the new algorithm are assessed and compared to currently available designs via analytical and computer simulation approaches. The results suggest that the block urn design simultaneously provides consistent imbalance control and high allocation randomness. It can be easily implemented for sequential clinical trials with two or more treatments and balanced or unbalanced allocation.

The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors

The present paper deals with sequential designs intended to balance the allocations of two competing treatments in the presence of prognostic factors. After giving a theoretical framework on the optimality of balanced designs that can arise when covariates are taken into account, we propose a new family of covariate-adaptive randomized designs that represents higher order approximation to balance treatments, both globally and also across covariates. We derive the theoretical properties of the suggested designs in terms of loss of precision and predictability. The performance of this proposal is illustrated through a simulation study and compared with those of other procedures suggested in the literature. Copyright 2011, Oxford University Press.

Minimum Effective Volume of Lidocaine for Ultrasound-Guided Infraclavicular Block

The aim of this study was to determine the minimum effective volume of lidocaine 1.5% with epinephrine 5 μg/mL in 90% of patients (MEV(90)) for single-injection ultrasound-guided infraclavicular block (ICB). Using an in-plane technique, a single-injection ultrasound-guided ICB was performed: a 17-gauge, 8-cm Tuohy needle was advanced until the tip was located dorsal to the axillary artery. Volume assignment was carried out using a biased coin design up-and-down sequential method, where the volume of local anesthetic administered to each patient depended on the response of the previous one. In case of failure, the next subject received a higher volume (defined as the previous volume with an increment of 2.5 mL). If the previous patient had a successful block, the next subject was randomized to a lower volume (defined as the previous volume with a decrement of 2.5 mL), with a probability of b=0.11, or the same volume, with a probability of 1-b=0.89. Lidocaine 1.5% with epinephrine 5 μg/mL was used in all subjects. Success was defined, at 30 mins, as a minimal score of 14 of 16 points using a composite scale encompassing sensory and motor block. Patients undergoing surgery of the elbow, forearm, wrist, or hand were prospectively enrolled until 45 successful blocks were obtained. Fifty-five patients were included in the study. Using isotonic regression and bootstrap confidence interval (CI), the MEV(90) for single-injection ultrasound-guided ICB was estimated to be 35 mL (95% CI, 30-37.5 mL). The probability of a successful response at 35 mL was estimated to be 0.91 (95% CI, 0.8-1.0). All patients with a minimal composite score of 14 points at 30 mins achieved surgical anesthesia intraoperatively. For single-injection ultrasound-guided ICB, the MEV(90) of lidocaine 1.5% with epinephrine 5 μg/mL is 35 mL. Further dose-finding studies are required for other concentrations of lidocaine, other local anesthetic agents as well as techniques involving multiple injections, a more medial approach to ICB, or precise location of all 3 cords of the brachial plexus.

Frequentist performance of Bayesian inference with response‐adaptive designs

In controlled clinical trials, where minimizing treatment failures is crucial, response-adaptive designs are attractive competitors to 1:1 randomized designs for comparing the success rates φ(1) and φ(2) of two treatments. In these designs each new treatment assignment depends on previous outcomes through some predefined rule. Here Play-The-Winner (PW), Randomized Play-The-Winner (RPW), Drop-The-Loser, Generalized Drop-the-Loser and Doubly adaptive Biased Coin Designs are considered for new treatment assignments. As frequentist inference relies on complex sampling distributions in those designs, we investigate how Bayesian inference, based on two independent Beta prior distributions, performs from a frequentist point-of-view. Performance is assessed through coverage probabilities of interval estimation procedures, power and minimization of failure count. It is shown that Bayesian inference can be favorably compared to frequentist procedures where the latter are available. The power of response-adaptive designs is generally very close to the power of 1:1 randomized design. However, failure count savings are generally small, except for the PW and Doubly adaptive Biased Coin designs in particular ranges of the true success rates. The RPW assignment rule has the worst performance, while PW, Generalized Drop-the-Loser or Doubly adaptive Biased Coin Designs may outperform other designs depending on different particular ranges of the true success rates.

Slower administration of propofol preserves adequate respiration in children

Propofol is a versatile anesthetic agent used in pediatric practice to facilitate investigational and interventional procedures. Propofol can cause significant respiratory depression, the management of which may require advanced airway management skills. This investigation aimed to increase the safety of propofol administration by developing a dosing schedule that would preserve spontaneous respiration in at least 95% of subjects. With Research Ethics Board approval and informed consent, American Society of Anesthesiologists' Status I and II children aged 6-15 years presenting for upper or lower gastrointestinal endoscopy were enrolled. An intravenous loading dose of propofol (4 mg·kg(-1) ) was administered at a rate determined by a randomization schedule in a two-phased study. Following the loading dose, additional propofol was infused at 200 mcg·kg(-1) ·min(-1) for 5 min or until respiratory insufficiency was observed. In Phase I, the infusion rate was modified by 100 mcg·kg(-1) ·min(-1) increments depending upon the respiratory response of the previous subject. In Phase II, the duration of infusion was randomized according to a Biased Coin Design principle to determine the 95% threshold for respiratory insufficiency. Fifty subjects were included in the analysis. Infusion rates ranged from 1000 to 2300 mcg·kg(-1) ·min(-1) . Seven subjects experienced respiratory insufficiency. The mean (sd) time to respiratory insufficiency was 104 (36) s and duration was 93 (51) s. A propofol loading dose administered over 3.0 min (CI = 1.9-3.4 min) maintained spontaneous respiration in 95% of subjects. The respiratory response to propofol is highly variable in children. Slower infusion of propofol will result in a lower risk of respiratory depression.

An optimal response adaptive biased coin design with k heteroscedastic treatments

For comparing treatments in clinical trials, Atkinson (1982) introduced optimal biased coins for balancing patients across treatment assignments by using D-optimality under the assumption of homoscedastic responses of different treatments. However, this assumption can be violated in many real applications. In this paper, we relax the homoscedasticity assumption in the k treatments setting with k > 2 . A general family of optimal response adaptive biased coin designs are proposed following Atkinson's procedure. Asymptotic properties of the proposed designs are obtained. Some advantages of the proposed design are discussed.

Exact properties of Efron’s biased coin randomization procedure

Efron [Biometrika 58 (1971) 403--417] developed a restricted randomization procedure to promote balance between two treatment groups in a sequential clinical trial. He called this the biased coin design. He also introduced the concept of accidental bias, and investigated properties of the procedure with respect to both accidental and selection bias, balance, and randomization-based inference using the steady-state properties of the induced Markov chain. In this paper we revisit this procedure, and derive closed-form expressions for the exact properties of the measures derived asymptotically in Efron's paper. In particular, we derive the exact distribution of the treatment imbalance and the variance-covariance matrix of the treatment assignments. These results have application in the design and analysis of clinical trials, by providing exact formulas to determine the role of the coin's bias probability in the context of selection and accidental bias, balancing properties and randomization-based inference.

Up-down determination of the ED90 of oxytocin infusions for the prevention of postpartum uterine atony in parturients undergoing Cesarean delivery

Use of the lowest effective dose of oxytocin may reduce side effects. This study was designed to determine the effective dose (ED)(90) of oxytocin infusion for an elective Cesarean delivery (CD) to prevent uterine atony. The participants were ASA I and II, non-obese, non-labouring adult women undergoing an elective CD at term with a singleton gestation. The spinal anesthetic technique was standardized, and a blinded infusion of oxytocin was administered after delivery. The obstetrician rated the uterine contraction as either satisfactory or unsatisfactory. The initial dose of oxytocin infusion was 0.4 IU.min(-1), and the dose for the next subject was based on the response of the preceding subject as per a biased-coin design up-down sequential method. The ED(90) was calculated using Firth's penalized likelihood estimation. Fifty subjects were screened, eight subjects were excluded, and two patients were withdrawn. Seven of the 40 subjects had uterine tone that was judged unsatisfactory by the obstetrician and required additional uterotonic medications. The ED(90), i.e., the dose at which 90% of women were judged to have satisfactory uterine tone, was 0.29 IU.min(-1) (95% confidence interval [CI] 0.15-0.43 IU.min(-1)). In this study, we found the ED(90) of oxytocin required to prevent uterine atony and postpartum hemorrhage after an elective CD to be 0.29 IU.min(-1)-approximately 15 IU of oxytocin in 1 L of intravenous fluid administered over a one-hour period-(95% CI 0.15-0.43 IU.min(-1)). This oxytocin infusion dose is 30% less than the clinical infusions currently in use. It remains to be seen whether this dosing will be required for higher risk individuals or for labouring parturients undergoing non-elective CD. (Clinical Trial gov. NCT00785395).

Up-Down Determination of the 90% Effective Dose of Phenylephrine for the Treatment of Spinal Anesthesia-Induced Hypotension in Parturients Undergoing Cesarean Delivery

Hypotension frequently complicates spinal anesthesia for cesarean delivery, and vasopressors are the mainstay for treatment. The most effective dose of phenylephrine for the treatment of spinal anesthesia-induced hypotension has not been estimated. Healthy nonlaboring women undergoing a cesarean delivery were recruited. All women received spinal anesthesia using hyperbaric bupivacaine 12 mg with fentanyl and morphine. Each subject received an i.v. crystalloid fluid bolus before and at the time of initiation of spinal anesthesia (preload and coload). An up-down sequential allocation method using the biased-coin design was used to estimate the 90% effective dose (ED(90)) of phenylephrine. The assigned phenylephrine dose was based on the response of the preceding subject. If the systolic blood pressure (SBP) decreased > 20% of baseline (i.e., SBP 20%) or to an SBP < 90 mm Hg, the assigned dose of phenylephrine was administered. If the SBP returned to within 20% of baseline or > or = 90 mm Hg within 1 min, this was considered a success, otherwise it was a failure. The initial dose of phenylephrine was 100 microg. The ED(90) with 95% confidence intervals (CIs) was calculated using the maximum likelihood estimation and Firth logistic regression. Sixty-nine subjects were screened to participate, of whom 66 subjects consented. Forty-five of the enrolled subjects experienced spinal anesthesia-induced hypotension and received a blinded dose of phenylephrine. Those subjects who developed hypotension received doses of phenylephrine between 80 and 180 microg. No subjects experienced hypertension. Determined with the maximum likelihood estimation method, the ED(90) of phenylephrine was 147 microg (95% CI, 98-222 microg). With Firth regression, the probability of a successful response at 150 microg is 90.5% (95% CI, 66.0%-99.0%). In this study, we estimated that the ED(90) of phenylephrine required to treat spinal anesthesia-induced hypotension in cesarean delivery is approximately 150 microg.

Efficient randomized-adaptive designs

Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer--Rao lower bounds on the allocation variances for any allocation proportions, including optimal allocation proportions. The allocation probability functions of proposed procedures are discontinuous. The existing large sample theory for adaptive designs relies on Taylor expansions of the allocation probability functions, which do not apply to nondifferentiable cases. In the present paper, we study stopping times of stochastic processes to establish the asymptotic efficiency results. Furthermore, we demonstrate our proposal through examples, simulations and a discussion on the relationship with earlier works, including Efron's biased coin design.

Applications of nonparametric adaptive methods for simple reaction time experiments

Adaptive methods are commonly used in psychophysical research for detection and discrimination (see Leek, 2001; Treutwein, 1995, for reviews). In recent years, researchers have investigated via simulations some asymptotic and small-sample properties of two nonparametric adaptive methods-namely, the fixed-step-size up-down (García-Pérez, 1998, 2001) and the (accelerated) stochastic approximation (Faes et al., 2007). In the present article, we extend both methods to the simple reaction time (RT) situation for the measure of signal intensities that elicit certain (fixed) RT percentiles. We focus on extending the following four methods: the stochastic approximation of Robbins and Monro (1951), its accelerated version of Kesten (1958), the transformed up-down of Wetherill (1963), and the "biased coin design" of Durham and Flournoy (1994, 1995). In all simulations, we assume that the RT is Weibull distributed and that there is a linear relationship between the mean RT and its standard deviation. The convergences of the asymptotic and small-sample properties for different starting values, step sizes, and response criteria are systematically investigated.