Statistical properties of the traditional algorithm-based designs for phase I cancer clinical trials

Although there are several new designs for phase I cancer clinical trials including the continual reassessment method and accelerated titration design, the traditional algorithm-based designs, like the '3 + 3' design, are still widely used because of their practical simplicity. In this paper, we study some key statistical properties of the traditional algorithm-based designs in a general framework and derive the exact formulae for the corresponding statistical quantities. These quantities are important for the investigator to gain insights regarding the design of the trial, and are (i) the probability of a dose being chosen as the maximum tolerated dose (MTD); (ii) the expected number of patients treated at each dose level; (iii) target toxicity level (i.e. the expected dose-limiting toxicity (DLT) incidences at the MTD); (iv) expected DLT incidences at each dose level and (v) expected overall DLT incidences in the trial. Real examples of clinical trials are given, and a computer program to do the calculation can be found at the authors' website approximately linyo" locator-type="url">http://www2.umdnj.edu/ approximately linyo.     

基于药物毒性反应等级的up-and-down自适应设计

Ⅰ期临床试验主要关心药物的毒性,目的是在给定的剂量水平中寻找最大耐受剂量（MTD）．本文提出了基于药物毒性反应等级的up-and-down自适应设计,调查了该设计在各种变化的剂量一毒性关系下的运作特征．结果表明：该设计方法对提高建议MTD的精确度,以及保护病人,防止病人暴露在较高毒性剂量下方面,对Ⅰ期临床试验的设计实现了有意义的改善．     

Efficiency of New Dose Escalation Designs in Dose-Finding Phase I Trials of Molecularly Targeted Agents

Background

Statistical simulations have consistently demonstrated that new dose-escalation designs such as accelerated titration design (ATD) and continual reassessment method (CRM)-type designs outperform the standard “3+3” design in phase I cancer clinical trials.

Methods

We evaluated the actual efficiency of different dose escalation methods employed in first-in-human phase I clinical trials of targeted agents administered as single agents published over the last decade.

Results

Forty-nine per cent of the 84 retrieved trials used the standard “3+3” design. Newer designs used included ATD in 42%, modified CRM [mCRM] in 7%, and pharmacologically guided dose escalation in 1%. The median numbers of dose levels explored in trials using “3+3”, ATD and mCRM designs were 6, 8 and 10, respectively. More strikingly, the mean MTD to starting dose ratio appeared to be at least twice as high for trials using mCRM or ATD designs as for trials using a standard “3+3” design. Despite this, the mean number of patients exposed to a dose below the MTD was similar in trials using “3+3”, ATD and mCRM designs.

Conclusion

Our results support a more extensive implementation of innovative dose escalation designs such as mCRM and ATD in phase I cancer clinical trials of molecularly targeted agents.     

Likelihood calculations to evaluate experimental designs to estimate genetic variances

Mixed model analyses via restricted maximum likelihood, fitting the so-called animal model, have become standard methodology for the estimation of genetic variances. Models involving multiple genetic variance components, due to different modes of gene action, are readily fitted. It is shown that likelihood-based calculations may provide insight into the quality of the resulting parameter estimates, and are directly applicable to the validation of experimental designs. This is illustrated for the example of a design suggested recently to estimate X-linked genetic variances. In particular, large sample variances and sampling correlations are demonstrated to provide an indication of 'problem' scenarios. Using simulation, it is shown that the profile likelihood function provides more appropriate estimates of confidence intervals than large sample variances. Examination of the likelihood function and its derivatives are recommended as part of the design stage of quantitative genetic experiments.     

Designs for phase I clinical trials with multiple courses of subjects at different doses

Summary .   The goal of this article is to provide a new design framework and its corresponding estimation for phase I trials. Existing phase I designs assign each subject to one dose level based on responses from previous subjects. Yet it is possible that subjects with neither toxicity nor efficacy responses can be treated at higher dose levels, and their subsequent responses to higher doses will provide more information. In addition, for some trials, it might be possible to obtain multiple responses (repeated measures) from a subject at different dose levels. In this article, a nonparametric estimation method is developed for such studies. We also explore how the designs of multiple doses per subject can be implemented to improve design efficiency. The gain of efficiency from "single dose per subject" to "multiple doses per subject" is evaluated for several scenarios. Our numerical study shows that using "multiple doses per subject" and the proposed estimation method together increases the efficiency substantially.     

Efficiency of balanced treatment allocation for survival analysis

We assess the efficiency of balanced treatment allocation methods in clinical trials for comparing treatments with respect to survival. We compare optimal designs for each of three standard survival analysis techniques (maximum partial likelihood estimation, log-rank test, exponential regression) with balanced designs, over a range of hypothetical trials. Although balanced designs are not optimal, we find them to be very efficient. In view of the high efficiency demonstrated in this and in a previous paper (Begg and Kalish, 1984, Biometrics 40, 409-420), and practical difficulties in implementing an optimal design, we recommend the use of balanced allocation methods in practice.     

Cancer phase I trial design using drug combinations when a fraction of dose limiting toxicities is attributable to one or more agents

Drug combination trials are increasingly common nowadays in clinical research. However, very few methods have been developed to consider toxicity attributions in the dose escalation process. We are motivated by a trial in which the clinician is able to identify certain toxicities that can be attributed to one of the agents. We present a Bayesian adaptive design in which toxicity attributions are modeled via copula regression and the maximum tolerated dose (MTD) curve is estimated as a function of model parameters. The dose escalation algorithm uses cohorts of two patients, following the continual reassessment method (CRM) scheme, where at each stage of the trial, we search for the dose of one agent given the current dose of the other agent. The performance of the design is studied by evaluating its operating characteristics when the underlying model is either correctly specified or misspecified. We show that this method can be extended to accommodate discrete dose combinations.     

Sequential designs for ordinal phase I clinical trials

Sequential designs for phase I clinical trials which incorporate maximum likelihood estimates (MLE) as data accrue are inherently problematic because of limited data for estimation early on. We address this problem for small phase I clinical trials with ordinal responses. In particular, we explore the problem of the nonexistence of the MLE of the logistic parameters under a proportional odds model with one predictor. We incorporate the probability of an undetermined MLE as a restriction, as well as ethical considerations, into a proposed sequential optimal approach, which consists of a start‐up design, a follow‐on design and a sequential dose‐finding design. Comparisons with nonparametric sequential designs are also performed based on simulation studies with parameters drawn from a real data set.     

Bayesian optimal designs for Phase I clinical trials

A broad approach to the design of Phase I clinical trials for the efficient estimation of the maximum tolerated dose is presented. The method is rooted in formal optimal design theory and involves the construction of constrained Bayesian c- and D-optimal designs. The imposed constraint incorporates the optimal design points and their weights and ensures that the probability that an administered dose exceeds the maximum acceptable dose is low. Results relating to these constrained designs for log doses on the real line are described and the associated equivalence theorem is given. The ideas are extended to more practical situations, specifically to those involving discrete doses. In particular, a Bayesian sequential optimal design scheme comprising a pilot study on a small number of patients followed by the allocation of patients to doses one at a time is developed and its properties explored by simulation.     

In vitro tests for haematotoxicity: prediction of drug-induced myelosuppression by the CFU-GM assay

In a prevalidation study, a standard operating procedure (SOP) for human and mouse in vitro tests was developed, for evaluating the potential haematotoxicity of xenobiotics in terms of their direct, adverse effects on the myeloid colony-forming unit (CFU-GM). Based on the adjustment of the mouse-derived maximum tolerated dose (MTD), a prediction model was set up to calculate the human MTD, and an international blind trial was designed to apply this model to the clinical neutropenia of 23 drugs including 17 antineoplastics. The model correctly predicted the human MTD for 20 drugs out of the 23 (87%). This high percentage of predictivity, and the reproducibility of the SOP testing, confirmed the scientific validation of this model, and suggest promising applications for developing and validating other in vitro methods for use in haematotoxicology.     

Likelihood inference for exchangeable binary data with varying cluster sizes

This article investigates maximum likelihood estimation with saturated and unsaturated models for correlated exchangeable binary data, when a sample of independent clusters of varying sizes is available. We discuss various parameterizations of these models, and propose using the EM algorithm to obtain maximum likelihood estimates. The methodology is illustrated by applications to a study of familial disease aggregation and to the design of a proposed group randomized cancer prevention trial.     

LOGIT: a program for dose-response analysis.

We describe a FORTRAN computer program for fitting the logistic distribution function: (formula: see text) Where x represents dose or time, to dose-response data. The program determines both weighted least squares and maximum likelihood estimates for the parameters alpha and beta. It also calculates the standard errors of alpha and beta under both estimation methods, as well as the median lethal dose (LD50) and its standard error. Dose--response curves found by both fitting methods can be plotted as well as the 95% confidence bands for these lines.     

Information fraction estimation based on the number of events within the standard treatment regimen

For a Phase III randomized trial that compares survival outcomes between an experimental treatment versus a standard therapy, interim monitoring analysis is used to potentially terminate the study early based on efficacy. To preserve the nominal Type I error rate, alpha spending methods and information fractions are used to compute appropriate rejection boundaries in studies with planned interim analyses. For a one-sided trial design applied to a scenario in which the experimental therapy is superior to the standard therapy, interim monitoring should provide the opportunity to stop the trial prior to full follow-up and conclude that the experimental therapy is superior. This paper proposes a method called total control only (TCO) for estimating the information fraction based on the number of events within the standard treatment regimen. Based on theoretical derivations and simulation studies, for a maximum duration superiority design, the TCO method is not influenced by departure from the designed hazard ratio, is sensitive to detecting treatment differences, and preserves the Type I error rate compared to information fraction estimation methods that are based on total observed events. The TCO method is simple to apply, provides unbiased estimates of the information fraction, and does not rely on statistical assumptions that are impossible to verify at the design stage. For these reasons, the TCO method is a good approach when designing a maximum duration superiority trial with planned interim monitoring analyses.     

Critical Assessment of the C-Optimality Design Criteria for Estimating the Median Effective Dose in Quantal Dose-Response Curves

In this paper the properties of C-optimal designs constructed for estimating the median effective dose within the framework of two-parametric linear logistic models are critically assessed. It is well known that this design criterion which is based on the first-order variance approximation of the exact variance of the maximum likelihood estimate of the ED50 leads to a one-point design where the maximum likelihood theory breaks down. The single dose used in this design is identical with the true but unknown value of the ED50. It will be shown, that at this one-point design the asymptotic variance does not exist. A two-point design in the neighbourhood of the one-point design which is symmetrical about the ED50 and associated with a small dose-distance would be nearly optimal, but extremely nonrobust if the best guess of the ED50 differs from the true value. In this situation the asymptotic variance of the two-point design converging towards the one-point design tends to infinity. Moreover, taking in consideration, that for searching an optimal design the exact variance is of primary interest and the asymptotic variance serves only as an approximation of the exact variance, we calculate the exact variance of the estimator from balanced, symmetric 2-point designs in the neighbourhood of the limiting 1-point design for various dose distances and initial best guesses of the ED50. We compare the true variance of the estimate of the ED50 with the asymptotic variance and show that the approximations generally do not represent suitable substitutes for the exact variance even in case of unrealistically large sample sizes. Kalish (1990) proposed a criterion based on the second-order asymptotic variance of the maximum likelihood estimate of the ED50 to overcome the degenerated 1-point design as the solution of the optimization procedure. In fact, we are able to show that this variance approximation does not perform substantially better than the first–order variance. From these considerations it follows, that the C-optimality criterion is not useful in this estimation problem. Other criteria like the F-optimality should be used.     

Inference for the effect of treatment on survival probability in randomized trials with noncompliance and administrative censoring

In many clinical studies with a survival outcome, administrative censoring occurs when follow-up ends at a prespecified date and many subjects are still alive. An additional complication in some trials is that there is noncompliance with the assigned treatment. For this setting, we study the estimation of the causal effect of treatment on survival probability up to a given time point among those subjects who would comply with the assignment to both treatment and control. We first discuss the standard instrumental variable (IV) method for survival outcomes and parametric maximum likelihood methods, and then develop an efficient plug-in nonparametric empirical maximum likelihood estimation (PNEMLE) approach. The PNEMLE method does not make any assumptions on outcome distributions, and makes use of the mixture structure in the data to gain efficiency over the standard IV method. Theoretical results of the PNEMLE are derived and the method is illustrated by an analysis of data from a breast cancer screening trial. From our limited mortality analysis with administrative censoring times 10 years into the follow-up, we find a significant benefit of screening is present after 4 years (at the 5% level) and this persists at 10 years follow-up.     

Maximum likelihood methods for cure rate models with missing covariates

We propose maximum likelihood methods for parameter estimation for a novel class of semiparametric survival models with a cure fraction, in which the covariates are allowed to be missing. We allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one-dimensional conditional distributions. We propose a novel EM algorithm for maximum likelihood estimation and derive standard errors by using Louis's formula (Louis, 1982, Journal of the Royal Statistical Society, Series B 44, 226-233). Computational techniques using the Monte Carlo EM algorithm are discussed and implemented. A real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology.     

PA-CRM: A continuous reassessment method for pediatric phase I oncology trials with concurrent adult trials

Pediatric phase I trials are usually carried out after the adult trial testing the same agent has started, but not completed yet. As the pediatric trial progresses, in light of the accrued interim data from the concurrent adult trial, the pediatric protocol often is amended to modify the original pediatric dose escalation design. In practice, this is done frequently in an ad hoc way, interrupting patient accrual and slowing down the trial. We developed a pediatric-continuous reassessment method (PA-CRM) to streamline this process, providing a more efficient and rigorous method to find the maximum tolerated dose for pediatric phase I oncology trials. We use a discounted joint likelihood of the adult and pediatric data, with a discount parameter controlling information borrowing between pediatric and adult trials. According to the interim adult and pediatric data, the discount parameter is adaptively updated using the Bayesian model averaging method. Numerical study shows that the PA-CRM improves the efficiency and accuracy of the pediatric trial and is robust to various model assumptions.     

A parallel phase I/II clinical trial design for combination therapies

The use of multiple drugs in a single clinical trial or as a therapeutic strategy has become common, particularly in the treatment of cancer. Because traditional trials are designed to evaluate one agent at a time, the evaluation of therapies in combination requires specialized trial designs. In place of the traditional separate phase I and II trials, we propose using a parallel phase I/II clinical trial to evaluate simultaneously the safety and efficacy of combination dose levels, and select the optimal combination dose. The trial is started with an initial period of dose escalation, then patients are randomly assigned to admissible dose levels. These dose levels are compared with each other. Bayesian posterior probabilities are used in the randomization to adaptively assign more patients to doses with higher efficacy levels. Combination doses with lower efficacy are temporarily closed and those with intolerable toxicity are eliminated from the trial. The trial is stopped if the posterior probability for safety, efficacy, or futility crosses a prespecified boundary. For illustration, we apply the design to a combination chemotherapy trial for leukemia. We use simulation studies to assess the operating characteristics of the parallel phase I/II trial design, and compare it to a conventional design for a standard phase I and phase II trial. The simulations show that the proposed design saves sample size, has better power, and efficiently assigns more patients to doses with higher efficacy levels.     

Continual reassessment method for ordered groups

We investigate the two-group continual reassessment method for a dose-finding study in which we anticipate some ordering between the groups. This is a situation in which, for either group, we have little or almost no knowledge about which of the available dose levels will correspond to the maximum tolerated dose (MTD), but we may have quite strong knowledge concerning which of the two groups will have the higher level of MTD, if indeed they do not have the same MTD. The motivation for studying this problem came from an investigation into a new therapy for acute leukemia in children. The background to this study is discussed. There were two groups of patients: one group already received heavy prior therapy while the second group had received relatively much lighter prior therapy. It was therefore anticipated that the second group would have an MTD higher or at least as high as the first. Generally, likelihood methods or, equivalently, the use of noninformative Bayes priors, can be used to model the main aspects of the study, i.e., the MTD for one of the groups, reserving more informative Bayes modeling to be applied to the secondary features of the study. These secondary features may simply be the direction of the difference between the MTD levels for the two groups or, possibly, information on the potential gap between the two MTDs.     

Pooling designs for outcomes under a Gaussian random effects model

Due to the rising cost of laboratory assays, it has become increasingly common in epidemiological studies to pool biospecimens. This is particularly true in longitudinal studies, where the cost of performing multiple assays over time can be prohibitive. In this article, we consider the problem of estimating the parameters of a Gaussian random effects model when the repeated outcome is subject to pooling. We consider different pooling designs for the efficient maximum likelihood estimation of variance components, with particular attention to estimating the intraclass correlation coefficient. We evaluate the efficiencies of different pooling design strategies using analytic and simulation study results. We examine the robustness of the designs to skewed distributions and consider unbalanced designs. The design methodology is illustrated with a longitudinal study of premenopausal women focusing on assessing the reproducibility of F2-isoprostane, a biomarker of oxidative stress, over the menstrual cycle.