Posterior maximization and averaging for Bayesian working model choice in the continual reassessment method.

The continual reassessment method (CRM) is a method for estimating the maximum tolerated dose in a dose-finding study. Traditionally, use is made of a single working model or 'skeleton' idealizing an underlying true dose-toxicity relationship. This working model is chosen either by discussion with investigators or published data, before the beginning of the trial or simply on the basis of operating characteristics. To overcome the arbitrariness of the choice of such a single working model, Yin and Yuan (biJ. Am. Statist. Assoc. 2009; 104:954-968) propose a model averaging over a set of working models. Here, instead of averaging, we investigate some alternative Bayesian model criteria that maximize the posterior distribution. We propose three adaptive model-selecting CRMs using the Bayesian model selection criteria, in which we specify in advance a collection of candidate working models for the dose-toxicity relationship, especially initial guesses of toxicity probabilities, and adaptively select the only one working model among the candidates updated by using the original CRM for each working model, based on the posterior model probability, the posterior predictive loss or the deviance information criteria, during the course of the trial. These approaches were compared via a simulation study with the model averaging approach.

Upper limb anthropometry: the value of measurement variance studies.

If a test involves subjective evaluation then different observers will record different findings. This is true of upper limb anthropometry. Unless the interobserver measurement variation is quantified then the detection of real, rather than apparent, measurement changes is hindered. This paper uses a new statistical approach to interpret apparent measurement changes in the presence of observer variation.

Graft failure in patients receiving T cell-depleted HLA-identical allogeneic marrow transplants.

Results of a previous study suggested that the risk of graft failure after transplantation of HLA-identical T cell-depleted marrow may be influenced by the preparative regimen. Subsequent clinical trials were carried out to clarify this relationship and to determine whether post-transplant immunosuppression could have an effect on graft durability. Two factors were found to be associated with graft failure. Patients with hematologic malignancy given a preparative regimen of cyclophosphamide (120 mg/kg) and 15.75 Gy fractionated total body irradiation (TBI) had a 27% cumulative incidence of graft failure, which was less than the 69% incidence seen previously in patients given cyclophosphamide and 12.0 Gy fractionated TBI (p less than 0.05, log-rank test). Patients with acute leukemia had a higher risk of graft failure than patients with chronic myelogenous leukemia (p less than 0.005). The incidence of graft failure was not influenced by post-transplant immunosuppression with cyclosporine, methotrexate or a combination of cyclosporine plus methotrexate or by the omission of all post-transplant immunosuppression. Similarly, graft failure was not associated with the complement lot used for marrow treatment, the recovery of BFU-E or CFU-GM, or with the number of nucleated cells or T cells in the graft. The effect of primary diagnosis and the inverse relationship between the amount of pretransplant TBI and the graft failure rate suggest that a host factor may have been involved in a presumably immune-mediated rejection. This observation further leads to the inference that certain T cells present in donor marrow can suppress host immunity or help to maintain function of the graft.

Gynecological abnormalities following allogeneic bone marrow transplantation.

Forty-four post-pubertal women were studied 261-4628 days after allogeneic transplantation to determine the nature and degree of gynecological abnormalities following bone marrow transplantation. Evaluations included pelvic examinations, exfoliative cytology, serum gonadotropin levels, direct preparations for micro-organisms, and microbial cultures. Pelvic abnormalities were detected in 35 of 44 (80%) women and resembled atrophic changes known to occur after ovarian failure. Findings included reduced vaginal elasticity and rugal folds, pale tissues, small vaginal, uterine and cervical size, atrophic vulvovaginitis, introital stenosis, and loss of pubic hair. Atrophic abnormalities were noted in 33 of 36 recipients of total body irradiation (TBI) compared to two of eight women not prepared with TBI (p = 0.02). Vasomotor symptoms were reported in 67% of TBI recipients compared to 38% of those not given TBI. Elevated serum gonadotropin levels suggested that TBI had caused the ovarian failure. Recognition of these gynecological abnormalities can lead to earlier hormone replacement, alleviating unnecessary discomfort and improving the well-being of the marrow transplant recipient.

Sequential design and analysis of dose finding studies in patients with life threatening disease.

We describe a recently developed approach to the design and analysis of dose finding studies in patients with life-threatening disease. Such patients may be terminally ill and, although interest is focussed on cancer, the methodology is more generally applicable. Of major interest is the identification of a dose with a given targeted toxicity level. Experimentation is carried out at a level for which all current available evidence, ie any information available before beginning the study, typically used in determining dose levels, together with information accumulated in the course of the study, indicates the best estimate of the target level. At the end of the study it is possible to obtain a statistical estimate of the probability of toxicity at the chosen level. Note that such estimation is not possible after a dose finding study carried out along traditional lines.

Cox's regression model: computing a goodness of fit statistic.

A simple test for goodness of fit of the proportional hazards regression model has recently been proposed. This article indicates how a large number of programs in current use to fit this model can be easily adapted to incorporate this goodness of fit statistic.

Homogeneity of relative risk against two-step alternatives.

In this paper the computational aspects of testing the null hypothesis of homogeneity of relative risk against two-step alternatives are examined. This representation is the same as that introduced by Anderson and Senthilselvan (Appl. Stat. 31 (1982) 44-51), i.e. a two-step model. Such alternatives may be used to represent decay in effect or, perhaps, inversion of the regression effect or crossing hazards. For such models inferential aspects are slightly more involved than for instance with proportional hazards models having fixed effects, even when time dependent as in O'Quigley and Pessione (Biometrics 45 (1989) 135-144). The necessary techniques for carrying out tests based on the two-stage model have recently been developed (O'Quigley and Pessione (Biometrics (1990) (in press] and in this paper we outline the necessary steps to be taken in the construction of algorithms to implement the proposed procedures. Programs enabling analyses based on the assumption of homogeneity of risk are very widely available. These include software packages such as BMDP, SAS, SPSS and GLIM. In the output of these packages, as well as that from most other standard routines, is contained all the necessary information to carry out the tests proposed by O'Quigley and Pessione. Here we detail the explicit formulae needed for carrying out the calculations in practice. The special cases of crossing hazards are considered in detail.

Integral evaluation for continual reassessment method.

In this paper we show how the exact analytical solutions to the numerical integrals required in the implementation of the continual reassessment method can be evaluated. The formulas have been given but, with increasing sample size, rapidly become unwieldy. We develop an algorithm which uses the numerical binary representation of the subset size and, in the process, enables us to easily identify those members of the subset needed in the integral evaluation. The complex combinatorial problem of selecting the set of all subsets with a particular characteristic is then greatly simplified. We describe the nature and type of all the variables and parameters used in a PASCAL procedure.

[Correlate non-Gaussian measurement]. / Mesures non-gaussiennes de corrélation.

A general approach for measuring correlation in non-normal populations is presented. Two ways of tackling the problem are considered. The first relies on an explicit parametric model and some non-elementary notions from probability theory. The second, which relies on a wide class of bivariate laws of which the bivariate normal one is a special case, is very simple to put into practice.

[Comparison of several percentages when the theoretical determinants are weak]. / Comparaison de plusieurs pourcentages lorsque les effectifs théoriques sont faibles.

The authors suggest a simple test for use in the comparison of several proportions. Its main advantage is that it may be used in the presence of low cell expectations. The price of this advantage is in having a sufficient number of proportions for the test to be valid. Other methods which have looked at this problem are examined.

Testing the proportional hazards regression model against some general alternatives.

A class of goodness of fit tests for the proportional hazards regression model is proposed. The alternatives considered permit the parameters of the model to vary as step functions with time. Restricting the type of step function allowed gives rise to tests against more specific alternatives. Computational details are given.

Experimental designs for phase I and phase I/II dose-finding studies.

We review the rationale behind the statistical design of dose-finding studies as used in phase I and phase I/II clinical trials. We underline what the objectives of such dose-finding studies should be and why the widely used standard design fails to meet any of these objectives. The standard design is a "memoryless" design and we discuss how this impacts on practical behaviour. Designs introduced over the last two decades can be viewed as designs with memory and we discuss how these designs are superior to memoryless designs. By superior we mean that they require less patients overall, less patients to attain the maximum tolerated dose (MTD), and concentrate a higher percentage of patients at and near to the MTD. We reanalyse some recently published studies in order to provide support to our contention that markedly better results could have been achieved had a design with memory been used instead of a memoryless design.

Dose finding and O6-alkylguanine-DNA alkyltransferase study of cisplatin combined with temozolomide in paediatric solid malignancies.

Cisplatin may have additive activity with temozolomide due to ablation of the DNA repair protein O6-alkylguanine-DNA alkyltransferase (MGMT). This phase I/II study determined recommended combination doses using the Continual Reassessment Method, toxicities and antitumour activity in paediatric patients, and evaluated MGMT in peripheral blood mononuclear cells (PBMCs) in order to correlate with haematological toxicity. In total, 39 patients with refractory or recurrent solid tumours (median age approximately 13 years; 14 pretreated with high-dose chemotherapy, craniospinal irradiation, or having bone marrow involvement) were treated with cisplatin, followed the next day by oral temozolomide for 5 days every 4 weeks at dose levels 80 mg m(-2)/150 mg m(-2) day(-1), 80/200, and 100/200, respectively. A total of 38 patients receiving 113 cycles (median 2, range 1-7) were evaluable for toxicity. Dose-limiting toxicity was haematological in all but one case. Treatment-related toxicities were thrombocytopenia, neutropenia, nausea-vomiting, asthenia. Hearing loss was experienced in five patients with prior irradiation to the brain stem or posterior fossa. Partial responses were observed in two malignant glioma, one brain stem glioma, and two neuroblastoma. Median MGMT activity in PBMCs decreased after 5 days of temozolomide treatment: low MGMT activity correlated with increased severity of thrombocytopenia. Cisplatin-temozolomide combinations are well tolerated without additional toxicity to single-agent treatments; the recommended phase II dosage is 80 mg m(-2) cisplatin and 150 mg m(-2) x 5 temozolomide in heavily treated, and 200 mg m(-2) x 5 temozolomide in less-heavily pretreated children.

Estimating the probability of toxicity at the recommended dose following a phase I clinical trial in cancer.

The problem of point and interval estimation following a Phase I trial, carried out according to the scheme outlined by O'Quigley, Pepe, and Fisher (1990, Biometrics 46, 33-48), is investigated. A reparametrization of the model suggested in this earlier work can be seen to be advantageous in some circumstances. Maximum likelihood estimators, Bayesian estimators, and one-step estimators are considered. The continual reassessment method imposes restrictions on the sample space such that it is not possible for confidence intervals to achieve exact coverage properties, however large a sample is taken. Nonetheless, our simulations, based on a small finite sample of 20, not atypical in studies of this type, indicate that the calculated intervals are useful in most practical cases and achieve coverage very close to nominal levels in a very wide range of situations. The relative merits of the different estimators and their associated confidence intervals, viewed from a frequentist perspective, are discussed.

Another look at two phase I clinical trial designs.

This note is a response to a recent paper by Korn et al. in which two phase I trial designs were compared, the designs in question being the standard design and the CRM design. The authors concluded that: (i) CRM designs will take longer to complete than standard designs; and (ii) CRM designs are less safe than the standard designs. These conclusions followed from a set of simulations for three different dose toxicity situations. The first purpose of this note is to point out that these conclusions lean on false assumptions. The claims are in error. In their comparisons Korn et al. never in fact used CRM, as defined in O'Quigley, Pepe and Fisher, but a modified version. The second purpose of this note is to look at the same cases studied by Korn et al. but this time using a correctly defined CRM model. Using the same comparison tools of Korn et al. we will see that for these situations, and indeed for a very wide class of other situations not presented here, not only are (i) and (ii) not true but that the exact opposite holds.

Methods for dose finding studies in cancer clinical trials: a review and results of a Monte Carlo study.

We discuss some of the statistical approaches to the design and analysis of phase I clinical trials in cancer. An attempt is made to identify the issues, particular to this type of trial, that should be addressed by an appropriate methodology. A brief review of schemes currently in use is provided together with our views of the extent to which any particular scheme addresses the main issues. Some simulations are provided together with graphical illustration of the operating characteristics of the particular methods. It appears that the continual reassessment method is preferable to other contending schemes.

The problem of a covariate-time qualitative interaction in a survival study.

We introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards. Although this kind of alternative is somewhat rare, designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures, upon which we can call in those few cases where such departures are suspected. Furthermore, the proposed test and an approximate version of the test are seen to suffer only moderate losses in power, when compared with their optimal counterparts, should the alternative be one of proportional hazards. Our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail. The model we use in this work is a special case of the one introduced by Anderson and Senthilselvan (1982. Applied Statistics 31, 44-51). We propose overcoming an inferential problem stemming from their model by using the methods of Davies (1977, Biometrika 64, 247-254; 1987, Biometrika 74, 33-43) backed up by resampling techniques. We also look at an approach relying directly on resampling techniques. The distributional aspects of this approach under the null hypothesis are interesting but, practically, its behaviour is such that its use cannot be generally recommended. Outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory.

Nonparametric tests of association between survival time and continuously measured covariates: the logit-rank and associated procedures.

O'Brien's logit-rank procedure (1978, Biometrics 34, 243-250) is shown to arise as a score test based on the partial likelihood for a proportional hazards model provided the covariate structure is suitably defined. Within this framework the asymptotic properties claimed by O'Brien can be readily deduced and can be seen to be valid under a more general model of censoring than that considered in his paper. More important, perhaps, it is now possible to make a more natural and interpretable generalization to the multiple regression problem than that suggested by O'Brien as a means of accounting for the effects of nuisance covariates. This can be achieved either by modelling or stratification. The proportional hazards framework is also helpful in that it enables us to recognize the logit-rank procedure as being one member of a class of contending procedures. One consequence of this is that the relative efficiencies of any two procedures can be readily evaluated using the results of Lagakos (1988, Biometrika 75, 156-160). Our own evaluations suggest that, for non-time-dependent covariates, a simplification of the logit-rank procedure, leading to considerable reduction in computational complexity, is to be preferred to the procedure originally outlined by O'Brien.

Score tests for homogeneity of regression effect in the proportional hazards model.

A simple model, containing the proportional hazards regression model as a special case, is presented. The purpose of the model is to provide a framework in which specific alternatives to the proportional hazards assumption may be tested. Rank-invariant score tests for linear, quadratic, or exponential trends can, for instance, all be undertaken within this framework. In the case of the two-sample problem the required calculations are shown to take a particularly simple form. Special consideration is given to the two-sample case in which there is an inversion of the regression effect, i.e., where the hazard functions cross at some given point. Both of the motivating examples are concerned with this problem. Computational aspects are relatively straightforward and some discussion on this is provided.