An optimal three-stage design for phase II clinical trials

A phase II clinical trial in cancer therapeutics is usually a single-arm study to determine whether an experimental treatment (E) holds sufficient promise to warrant further testing. When the criterion of treatment efficacy is a binary endpoint (response/no response) with probability of response p, we propose a three-stage optimal design for testing H₀: p ≤ p₀ versus H₁: p ≥ p₁, where p₁ and p₀ are response rates such that E does or does not merit further testing at given levels of statistical significance (α) and power (1 ? β). The proposed design is essentially a combination of earlier proposals by Gehan and Simon. The design stops with rejection of H₁ at stage 1 when there is an initial moderately long run of consecutive treatment failures; otherwise there is continuation to stage 2 and (possibly) stage 3 which have decision rules analogous to those in stages 1 and 2 of Simon's design. Thus, rejection of H₁ is possible at any stage, but acceptance only at the final stage. The design is optimal in the sense that expected sample size is minimized when p = p₀, subject to the practical constraint that the minimum stage 1 sample size is at least 5. The proposed design has greatest utility when the true response rate of E is small, it is desirable to stop early if there is a moderately long run of early treatment failures, and it is practical to implement a three-stage design. Compared to Simon's optimal two-stage design, the optimal three-stage design has the following features: stage 1 is the same size or smaller and has the possibility of stopping earlier when 0 successes are observed; the expected sample size under the null hypothesis is smaller; stages 1 and 2 generally have more patients than stage 1 of the two-stage design, but a higher probability of early termination under H₀; and the total sample size and criteria for rejection of H₁ at stage 3 are similar to the corresponding values at the end of stage 2 in the two-stage optimal design.     

Estimation of rank correlation for clustered data

It is well known that the sample correlation coefficient (R_xy) is the maximum likelihood estimator of the Pearson correlation (ρ_xy) for independent and identically distributed (i.i.d.) bivariate normal data. However, this is not true for ophthalmologic data where X (e.g., visual acuity) and Y (e.g., visual field) are available for each eye and there is positive intraclass correlation for both X and Y in fellow eyes. In this paper, we provide a regression‐based approach for obtaining the maximum likelihood estimator of ρ_xy for clustered data, which can be implemented using standard mixed effects model software. This method is also extended to allow for estimation of partial correlation by controlling both X and Y for a vector of other covariates. In addition, these methods can be extended to allow for estimation of rank correlation for clustered data by (i) converting ranks of both X and Y to the probit scale, (ii) estimating the Pearson correlation between probit scores for X and Y, and (iii) using the relationship between Pearson and rank correlation for bivariate normally distributed data. The validity of the methods in finite‐sized samples is supported by simulation studies. Finally, two examples from ophthalmology and analgesic abuse are used to illustrate the methods. Copyright © 2017 John Wiley & Sons, Ltd.     

Imputing missing covariate values for the Cox model

Multiple imputation is commonly used to impute missing data, and is typically more efficient than complete cases analysis in regression analysis when covariates have missing values. Imputation may be performed using a regression model for the incomplete covariates on other covariates and, importantly, on the outcome. With a survival outcome, it is a common practice to use the event indicator D and the log of the observed event or censoring time T in the imputation model, but the rationale is not clear. We assume that the survival outcome follows a proportional hazards model given covariates X and Z. We show that a suitable model for imputing binary or Normal X is a logistic or linear regression on the event indicator D, the cumulative baseline hazard H₀(T), and the other covariates Z. This result is exact in the case of a single binary covariate; in other cases, it is approximately valid for small covariate effects and/or small cumulative incidence. If we do not know H₀(T), we approximate it by the Nelson–Aalen estimator of H(T) or estimate it by Cox regression. We compare the methods using simulation studies. We find that using logT biases covariate‐outcome associations towards the null, while the new methods have lower bias. Overall, we recommend including the event indicator and the Nelson–Aalen estimator of H(T) in the imputation model. Copyright © 2009 John Wiley & Sons, Ltd.     

Centile estimation for a proportion response variable

This paper introduces two general models for computing centiles when the response variable Y can take values between 0 and 1, inclusive of 0 or 1. The models developed are more flexible alternatives to the beta inflated distribution. The first proposed model employs a flexible four parameter logit skew Student t ( logitSST ) distribution to model the response variable Y on the unit interval (0, 1), excluding 0 and 1. This model is then extended to the inflated logitSST distribution for Y on the unit interval, including 1. The second model developed in this paper is a generalised Tobit model for Y on the unit interval, including 1. Applying these two models to (1‐Y) rather than Y enables modelling of Y on the unit interval including 0 rather than 1. An application of the new models to real data shows that they can provide superior fits. Copyright © 2015 John Wiley & Sons, Ltd.     

Noninferiority trial designs for odds ratios and risk differences

This study presents constrained maximum likelihood derivations of the design parameters of noninferiority trials for binary outcomes with the margin defined on the odds ratio (ψ) or risk‐difference (δ) scale. The derivations show that, for trials in which the group‐specific response rates are equal under the point‐alternative hypothesis, the common response rate, π^N, is a fixed design parameter whose value lies between the control and experimental rates hypothesized at the point‐null, {π_C, π_E}. We show that setting π^N equal to the value of π_C that holds under H₀ underestimates the overall sample size requirement. Given {π_C, ψ} or {π_C, δ} and the type I and II error rates, or algorithm finds clinically meaningful design values of π^N, and the corresponding minimum asymptotic sample size, N=n_E+n_C, and optimal allocation ratio, γ=n_E/n_C. We find that optimal allocations are increasingly imbalanced as ψ increases, with γ_ψ<1 and γ_δ≈1/γ_ψ, and that ranges of allocation ratios map to the minimum sample size. The latter characteristic allows trialists to consider trade‐offs between optimal allocation at a smaller N and a preferred allocation at a larger N. For designs with relatively large margins (e.g. ψ>2.5), trial results that are presented on both scales will differ in power, with more power lost if the study is designed on the risk‐difference scale and reported on the odds ratio scale than vice versa. Copyright © 2010 John Wiley & Sons, Ltd.     

Cost-effectiveness of screening asymptomatic women for Chlamydia trachomatis

We estimate the cost-effectiveness of screening women for asymptomatic infection with Chlamydia trachomatis in general practice. A decision-analysis model was constructed for health effects of the program: averted pelvic inflammatory disease, chronic pelvic pain, ectopic pregnancy, infertility, and neonatal pneumonia (major outcomes averted). We explicitly included reinfection due to failed partner referral in the model. Cost-effectiveness estimates included direct and indirect costs. At current test costs - of US17 for ligase chain reaction test on urine - only screening women aged 15-19 years is cost saving. Net costs per cured woman and major outcome averted for screening women younger than 30 are below US 17 for ligase chain reaction test on urine - only screening women aged 15-19 years is cost saving. Net costs per cured woman and major outcome averted for screening women younger than 30 are below US 150 and US$ 410, respectively. These results are sensitive to reinfection. We conclude that explicit inclusion of reinfection is relevant for valid estimations of cost-effectiveness of screening for C. trachomatis. Based on cost-effectiveness considerations, we suggest implementation of a screening program in Amsterdam for sexually active women younger than 30 years.     

Testing for improvement in prediction model performance

Authors have proposed new methodology in recent years for evaluating the improvement in prediction performance gained by adding a new predictor, Y, to a risk model containing a set of baseline predictors, X, for a binary outcome D. We prove theoretically that null hypotheses concerning no improvement in performance are equivalent to the simple null hypothesis that Y is not a risk factor when controlling for X, H₀ : P(D = 1 | X,Y ) = P(D = 1 | X). Therefore, testing for improvement in prediction performance is redundant if Y has already been shown to be a risk factor. We also investigate properties of tests through simulation studies, focusing on the change in the area under the ROC curve (AUC). An unexpected finding is that standard testing procedures that do not adjust for variability in estimated regression coefficients are extremely conservative. This may explain why the AUC is widely considered insensitive to improvements in prediction performance and suggests that the problem of insensitivity has to do with use of invalid procedures for inference rather than with the measure itself. To avoid redundant testing and use of potentially problematic methods for inference, we recommend that hypothesis testing for no improvement be limited to evaluation of Y as a risk factor, for which methods are well developed and widely available. Analyses of measures of prediction performance should focus on estimation rather than on testing for no improvement in performance. Copyright © 2013 John Wiley & Sons, Ltd.     

The Ventura planning model: A proposal for mental health reform

The Ventura Planning Model is a proposal for public mental health reform. It addresses the decline in mental health funding. It offers a rationale for increased support—and funding—for public mental health services. The Planning Model grew out of the experience of implementing and operating the Ventura Children’s Demonstration Project. The model has five characteristics, or planning steps: 1) multi-problem target population; 2) systems goals; 3) interagency coalitions; 4) services and standards; and 5) systems monitoring and evaluation. The Ventura Children’s Demonstration Project implemented these planning steps, with an infusion of 1.54 million in funds from the state legislature. The project offset at least 66 percent of its cost by reducing other public agency costs and improved a variety of client-oriented outcomes. The success of the project in offsetting its costs has led the legislature to provide additional funds for three more California counties to implement the model for children and youth, and1.54 million in funds from the state legislature. The project offset at least 66 percent of its cost by reducing other public agency costs and improved a variety of client-oriented outcomes. The success of the project in offsetting its costs has led the legislature to provide additional funds for three more California counties to implement the model for children and youth, and 4 million a year for four years for Ventura County to test the model for adults and seniors. Emphasizing cost offsets in addition to client-oriented outcomes provides a practical rationale for proposing increases in public mental health funds. This rationale also implies substantial changes in the operations of many public mental health agencies.     

Comparison of objective Bayes factors for variable selection in parametric regression models for survival analysis

This paper considers the problem of selecting a set of regressors when the response variable is distributed according to a specified parametric model and observations are censored. Under a Bayesian perspective, the most widely used tools are Bayes factors (BFs), which are undefined when improper priors are used. In order to overcome this issue, fractional (FBF) and intrinsic (IBF) BFs have become common tools for model selection. Both depend on the size, N_t, of a minimal training sample (MTS), while the IBF also depends on the specific MTS used. In the case of regression with censored data, the definition of an MTS is problematic because only uncensored data allow to turn the improper prior into a proper posterior and also because full exploration of the space of the MTSs, which includes also censored observations, is needed to avoid bias in model selection. To address this concern, a sequential MTS was proposed, but it has the drawback of an increase of the number of possible MTSs as N_t becomes random. For this reason, we explore the behaviour of the FBF, contextualizing its definition to censored data. We show that these are consistent, providing also the corresponding fractional prior. Finally, a large simulation study and an application to real data are used to compare IBF, FBF and the well‐known Bayesian information criterion. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal sample size planning for the Wilcoxon-Mann-Whitney test

There are many different proposed procedures for sample size planning for the Wilcoxon-Mann-Whitney test at given type-I and type-II error rates α and β, respectively. Most methods assume very specific models or types of data to simplify calculations (eg, ordered categorical or metric data, location shift alternatives, etc). We present a unified approach that covers metric data with and without ties, count data, ordered categorical data, and even dichotomous data. For that, we calculate the unknown theoretical quantities such as the variances under the null and relevant alternative hypothesis by considering the following “synthetic data” approach. We evaluate data whose empirical distribution functions match the theoretical distribution functions involved in the computations of the unknown theoretical quantities. Then, well-known relations for the ranks of the data are used for the calculations. In addition to computing the necessary sample size N for a fixed allocation proportion t = n₁/N, where n₁ is the sample size in the first group and N = n₁ + n₂ is the total sample size, we provide an interval for the optimal allocation rate t, which minimizes the total sample size N. It turns out that, for certain distributions, a balanced design is optimal. We give a characterization of such distributions. Furthermore, we show that the optimal choice of t depends on the ratio of the two variances, which determine the variance of the Wilcoxon-Mann-Whitney statistic under the alternative. This is different from an optimal sample size allocation in case of the normal distribution model.     

Healthy minds for country youth: Help‐seeking for depression among rural adolescents

Objective: To assess depression recognition, barriers to accessing help from health professionals and potential sources of help for depression among rural adolescents. Design: Cross‐sectional survey. Setting: Two rural secondary schools in south‐east South Australia. Participants: Seventy‐four secondary school students aged 14 to 16 years. Main outcome measure(s): Depression recognition was measured using a depression vignette. Helpfulness of professionals, barriers to seeking help and help‐seeking behaviours for depression were assessed by self‐report questionnaire. Results: Depression was identified in the vignette by 73% (n = 54) of participants. Participants indicated that it would be more helpful for the vignette character to see other health professionals (98.6%, 95% CI, 92.0–100.0%) than a doctor (82.4%, 72.1–89.6%). Barriers to seeking help from doctors and other health professionals were categorised into logistical and personal barriers. Participants agreed more strongly to personal (mean = 2.86) than logistical barriers (mean = 2.67, P < 0.05) for seeing a doctor. Boys and girls responded differently overall, and to personal barriers to seeing an other health professional. Sources of help were divided into three categories: formal, informal and external. Informal sources of help (mean = 4.02) were identified as more helpful than both formal (mean = 3.66) and external sources (mean = 3.72, P < 0.001). Gender differences were observed within and between the three sources of help categories. Conclusions: Recognising symptoms of depression was demonstrated in this study. Helpfulness of professionals, barriers to seeking help and potential sources of help for depression were identified. More work is required for improving depression literacy and providing effective interventions specifically for rural adolescents.     

Simultaneous confidence regions for multivariate bioequivalence

Demonstrating bioequivalence of several pharmacokinetic (PK) parameters, such as AUC and C_max, that are calculated from the same biological sample measurements is in fact a multivariate problem, even though this is neglected by most practitioners and regulatory bodies, who typically settle for separate univariate analyses. We believe, however, that a truly multivariate evaluation of all PK measures simultaneously is clearly more adequate. In this paper, we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation. Some of them work well for idealised scenarios but break down when faced with real‐data challenges such as unknown variance and correlation among the PK parameters. We study the shapes of the confidence regions resulting from different methods, discuss how marginal simultaneous confidence intervals for the individual PK measures can be derived, and illustrate the application to data from a trial on ticlopidine hydrochloride. An R package is available.     

Half blind superiority tests for clinical trials of anti-infective drugs

This paper introduces a test of superiority of new anti-infective drug B over comparator drug A based on a randomized clinical trial. This test can be used to demonstrate assay (trial) sensitivity for noninferiority trials and rigorously tailor drug choice for individual patients. Our approach uses specialized baseline covariates X_A,X_B, which should predict the benefits of drug A and drug B, respectively. Using a response surface model for the treatment effect, we test for superiority at the (X_A,X_B) point that is most likely to show superiority. We identify this point based on estimates from a novel half-blind pseudo likelihood, where we augment a blinded likelihood (mixed over the treatment indicator) with likelihoods for the overall success rates for drug A and drug B (mixed over X_A,X_B). The augmentation results in much better estimates than those based on the mixed blinded likelihood alone but, interestingly, the estimates almost behave as if they were based on fully blinded data. We also develop an analogous univariate method using X_A for settings where X_B has little variation. Permutation methods are used for testing. If the “half-blind” test rejects, pointwise confidence interval can be used to identify patients who would benefit from drug B. We compare the new tests to other methods with an example and via simulations.     

Psychosocial outcomes of Lunch is in the Bag, a parent program for packing healthful lunches for preschool children

Objective

This pilot study evaluated effects of Lunch is in the Bag on behavioral constructs and their predictive relationship to lunch-packing behaviors of parents of young children.

Methods

Six child care centers were pair-matched and randomly assigned to intervention (n = 3) and comparison (n = 3) groups. Parent/child dyads participated. Constructs of knowledge, outcome expectations, perceived control, subjective norms, and intentions were measured by a pre/post questionnaire. Hierarchical linear regression was used, and P < .05 was considered significant.

Results

There were significant increases in knowledge (P = .01); outcome expectations for whole grains (P < .001); and subjective norms for fruit (P = .002), vegetables (P = .046), and whole grains (P = .02). Perceived control, outcome expectations, and intentions significantly predicted packing vegetables and knowledge predicted whole grains.

Conclusions and Implications

Lunch is in the Bag is a feasible intervention to improve the lunch-packing behaviors of parents of preschool-aged children.     

An algorithm for the design of group sequential triangular tests for single‐arm clinical trials with a binary endpoint

Consider the problem of testing H₀:p?p₀ vs H₁:p>p₀, where p could, for example, represent the response rate to a new drug. The group sequential TT is an efficient alternative to a single‐stage test as it can provide a substantial reduction in the expected number of test subjects. Whitehead provides formulas for determining stopping boundaries for this test. Existing research shows that test designs based on these formulas (WTTs) may not meet Type I error and/or power specifications, or may be over‐powered at the expense of requiring more test subjects than are necessary. We present a search algorithm, with program available from the author, which provides an alternative approach to triangular test design. The primary advantage of the algorithm is that it generates test designs that consistently meet error specifications. In tests on nearly 1000 example combinations of n (group size), p₀, p₁, α, and β the algorithm‐determined triangular test (ATT) design met specified Type I error and power constraints in every case considered, whereas WTT designs met constraints in only 10 cases. Actual Type I error and power values for the ATTs tend to be close to specified values, leading to test designs with favorable average sample number performance. For cases where the WTT designs did meet Type I error and power constraints, the corresponding ATT designs also had the advantage of providing, on average, a modest reduction in average sample numbers calculated at p₀, p₁, and (p₀ + p₁)/2. Copyright © 2010 John Wiley & Sons, Ltd.     

Author Index for Volume 8

Fumigation of a Euglena gracilis suspension for one hour with 0.80 ppm ozone in the absence of light does not affect the concentration of reduced pyridine nucleotide (NADH) in the cells. Oxidative phosphorylation is increased by 9.4%, following fumigation with 0.80 ppm ozone; its efficiency (P/O ratio) remains unchanged.

Exposure of Euglena cells to ozone (0.80 ppm) in the presence of light diminishes the rate of NADH formation by 9% to 12% when compared with samples treated with pure air. Photosynthetic phosphorylation of Euglena samples treated with 0.80 ppm ozone is diminished by 3.6%.

Data that were obtained following fumigation with ozone in the dark suggest the formation of modified cell structures. Results obtained following fumigation with ozone in the presence of light explain the inhibitory effect of ozone on the rate of photosynthesis of E gracilis in more detail.     

Development and Validation of the Chinese Health Literacy Scale for Chronic Care

This study aims to develop and test the psychometric properties of the Chinese Health Literacy Scale for Chronic Care (CHLCC). This is a methodological study with a sample of 262 patients 65 years of age and older who had chronic illnesses. Pearson's correlation, independent sample t tests, and analyses of variance were used. The CHLCC showed a significant positive correlation with Chinese literacy levels (r = 0.80; p < .001) but was negatively correlated with age (r =?0.31; p <.001). Respondents who were male (t =4.34; p <.001) and who had reached Grade 12 or higher in school (F = 51.80; p <.001) had higher CHLCC scores than did their counterparts. Individuals with high levels of health literacy had fewer hospitalizations than did their counterparts (β =?0.31; incidence rate ratio = 0.73; p <.05). The CHLCC also displayed good internal reliability (Cronbach'sα =0.91) and good test–retest reliability (intraclass correlation coefficient = 0.77; p <.01). The CHLCC is a valid and reliable measure for assessing health literacy among Chinese patients with chronic illness. The scale could be used by practitioners before implementing health promotion and education.     

Multiplicity adjustments in testing for bioequivalence

Bioequivalence of two drugs is usually demonstrated by rejecting two one‐sided null hypotheses using the two one‐sided tests for pharmacokinetic parameters: area under the concentration‐time curve (AUC) and maximum concentration (Cmax). By virtue of the intersection–union test, there is no need for multiplicity adjustment in testing the two one‐sided null hypotheses within each parameter. However, the decision rule for bioequivalence often requires equivalence to be achieved simultaneously on both parameters that contain four one‐sided null hypotheses together; without adjusting for multiplicity, the family wise error rate (FWER) could fail to be controlled at the nominal type‐I error rate α. The multiplicity issue for bioequivalence in this regard is scarcely discussed in the literature. To address this issue, we propose two approaches including a closed test procedure that controls FWER for the simultaneous AUC and Cmax bioequivalence and requires no adjustment of the type‐I error, and an alpha‐adaptive sequential testing (AAST) that controls FWER by pre‐specifying the significance level on AUC (α₁) and obtaining it for Cmax (α₂) adaptively after testing of AUC. While both methods control FWER, the closed test requires testing of eight intersection null hypotheses each at α, and AAST is at times accomplished through a slight deduction in α₁ and no deduction in α₂ relative to α. The latter considers equivalence reached in AUC a higher importance than that in Cmax. Illustrated with published data, the two approaches, although operate differently, can lead to the same substantive conclusion and are better than a traditional method like Bonferroni adjustment. Copyright © 2014 John Wiley & Sons, Ltd.     

Confidence intervals for a binomial proportion

Thirteen methods for computing binomial confidence intervals are compared based on their coverage properties, widths and errors relative to exact limits. The use of the standard textbook method, x/n ± 1.96√[(x/n) (1 ? x/n)/n], or its continuity corrected version, is strongly discouraged. A commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p? is such that np? and n(1 ? p?) both exceed 5 does not ensure adequate accuracy. Score limits are easily calculated from closed from solutions to quadratic equations and can be used at all times. Based on coverage functions, the continuity corrected score method is recommended over exact methods. Its conservative nature should be kept in mind, as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction.     

Estimation of smooth ROC curves for biomarkers with limits of detection

Protein biomarkers found in plasma are commonly used for cancer screening and early detection. Measurements obtained by such markers are often based on different assays that may not support detection of accurate measurements due to a limit of detection. The ROC curve is the most popular statistical tool for the evaluation of a continuous biomarker. However, in situations where limits of detection exist, the empirical ROC curve fails to provide a valid estimate for the whole spectrum of the false positive rate (FPR). Hence, crucial information regarding the performance of the marker in high sensitivity and/or high specificity values is not revealed. In this paper, we address this problem and propose methods for constructing ROC curve estimates for all possible FPR values. We explore flexible parametric methods, transformations to normality, and robust kernel‐based and spline‐based approaches. We evaluate our methods though simulations and illustrate them in colorectal and pancreatic cancer data.