ANALYZING COUNTS,DURATIONS, AND RECURRENCES IN CLINICAL TRIALS

In 1985 the (Byar and Blackard, Urology, Vol. X, 556–561, 1978) data set on bladder cancer became available to researchers. Since then, a number of studies have made use of it. However, none of these has fully utilized all of the data nor have they developed a methodology in which it is possible to estimate models of the number of recurrences and durations that are consistent with each other.

The purpose of this research is to determine which, if any, of the two drugs used in the trial, pyridoxine and theotepa, were effective and, by example, illustrate procedures that could be useful in the analysis of other clinical trial data sets.

First, the number of recurrences is modeled as a count using the Poisson and negative binomial distributions with covariates. Then Poisson models are tested on the durations. Finally, durations and tumor counts per recurrence are fitted to more general autoregressive Wiebull and negative binomial distributions, respectively.

Poisson models for durations are rejected in favor of the more general autoregressive models. The data on durations and tumor counts are shown to be more reliable from an inference point of view than the data on the number of recurrences.

The data on durations and tumor counts show quite conclusively that both drugs are effective in treating bladder cancer, a result that differs from what others have found.     

Sample Size Calculation for Comparing Two Poisson or Negative Binomial Rates in Noninferiority or Equivalence Trials

Poisson and negative binomial models are frequently used to analyze count data in clinical trials. While several sample size calculation methods have recently been developed for superiority tests for these two models, similar methods for noninferiority and equivalence tests are not available. When a noninferiority or equivalence trial is designed to compare Poisson or negative binomial rates, an appropriate method is needed to estimate the sample size to ensure the trial is properly powered. In this article, several sample size calculation methods for noninferiority and equivalence tests have been derived based on Poisson and negative binomial models. All of these methods accounted for potential over-dispersion that commonly exists in count data obtained from clinical trials. The precision of these methods was evaluated using simulations. Supplementary materials for this article are available online.     

Flexible parametrization of variance functions for quantal response data derived from counts

Although the Poisson model has been widely used to fit count data, a well-known drawback is that the Poisson mean equals its variance. Many alternative models for counts that are overdispersed relative to Poisson have been developed to solve this issue, including the negative binomial model. In this article, the negative binomial model with a four-parameter logistic mean is proposed to handle these types of counts, with variance that flexibly depends on the mean. Various parameterizations for the variance are considered, including extra-Poisson variability modeled as an exponentiated B-spline. Thus, the proposed model ably captures the leveling off of the mean, i.e., the “lazy-S” shape often encountered for overdispersed dose–response counts, simultaneously taking into account both overdispersion and natural mortality. Two real datasets illustrate the merits of the proposed approach: media colony counts after tuberculosis decontamination, and the number of monkeys killed by Ache hunters over several hunting trips in the Paraguayan tropical forest.     

Comparing statistical methods for analyzing skewed longitudinal count data with many zeros: An example of smoking cessation

Count data with skewness and many zeros are common in substance abuse and addiction research. Zero-adjusting models, especially zero-inflated models, have become increasingly popular in analyzing this type of data. This paper reviews and compares five mixed-effects Poisson family models commonly used to analyze count data with a high proportion of zeros by analyzing a longitudinal outcome: number of smoking quit attempts from the New Hampshire Dual Disorders Study. The findings of our study indicated that count data with many zeros do not necessarily require zero-inflated or other zero-adjusting models. For rare event counts or count data with small means, a simpler model such as the negative binomial model may provide a better fit.     

A procedure for group sequential comparative poisson trials

This paper develops a group sequential procedure for comparative Poisson trials that are commonly used in vaccine studies. This procedure is based on exact conditional binomial distributions of number of events from the treated subjects conditional on total numbers of events at each interim analysis stage. We show that this procedure (vs. non interim analysis) can greatly reduce the trial length when the null hypothesis is false. We also discuss the impact of number of interim analyses, different alpha spending functions, and the discreetness of binomial distribution on the efficiency of this procedure. Corresponding Splus programs were also developed.     

A Procedure for Group Sequential Comparative Poisson Trials

This paper develops a group sequential procedure for comparative Poisson trials that are commonly used in vaccine studies. This procedure is based on exact conditional binomial distributions of number of events from the treated subjects conditional on total numbers of events at each interim analysis stage. We show that this procedure (vs. non interim analysis) can greatly reduce the trial length when the null hypothesis is false. We also discuss the impact of number of interim analyses, different α spending functions, and the discreetness of binomial distribution on the efficiency of this procedure. Corresponding Splus programs were also developed.     

Modeling change trajectories with count and zero-inflated outcomes: Challenges and recommendations

The goal of this article is to describe models to examine change over time with an outcome that represents a count, such as the number of alcoholic drinks per day. Common challenges encountered with this type of data are: (1) the outcome is discrete, may have a large number of zeroes, and may be overdispersed, (2) the data are clustered (multiple observations within each individual), (3) the researchers needs to carefully consider and choose an appropriate time metric, and (4) the researcher needs to identify both a proper individual (potentially nonlinear) change model and an appropriate distributional form that captures the properties of the data. In this article, we provide an overview of generalized linear models, generalized estimating equation models, and generalized latent variable (mixed-effects) models for longitudinal count outcomes focusing on the Poisson, negative binomial, zero-inflated, and hurdle distributions. We review common challenges and provide recommendations for identifying an appropriate change trajectory while determining an appropriate distributional form for the outcome (e.g., determining zero-inflation and overdispersion). We demonstrate the process of fitting and choosing a model with empirical longitudinal data on alcohol intake across adolescence collected as part of the National Longitudinal Survey of Youth 1997.     

Analysis of Zero-Inflated Count Data From Clinical Trials With Potential Dropouts

Counts of prespecified events are important endpoints for many safety and efficacy clinical trials. The conventional Poisson model might not be ideal due to three potential issues: (1) overdispersion arising from intra-subject correlation, (2) zero inflation when the prespecified event is rare, and (3) missing observations due to early dropouts. Negative binomial (NB), Poisson hurdle (PH), and negative binomial hurdle (NBH) models are more appropriate for overdispersed and/or zero-inflated count data. An offset can be included in these models to adjust for differential exposure duration due to early dropouts. In this article, we propose new link functions for the hurdle part of a PH/NBH model to facilitate testing for zero-inflation and model selection. The proposed link function particularly improves the model fit of a NBH model when an offset is included to adjust for differential exposure. A simulation study is conducted to compare the existing and proposed models, which are then applied to data from two clinical trials to demonstrate application and interpretation of these methods.     

Sample size determination for a three-arm equivalence trial of Poisson and negative binomial responses

ABSTRACT

Assessing equivalence or similarity has drawn much attention recently as many drug products have lost or will lose their patents in the next few years, especially certain best-selling biologics. To claim equivalence between the test treatment and the reference treatment when assay sensitivity is well established from historical data, one has to demonstrate both superiority of the test treatment over placebo and equivalence between the test treatment and the reference treatment. Thus, there is urgency for practitioners to derive a practical way to calculate sample size for a three-arm equivalence trial. The primary endpoints of a clinical trial may not always be continuous, but may be discrete. In this paper, the authors derive power function and discuss sample size requirement for a three-arm equivalence trial with Poisson and negative binomial clinical endpoints. In addition, the authors examine the effect of the dispersion parameter on the power and the sample size by varying its coefficient from small to large. In extensive numerical studies, the authors demonstrate that required sample size heavily depends on the dispersion parameter. Therefore, misusing a Poisson model for negative binomial data may easily lose power up to 20%, depending on the value of the dispersion parameter.     

Statistical models for numbers of implantation sites and embryonic deaths in mice

The number of implantation sites and early and late embryonic deaths were recorded for 2131 Charles River mice. Several probability distributions were tried as models to describe the data. The negative binomial distribution was found to be an excellent model for embryonic deaths. None of the models fits the implantation site data precisely, but the normal distribution was found adequate.     

Screening of well-established drugs targeting cancer metabolism: reproducibility of the efficacy of a highly effective drug combination in mice.

Alterations in metabolic pathways are known to characterize cancer. In order to suppress cancer growth, however, multiple proteins involved in these pathways have to be targeted simultaneously. We have developed a screening method to assess the best drug combination for cancer treatment based on targeting several factors implicated in tumor specific metabolism. Following a review of the literature, we identified those enzymes known to be deregulated in cancer and established a list of sixty-two drugs targeting them. These molecules are used routinely in clinical settings for diseases other than cancer. We screened a first library in vitro against four cell lines and then evaluated the most promising binary combinations in vivo against three murine syngeneic cancer models, (LL/2, Lewis lung carcinoma; B16-F10, melanoma; and MBT-2, bladder cancer). The optimum result was obtained using a combination of α-lipoic acid and hydroxycitrate (METABLOC(TM)). In this study, a third agent was added by in vivo evaluation of a large number of combinations. The addition of octreotide strongly reduced tumor development (T/C% value of 30.2 to 34.5%; P?相似文献   

Bias estimation in method comparison studies

A test and a reference analytical method are usually compared for agreement based on paired data obtained from several independent subjects. Bias between two methods can be classified as constant and proportional. In this article, we provide an approach for maximum likelihood estimation of total bias between two methods and partitioning it into constant and proportional bias for each subject. Normal, binomial, or Poisson distribution are the conditional distributions of the response variable that we have considered here, whereas subjects are considered to be random sample from a normally distributed population. Real data on blood cell counts and hemoglobin are used for demonstration. The estimate of biases can be used to test different statistical hypotheses and/or for graphical interpretation of the agreement. The partitioning of total biases in terms of constant and proportional gives an insight on the sources of disagreement between two methods and helps designers and manufacturer's define a remedial strategy.     

Algorithms for imputing partially observed recurrent events with applications to multiple imputation in pattern mixture models

Five algorithms are described for imputing partially observed recurrent events modeled by a negative binomial process, or more generally by a mixed Poisson process when the mean function for the recurrent events is continuous over time. We also discuss how to perform the imputation when the mean function of the event process has jump discontinuities. The validity of these algorithms is assessed by simulations. These imputation algorithms are potentially very useful in the implementation of pattern mixture models, which have been popularly used as sensitivity analysis under the non-ignorability assumption in clinical trials. A chronic granulomatous disease trial is analyzed for illustrative purposes.     

A Case Study of Modeling and Exposure-Response Prediction for Count Data

Even with two doses of an experimental drug in Phase III studies, with the commonly used approach for assessing treatment effects of individual doses, it may still be difficult to determine the final commercial dose. In such a scenario, with plasma concentration data collected in the studies, a modeling approach can be applied to predict treatment effects at different plasma concentration levels. Through an established relationship between plasma concentration and dose, the treatment effects of doses not studied in the Phase III studies can then be predicted. The results can further be applied to justify the final dose confirmation or selection. In this article, a Phase III program example with count data as the primary endpoint in the multiple sclerosis area is used to illustrate the application of such a technique for dose confirmation. Several models, such as the overdispersion Poisson model, negative binomial model, and recurrent event models, are considered. The negative binomial model is preferable due to better data fitting and the capability of within-treatment assessment and between-treatment comparison.     

Responder cell frequency estimation and binomial three-level nonlinear mixed effects model in limiting dilution assays

Responder cell frequencies (RCF), which describe vaccine-boosted immune responses in herpes zoster (HZ) prevention studies, have been estimated by using limiting dilution assays (LDA). The theoretical linearity assumption between the logarithm of the proportion of nonresponding wells (s) and the cell concentration (N) (or dilution level) in LDA, based on the single-hit Poisson model, is often violated with observed data resulting in biased estimates of RCF. In this article, the Poisson assumption is modified by applying a mixture of Poisson and gamma distributions, resulting in a negative binomial assumption, which presents a better fit between s and N. In LDA for HZ prevention studies, binary responses (responder or non-responder wells) are measured repeatedly at different cell concentrations and over time. To account for the correlation between responses to varying dilution levels from individuals, and the correlation between repeated assays of individuals over time simultaneously, a binomial three-level nonlinear mixed-effects model is proposed. For parameter estimation, a maximum likelihood method is applied via adaptive Gaussian quadrature. There is a lack of non-Gaussian multilevel nonlinear mixed-effects software, which can execute such a complicated fit. In this article, an algorithm for the three-level nonlinear mixed-effects model, which can be inserted into the code in the SAS procedure NLMIXED, is suggested.     

A hierarchical Binomial-Poisson model for the analysis of a crossover design for correlated binary data when the number of trials is dose-dependent

The differential reinforcement of a low-rate 72-seconds schedule (DRL-72) is a standard behavioral test procedure for screening a potential antidepressant compound. The data analyzed in the article are binary outcomes from a crossover design for such an experiment. Recently, Shkedy et al. (2004) proposed to estimate the treatments effect using either generalized linear mixed models (GLMM) or generalized estimating equations (GEE) for clustered binary data. The models proposed by Shkedy et al. (2004) assumed the number of responses at each binomial observation is fixed. This might be an unrealistic assumption for a behavioral experiment such as the DRL-72 because the number of responses (the number of trials in each binomial observation) is expected to be influenced by the administered dose level. In this article, we extend the model proposed by Shkedy et al. (2004) and propose a hierarchical Bayesian binomial-Poisson model, which assumes the number of responses to be a Poisson random variable. The results obtained from the GLMM and the binomial-Poisson models are comparable. However, the latter model allows estimating the correlation between the number of successes and number of trials.     

Bladder/lung cancer mortality in Blackfoot-disease (BFD)-endemic area villages with low (<150 μg/L) well water arsenic levels – An exploration of the dose–response Poisson analysis

ObjectiveTo examine the analytic role of arsenic exposure on cancer mortality among the low-dose (well water arsenic level <150 μg/L) villages in the Blackfoot-disease (BFD) endemic area of southwest Taiwan and with respect to the southwest regional data.MethodPoisson analyses of the bladder and lung cancer deaths with respect to arsenic exposure (μg/kg/day) for the low-dose (<150 μg/L) villages with exposure defined by the village median, mean, or maximum and with or without regional data.ResultsUse of the village median well water arsenic level as the exposure metric introduced misclassification bias by including villages with levels >500 μg/L, but use of the village mean or the maximum did not. Poisson analyses using mean or maximum arsenic levels showed significant negative cancer slope factors for models of bladder cancers and of bladder and lung cancers combined. Inclusion of the southwest Taiwan regional data did not change the findings when the model contained an explanatory variable for non-arsenic differences. A positive slope could only be generated by including the comparison population as a separate data point with the assumption of zero arsenic exposure from drinking water and eliminating the variable for non-arsenic risk factors.ConclusionThe cancer rates are higher among the low-dose (<150 μg/L) villages in the BFD area than in the southwest Taiwan region. However, among the low-dose villages in the BFD area, cancer risks suggest a negative association with well water arsenic levels. Positive differences from regional data seem attributable to non-arsenic ecological factors.     

Occupational bladder cancer: Polymorphisms of xenobiotic metabolizing enzymes,exposures, and prognosis

ABSTRACT

Approximately 7% of all bladder cancer cases in males are associated with occupation. The question arises whether the use of genome-wide association studies was able to identify bladder cancer risk factors that may modulate occupational bladder cancer risk and prognosis. One hundred and forty-three bladder cancer cases with suspected occupational bladder cancer and 337 controls were genotyped for the following polymorphisms: N-acetyltransferase 2 (NAT2), glutathione S-transferase M1 (GSTM1), glutathione S-transferase T1 (GSTT1), UDP-glucuronyltransferase 1A rs11892031 (UGT1A), rs9642880 (close to c-MYC), and rs710521 (close to TP63). The most relevant polymorphisms for occupational bladder cancer risk were GSTM1 and UGT1A, especially when co-occurring (GSTM1 negative and rs11892031[A/A]: 48% cases vs. 38% controls, OR 1.47, 95% CI 0.99–2.20). The effect was more pronounced in smokers. GSTM1 negative genotype occurred more frequently in cancer cases exposed to aromatic amines, carbolineum, and in painters and varnishers. UGT1A (rs11892031[A/A]) was found frequently in cases exposed to carbolineum, crack test spray, PAH, and in painters and varnishers. All investigated polymorphisms except rs710521 (TP63) seemed to exert an impact on recurrence risk. Relapse-free times were shorter for NAT2 slow and ultra-slow, GSTT1 positive and GSTM1 negative cases. Occupational bladder cancer cases with a number of risk variants displayed significantly shorter relapse-free times compared to cases with few, less relevant risk alleles as evidenced by median difference 8 months. In conclusion, in the present, suspected occupational bladder cancer cases phase II polymorphisms involved in bladder carcinogen metabolism modulate bladder cancer recurrence. Most relevant for bladder cancer risk were GSTM1 and UGT1A but not NAT2.     

Electrostatic interaction of tumor-targeting adenoviruses with aminoclay acquires enhanced infectivity to tumor cells inside the bladder and has better cytotoxic activity

In a previous report, 3-aminopropyl functionalized magnesium phyllosilicate (aminoclay) improved adenovirus transduction efficiency by shielding the negative surface charges of adenovirus particles. The present study analyzed the physicochemical characterization of the electrostatic complex of adenoviruses with aminoclay and explored whether it could be utilized for enhancing tumor suppressive activity in the bladder. As a result of aminoclay-adenovirus nanobiohybridization, its transduction was enhanced in a dose-dependent manner, increasing transgene expression in bladder cancer cells and in in vivo animal models. Physicochemical studies demonstrated that positively charged aminoclay led to the neutralization of negative surface charges of adenoviruses, protection of adenoviruses from neutralizing antibodies and lowered transepithelial electrical resistance (TEER). As expected from the physicochemical properties, the aminoclay enabled tumor-targeting adenoviruses to be more potent in killing bladder cancer cells and suppressing tumor growth in orthotopic bladder tumors, suggesting that aminoclay would be an efficient, versatile and biocompatible delivery carrier for intravesical instillation of adenoviruses.     

Aberrant PGE₂ metabolism in bladder tumor microenvironment promotes immunosuppressive phenotype of tumor-infiltrating myeloid cells

Bladder cancer is associated with enhanced inflammation and characterized by deregulated prostanoid metabolism. Here we examined prostaglandin E? (PGE?) metabolism and myeloid cell subsets that infiltrate tumor tissue using two xenograft models of human bladder cancer. Human bladder tumor xenografts implanted into athymic nude mice become highly infiltrated with host CD11b myeloid cells of bone marrow origin. Fast growing SW780 bladder tumor xenografts were infiltrated with heterogeneous CD11b myeloid cell subsets including tumor-associated macrophages and myeloid-derived suppressor cells. In contrast, majority of myeloid cells in tumor tissue from slow growing bladder cancer Urothel 11 displayed more immature, homogenous phenotype and comprised mostly MHC II class-negative myeloid-derived suppressor cells. We demonstrate that human bladder tumors secrete substantial amounts of PGE?. Normal bone marrow myeloid cell progenitors cultured in the presence of a bladder tumor-conditioned medium, which is enriched for PGE?, failed to differentiate into mature APCs and acquired phenotype of the myeloid-derived suppressor cells or inflammatory macrophages with up-regulated chemokine receptor CXCR4. Collectively our data demonstrate that enhanced cancer-related inflammation and deregulated PGE? metabolism in tumor microenvironment promote immunosuppressive pro-tumoral phenotype of myeloid cells in bladder cancer. These data also suggest that not only local tumor microenvironment but other factors such as stage of cancer disease and pace of tumor growth could markedly influence the phenotype, differentiation and immune function of myeloid cells in tumor tissue.