Statistical inference for the effect of magnetic brain stimulation on a motoneurone

A stochastic model is developed for the possible excitatory and inhibitory effects of a stimulus to the brain on the activity of single human motoneurones. The model consists of a Wiener process for the build-up of underlying potential, a deterministic effect due to the stimulus and a random lag from brain to muscle. Direct likelihood inference for its parameters seems impossible, and we study the use of simulation to estimate the log-likelihood for the parameters of substantive interest. Monte Carlo methods yield point and confidence interval estimates of the membrane excitability underlying excitatory and inhibitory effects. The main qualitative conclusion is that both excitatory and inhibitory effects are unambiguously present. The contribution of statistical analysis to this problem is to provide accurate and apparently reliable inference for the quantities of neurophysiological interest. More generally, our methodology has the potential to make accurate likelihood-based inferences in challenging problems, but the computational burden can be large, particularly if the model is not fully adequate for the data, as in our application.     

Estimating progression-free survival in paediatric brain tumour patients when some progression statuses are unknown

In oncology, progression-free survival time, which is defined as the minimum of the times to disease progression or death, often is used to characterize treatment and covariate effects. We are motivated by the desire to estimate the progression time distribution on the basis of data from 780 paediatric patients with choroid plexus tumours, which are a rare brain cancer where disease progression always precedes death. In retrospective data on 674 patients, the times to death or censoring were recorded but progression times were missing. In a prospective study of 106 patients, both times were recorded but there were only 20 non-censored progression times and 10 non-censored survival times. Consequently, estimating the progression time distribution is complicated by the problems that, for most of the patients, either the survival time is known but the progression time is not known, or the survival time is right censored and it is not known whether the patient's disease progressed before censoring. For data with these missingness structures, we formulate a family of Bayesian parametric likelihoods and present methods for estimating the progression time distribution. The underlying idea is that estimating the association between the time to progression and subsequent survival time from patients having complete data provides a basis for utilizing covariates and partial event time data of other patients to infer their missing progression times. We illustrate the methodology by analysing the brain tumour data, and we also present a simulation study.     

The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

Reduced rank proportional hazards model for competing risks: An application to a breast cancer trial

In many cancer trials patients are at risk of recurrence and death after the appearance and the successful treatment of the first diagnosed tumour. In this situation competing risks models that model several competing causes of therapy or surgery failure are a natural framework to describe the evolution of the disease.Typically, regression models for competing risks outcomes are based on proportional hazards model for each of the cause-specific hazard rates. An immediate practical problem is then how to deal with the abundance of regression parameters. The aim of reduced rank proportional hazards models is to reduce the number of parameters that need to be estimated while at the same time keeping the distinction between different transitions. They have the advantage of describing the competing risks model in fewer parameters, cope with transitions where few events are present and facilitate the interpretation of these estimates.We shall illustrate the use of this technique on 2795 patients from a breast cancer trial (EORTC 10854).     

A three-state continuous time Markov chain model for HIV disease burden

Plasma HIV viral load (VL) is the clinical indicator used to evaluate disease burden for HIV-infected patients. We developed a covariate-adjusted, three-state, homogenous continuous time Markov chain model for HIV/AIDS disease burden among subgroups. We defined Detectable and Undetectable HIV VL levels as two transient states and Death as the third absorbing state. We implemented the exact maximum likelihood method to estimate the parameters with related asymptotic distribution to conduct hypothesis testing. We evaluated the proposed model using HIV-infected individuals from South Carolina (SC) HIV surveillance data. Using the developed model, we estimated and compared the transition hazards, transition probabilities, and the state-specific duration for HIV-infected individuals. We examined gender, race/ethnicity, age, CD4 count, place of residence, and antiretroviral treatment regimen prescribed at the beginning of the study period. We found that patients with a higher CD4 count, increased age, heterosexual orientation, white, and single tablet regimen users were associated with reduced risk of transitioning to a Detectable VL from an Undetectable VL, whereas shorter time since diagnosis, being male, and injection drug use increased the risk of the same transition.     

Bayesian incidence analysis of animal tumorigenicity data

Statistical inference about tumorigenesis should focus on the tumour incidence rate. Unfortunately, in most animal carcinogenicity experiments, tumours are not observable in live animals and censoring of the tumour onset times is informative. In this paper, we propose a Bayesian method for analysing data from such studies. Our approach focuses on the incidence of tumours and accommodates occult tumours and censored onset times without restricting tumour lethality, relying on cause-of-death data, or requiring interim sacrifices. We represent the underlying state of nature by a multistate stochastic process and assume general probit models for the time-specific transition rates. These models allow the incorporation of covariates, historical control data and subjective prior information. The inherent flexibility of this approach facilitates the interpretation of results, particularly when the sample size is small or the data are sparse. We use a Gibbs sampler to estimate the relevant posterior distributions. The methods proposed are applied to data from a US National Toxicology Program carcinogenicity study.     

The meta-analytic framework for the evaluation of surrogate endpoints in clinical trials

For a number of reasons, surrogate endpoints are considered instead of the so-called true endpoint in clinical studies, especially when such endpoints can be measured earlier, and/or with less burden for patient and experimenter. Surrogate endpoints may occur more frequently than their standard counterparts. For these reasons, it is not surprising that the use of surrogate endpoints in clinical practice is increasing.     

Bayesian analysis of dynamic magnetic resonance breast images

Summary.  We describe an integrated methodology for analysing dynamic magnetic resonance images of the breast. The problems that motivate this methodology arise from a collaborative study with a tumour institute. The methods are developed within the Bayesian framework and comprise image restoration and classification steps. Two different approaches are proposed for the restoration. Bayesian inference is performed by means of Markov chain Monte Carlo algorithms. We make use of a Metropolis algorithm with a specially chosen proposal distribution that performs better than more commonly used proposals. The classification step is based on a few attribute images yielded by the restoration step that describe the essential features of the contrast agent variation over time. Procedures for hyperparameter estimation are provided, so making our method automatic. The results show the potential of the methodology to extract useful information from acquired dynamic magnetic resonance imaging data about tumour morphology and internal pathophysiological features.     

A simple estimator for a shared frailty regression model

Summary. We propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution. Inferences for the frailty parameter can be obtained by using output from Cox regression analyses. The computational burden is substantially less than that of the other approaches to estimation. The large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes. The methods are motivated by studies of familial associations in the natural history of diseases. Their practical utility is illustrated with sib pair data from Beaver Dam, Wisconsin.     

A functional marked point process model for lupus data

Modelling for marked point processes is an important problem, but has received remarkably little attention in the statistical literature. The authors developed a marked point process model that incorporates the use of functional data analysis in a joint estimation of the frequency function of the point process and the intensity of the mark, with application to data from 22 lupus patients consisting of times of flares in symptom severity combined with a quantitative assessment of the severity. The data indicate that a rapid decrease in drug dose is significantly associated with a decrease in flare frequency. Experiments with simulated data designed to model the actual data further support this conclusion. The Canadian Journal of Statistics 40: 517–529; 2012 © 2012 Statistical Society of Canada     

A comparison of tests for trend with historical controls in carcinogen bioassay

ABSTRACT Tests for trend in tumour response rates with increasing dose in long-term laboratory studies of carcinogenicity that take into account historical control information are discussed. The theoretical basis for these tests is described, and their small-sample properties evaluated using computer simulation. The performance of these tests is also evaluated using data from carcinogenicity experiments conducted under the U.S. National Toxicology Program. Based on these results, recommendations are made as to the most appropriate tests in practice. When the assumptions underlying these tests are satisfied, the use of historical control information is shown to result in an increase in power relative to the classical Cochran-Armitage test that is widely used without historical controls.     

Conditional and unconditional tests with historical controls

Score statistics utilizing historical control data have been proposed to test for increasing trend in tumour occurrence rates in laboratory carcinogenicity studies. Novel invariance arguments are used to confirm, under slightly weaker conditions, previously established asymptotic distributions (mixtures of normal distributions) of tests unconditional on the tumor response rate in the concurrent control group. Conditioning on the control response rate, an ancillary statistic, leads to a new conditional limit theorem in which the test statistic converges to an unknown random variable. Because of this, a subasymptotic approximation to the conditional limiting distribution is also considered. The adequacy of these large-sample approximations in finite samples is evaluated using computer simulation. Bootstrap methods for use in finite samples are also proposed. The application of the conditional and unconditional tests is illustrated using bioassay data taken from the literature. The results presented in this paper are used to formulate recommendations for the use of tests for trend with historical controls in practice.     

Reducing data dimension for cluster detection

Clustering high-dimensional data is often a challenging task both because of the computational burden required to run any technique, and because the difficulty in interpreting clusters generally increases with the data dimension. In this work, a method for finding low-dimensional representations of high-dimensional data is discussed, specifically conceived to preserve possible clusters in data. It is based on the critical bandwidth, a nonparametric statistic to test unimodality, related to kernel density estimation. Some useful properties of the aforementioned statistic are enlightened and an adjustment to use it as a basis for reducing dimensionality is suggested. The method is illustrated by simulated and real data examples.     

Flexible estimates of tumour incidence for intermediately lethal tumours in a typical long-term animal bioassay

The estimation of the incidence of tumours in an animal carcinogenicity study is complicated by the occult nature of the tumours involved (i.e. tumours are not observable before an animal's death). Also, the lethality of tumours is generally unknown, making the tumour incidence function non-identifiable without interim sacrifices, cause-of-death data or modelling assumptions. Although Kaplan–Meier curves for overall survival are typically displayed, obtaining analogous plots for tumour incidence generally requires fairly elaborate model fitting. We present a case-study of tetrafluoroethylene to illustrate a simple method for estimating the incidence of tumours as a function of more easily estimable components. One of the components, tumour prevalence, is modelled by using a generalized additive model, which leads to estimates that are more flexible than those derived under the usual parametric models. A multiplicative assumption for tumour lethality allows for the incorporation of concomitant information, such as the size of tumours. Our approach requires only terminal sacrifice data although additional sacrifice data are easily accommodated. Simulations are used to illustrate the estimator proposed and to evaluate its properties. The method also yields a simple summary measure of tumour lethality, which can be helpful in interpreting the results of a study.     

Attribution of tumour lethality and estimation of the time to onset of occult tumours in the absence of cause-of-death Information

A new statistical approach is developed for estimating the carcinogenic potential of drugs and other chemical substances used by humans. Improved statistical methods are developed for rodent tumorigenicity assays that have interval sacrifices but not cause-of-death data. For such experiments, this paper proposes a nonparametric maximum likelihood estimation method for estimating the distributions of the time to onset of and the time to death from the tumour. The log-likelihood function is optimized using a constrained direct search procedure. Using the maximum likelihood estimators, the number of fatal tumours in an experiment can be imputed. By applying the procedure proposed to a real data set, the effect of calorie restriction is investigated. In this study, we found that calorie restriction delays the tumour onset time significantly for pituitary tumours. The present method can result in substantial economic savings by relieving the need for a case-by-case assignment of the cause of death or context of observation by pathologists. The ultimate goal of the method proposed is to use the imputed number of fatal tumours to modify Peto's International Agency for Research on Cancer test for application to tumorigenicity assays that lack cause-of-death data.     

The assessment of tumour response to treatment

Summary.  A parsimonious model for treated tumours is developed as a continuation of our previous work on regrowth curve theory. The statistical model belongs to the family of marginal non-linear models since the only linear parameters of the model are tumour specific and random facilitating parameter estimation. An important feature of the model is that it enables the estimation of the fraction of cancer cells surviving the treatment in vivo having easy-to-obtain longitudinal measurements of tumour volume. We compare several methods of estimation, including Lindstrom–Bates, iterated reweighted least squares and maximum likelihood. The last two methods are computed via the total estimating equations approach and variance least squares. The theory is illustrated with a photodynamic tumour therapy example.     

Application of a stochastic model to response assessments in a study of squamous cell carcinoma of the head and neck

This paper discusses the application of a stochastic model in the analysis of response assessments made at various time points in a clinical trial of patients with squamous cell carcinoma of the head and neck. The transition rates and probabilities during treatment administration are derived using maximum likelihood methods. The results are then compared with the standard analyses used in solid tumour studies. Stochastic modelling is considered to complement the standard analyses, provide a holistic approach and better explain the underlying disease process. Copyright © 2012 John Wiley & Sons, Ltd.     

A parametric multistate model for the analysis of carcinogenicity experiments

A fully parametric multistate model is explored for the analysis of animal carcinogenicity experiments in which the time of tumour onset is not known. This model does not require assumptions about tumour lethality or cause of death judgements and can be fitted in the absence of sacrifice data. The model is constructed as a three-state model with simple parametric forms for the transition rates. Maximum likelihood methods are used to estimate the transition rates and different treatment groups are compared using likelihood ratio tests. Selection of an appropriate model and methods to assess the fit of the model are illustrated with data from animal experiments. Comparisons with standard methods are made.     

基于SNA生产观的生产负担不均等测度与分解

 基于SNA生产观，本文讨论了总生产负担、SNA生产负担和非SNA生产负担的不均等规律。理论分析表明，三类生产负担的具体分布取决于个人或家庭的生产时间分配模式，个人受实际SNA报酬率和总生产时间的影响较大，而家庭往往视性别因素为基本决策前提。本文据此实际测度了我国居民各类生产负担不均等现状并对形成总不均等的要素及子群来源进行了分解。研究表明：(1)与城乡区域因素相比，生产负担不均等更易受性别因素的影响，影响力度与生产负担的具体形式密切相关；(2)女性居民承担了更沉重的总生产负担，非SNA生产为其主要负担来源，男性居民的总生产负担较轻，其主要负担来源为SNA生产；(3)无论是居民总体还是各子群体，生产负担不均等主要归因于SNA生产负担，而子群内部不均等是造成总不均等的决定力量。     

Identification of Multivariate Responders/Non-Responders Using Bayesian Growth Curve Latent Class Models

In this paper, we propose a multivariate growth curve mixture model that groups subjects based on multiple symptoms measured repeatedly over time. Our model synthesizes features of two models. First, we follow Roy and Lin (2000) in relating the multiple symptoms at each time point to a single latent variable. Second, we use the growth mixture model of Muthén and Shedden (1999) to group subjects based on distinctive longitudinal profiles of this latent variable. The mean growth curve for the latent variable in each class defines that class's features. For example, a class of "responders" would have a decline in the latent symptom summary variable over time. A Bayesian approach to estimation is employed where the methods of Elliott et al (2005) are extended to simultaneously estimate the posterior distributions of the parameters from the latent variable and growth curve mixture portions of the model. We apply our model to data from a randomized clinical trial evaluating the efficacy of Bacillus Calmette-Guerin (BCG) in treating symptoms of Interstitial Cystitis. In contrast to conventional approaches using a single subjective Global Response Assessment, we use the multivariate symptom data to identify a class of subjects where treatment demonstrates effectiveness. Simulations are used to confirm identifiability results and evaluate the performance of our algorithm. The definitive version of this paper is available at onlinelibrary.wiley.com.