Modelling longitudinal semicontinuous emesis volume data with serial correlation in an acupuncture clinical trial

Summary.  In longitudinal studies, we are often interested in modelling repeated assessments of volume over time. Our motivating example is an acupuncture clinical trial in which we compare the effects of active acupuncture, sham acupuncture and standard medical care on chemotherapy-induced nausea in patients being treated for advanced stage breast cancer. An important end point for this study was the daily measurement of the volume of emesis over a 14-day follow-up period. The repeated volume data contained many 0s, had apparent serial correlation and had missing observations, making analysis challenging. The paper proposes a two-part latent process model for analysing the emesis volume data which addresses these challenges. We propose a Monte Carlo EM algorithm for parameter estimation and we use this methodology to show the beneficial effects of acupuncture on reducing the volume of emesis in women being treated for breast cancer with chemotherapy. Through simulations, we demonstrate the importance of correctly modelling the serial correlation for making conditional inference. Further, we show that the correct model for the correlation structure is less important for making correct inference on marginal means.     

Two-Sample Statistics for Testing the Equality of Survival Functions Against Improper Semi-parametric Accelerated Failure Time Alternatives: An Application to the Analysis of a Breast Cancer Clinical Trial

This paper presents two-sample statistics suited for testing equality of survival functions against improper semi-parametric accelerated failure time alternatives. These tests are designed for comparing either the short- or the long-term effect of a prognostic factor, or both. These statistics are obtained as partial likelihood score statistics from a time-dependent Cox model. As a consequence, the proposed tests can be very easily implemented using widely available software. A breast cancer clinical trial is presented as an example to demonstrate the utility of the proposed tests.     

Analysis of longitudinal data with non-ignorable non-monotone missing values

A full likelihood method is proposed to analyse continuous longitudinal data with non-ignorable (informative) missing values and non-monotone patterns. The problem arose in a breast cancer clinical trial where repeated assessments of quality of life were collected: patients rated their coping ability during and after treatment. We allow the missingness probabilities to depend on unobserved responses, and we use a multivariate normal model for the outcomes. A first-order Markov dependence structure for the responses is a natural choice and facilitates the construction of the likelihood; estimates are obtained via the Nelder–Mead simplex algorithm. Computations are difficult and become intractable with more than three or four assessments. Applying the method to the quality-of-life data results in easily interpretable estimates, confirms the suspicion that the data are non-ignorably missing and highlights the likely bias of standard methods. Although treatment comparisons are not affected here, the methods are useful for obtaining unbiased means and estimating trends over time.     

Latent class piecewise linear trajectory modelling for short-term cognition responses after chemotherapy for breast cancer patients

This paper investigates the impact of chemotherapy on cognitive function of breast cancer patients and whether this response is homogeneous for all patients. Latent class piecewise linear trajectory (growth) models were employed to describe changes and identify subgroups in three Auditory Verbal Learning Test measures (learning, immediate retention and delayed recall) in 130 breast cancer patients taken at three time periods: before chemotherapy and 1 and 6 months post-chemotherapy. Two distinct subgroups of women exhibiting different patterns of response were identified for learning and delayed recall and three for immediate retention. The groups differed in level (intercept) at 1 month post-chemotherapy and patterns of decline and recovery. Binomial and multinomial logistic regressions on the latent classes found that age, initial National Adult Reading Test (NART)-predicted IQ, stage of cancer and the initial Functional Assessment of Cancer Therapy-Breast subscale (or subsets thereof) to be significant predictors of classes.     

Bayesian assessment of times to diagnosis in breast cancer screening

Breast cancer is one of the diseases with the most profound impact on health in developed countries and mammography is the most popular method for detecting breast cancer at a very early stage. This paper focuses on the waiting period from a positive mammogram until a confirmatory diagnosis is carried out in hospital. Generalized linear mixed models are used to perform the statistical analysis, always within the Bayesian reasoning. Markov chain Monte Carlo algorithms are applied for estimation by simulating the posterior distribution of the parameters and hyperparameters of the model through the free software WinBUGS.     

Multilevel models for longitudinal data

Summary.  Repeated measures and repeated events data have a hierarchical structure which can be analysed by using multilevel models. A growth curve model is an example of a multilevel random-coefficients model, whereas a discrete time event history model for recurrent events can be fitted as a multilevel logistic regression model. The paper describes extensions to the basic growth curve model to handle auto-correlated residuals, multiple-indicator latent variables and correlated growth processes, and event history models for correlated event processes. The multilevel approach to the analysis of repeated measures data is contrasted with structural equation modelling. The methods are illustrated in analyses of children's growth, changes in social and political attitudes, and the interrelationship between partnership transitions and childbearing.     

Multilevel models for longitudinal variables prognostic for survival

The issue of modelling the joint distribution of survival time and of prognostic variables measured periodically has recently become of interest in the AIDS literature but is of relevance in other applications. The focus of this paper is on clinical trials where follow-up measurements of potentially prognostic variables are often collected but not routinely used. These measurements can be used to study the biological evolution of the disease of interest; in particular the effect of an active treatment can be examined by comparing the time profiles of patients in the active and placebo group. It is proposed to use multilevel regression analysis to model the individual repeated observations as function of time and, possibly, treatment. To address the problem of informative drop-out—which may arise if deaths (or any other censoring events) are related to the unobserved values of the prognostic variables—we analyse sequentially overlapping portions of the follow-up information. An example arising from a randomized clinical trial for the treatment of primary biliary cirrhosis is examined in detail.     

Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm

We propose a nonlinear mixed-effects framework to jointly model longitudinal and repeated time-to-event data. A parametric nonlinear mixed-effects model is used for the longitudinal observations and a parametric mixed-effects hazard model for repeated event times. We show the importance for parameter estimation of properly calculating the conditional density of the observations (given the individual parameters) in the presence of interval and/or right censoring. Parameters are estimated by maximizing the exact joint likelihood with the stochastic approximation expectation–maximization algorithm. This workflow for joint models is now implemented in the Monolix software, and illustrated here on five simulated and two real datasets.     

Weak convergence of bounded influence regression estimates with applications to repeated significance testing

We obtained weak convergence results for bounded influence regression M-estimates and apply the results to sequential clinical trials, with special reference to repeated significance tests in the two-sample problem with covariates.     

A review of cancer screening evaluation techniques, with some particular examples in breast cancer screening

Summary.  The instigation of mass screening for breast cancer has, over the last three decades, raised various statistical issues and led to the development of new statistical approaches. Initially, the design of screening trials was the main focus of research but, as the evidence in favour of population-based screening programmes mounts, a variety of other applications have also been identified. These include administrative and quality control tasks, for monitoring routine screening services, as well as epidemiological modelling of incidence and mortality. We review the commonly used methods of cancer screening evaluation, highlight some current issues in breast screening and, using examples from randomized trials and established screening programmes, illustrate the role that statistical science has played in the development of clinical research in this field.     

Bartlett's Test Applied to Variance Component Models

Exact methods for testing equality between variance components obtained from several cases of the same type of balanced orthogonal design are discussed. In particular, methods for successively testing equality of a number of components using Bartlett's tests are outlined for univariate and multivariate responses. Two clinical trial examples of repeated‐measures data are presented.     

A Baseline-free Procedure for Transformation Models Under Interval Censorship

An important property of Cox regression model is that the estimation of regression parameters using the partial likelihood procedure does not depend on its baseline survival function. We call such a procedure baseline-free. Using marginal likelihood, we show that an baseline-free procedure can be derived for a class of general transformation models under interval censoring framework. The baseline-free procedure results a simplified and stable computation algorithm for some complicated and important semiparametric models, such as frailty models and heteroscedastic hazard/rank regression models, where the estimation procedures so far available involve estimation of the infinite dimensional baseline function. A detailed computational algorithm using Markov Chain Monte Carlo stochastic approximation is presented. The proposed procedure is demonstrated through extensive simulation studies, showing the validity of asymptotic consistency and normality. We also illustrate the procedure with a real data set from a study of breast cancer. A heuristic argument showing that the score function is a mean zero martingale is provided.     

Analysis of repeated failures or durations, with application to shunt failures for patients with paediatric hydrocephalus

We consider studies involving the repeated occurrence of certain events, in which the emphasis is on the gaps or times between events. Interesting methodological issues arise in such situations, including the validity of semiparametric methods for multiplicative hazard-based models and the possibilities for marginal analysis of successive gap times. We discuss these and other points in conjunction with an examination of observational data on repeated shunt failures for a population of children with hydrocephalus.     

Screening for prostate cancer by using random-effects models

Summary. Random-effects models are used to screen male participants in a long-term longitudinal study for prostate cancer. By using posterior probabilities, each male can be classified into one of four diagnostic states for prostate disease: normal, benign prostatic hyperplasia, local cancer and metastatic cancer. Repeated measurements of prostate-specific antigen, collected when there was no clinical evidence of prostate disease, are used in the classification process. An individual's screening data are considered one repeated measurement at a time as his data are collected longitudinally over time. Posterior probabilities are calculated on the basis of data from other individuals with confirmed diagnoses of each of the four diagnostic states.     

Analysis of a longitudinal ordinal response clinical trial using dynamic models

Summary.  In many areas of pharmaceutical research, there has been increasing use of categorical data and more specifically ordinal responses. In many cases, complex models are required to account for different types of dependences among the responses. The clinical trial that is considered here involved patients who were required to remain in a particular state to enable the doctors to examine their heart. The aim of this trial was to study the relationship between the dose of the drug administered and the time that was spent by the patient in the state permitting examination. The patient's state was measured every second by a continuous Doppler signal which was categorized by the doctors into one of four ordered categories. Hence, the response consisted of repeated ordinal series. These series were of different lengths because the drug effect wore off faster (or slower) on certain patients depending on the drug dose administered and the infusion rate, and therefore the length of drug administration. A general method for generating new ordinal distributions is presented which is sufficiently flexible to handle unbalanced ordinal repeated measurements. It consists of obtaining a cumulative mixture distribution from a Laplace transform and introducing into it the integrated intensity of a binary logistic, continuation ratio or proportional odds model. Then, a multivariate distribution is constructed by a procedure that is similar to the updating process of the Kalman filter. Several types of history dependences are proposed.     

Semiparametric model for semi-competing risks data with application to breast cancer study

For many forms of cancer, patients will receive the initial regimen of treatments, then experience cancer progression and eventually die of the disease. Understanding the disease process in patients with cancer is essential in clinical, epidemiological and translational research. One challenge in analyzing such data is that death dependently censors cancer progression (e.g., recurrence), whereas progression does not censor death. We deal with the informative censoring by first selecting a suitable copula model through an exploratory diagnostic approach and then developing an inference procedure to simultaneously estimate the marginal survival function of cancer relapse and an association parameter in the copula model. We show that the proposed estimators possess consistency and weak convergence. We use simulation studies to evaluate the finite sample performance of the proposed method, and illustrate it through an application to data from a study of early stage breast cancer.     

Change point-cure models with application to estimating the change-point effect of age of diagnosis among prostate cancer patients

Previous research on prostate cancer survival trends in the United States National Cancer Institute's Surveillance Epidemiology and End Results database has indicated a potential change-point in the age of diagnosis of prostate cancer around age 50. Identifying a change-point value in prostate cancer survival and cure could have important policy and health care management implications. Statistical analysis of this data has to address two complicating features: (1) change-point models are not smooth functions and so present computational and theoretical difficulties; and (2) models for prostate cancer survival need to account for the fact that many men diagnosed with prostate cancer can be effectively cured of their disease with early treatment. We develop a cure survival model that allows for change-point effects in covariates to investigate a potential change-point in the age of diagnosis of prostate cancer. Our results do not indicate that age under 50 is associated with increased hazard of death from prostate cancer.     

Modeling potential time to event data with competing risks

Patients receiving radical prostatectomy are at risk of metastasis or prostate cancer related death, and often need repeated clinical evaluations to determine whether additional adjuvant or salvage therapies are needed. Since the prostate cancer is a slowly progressing disease, and these additional therapies come with significant side effects, it is important for clinical decision making purposes to estimate a patient’s risk of cancer metastasis, in the presence of a competing risk by death, under the hypothetical condition that the patient does not receive any additional therapy. In observational studies, patients may receive additional therapy by choice; the time to metastasis without any therapy is often a potential outcome and not always observed. We study the competing risks model of Fine and Gray (J Am Stat Assoc, 94:496–509, 1999) with adjustment for treatment choice by inverse probability censoring weighting (IPCW). The model can be fit using standard software for partial likelihood with double IPCW weights. The proposed methodology is used in a prostate cancer study to predict the post-prostatectomy cumulative incidence probability of cancer metastasis without additional adjuvant or salvage therapies.     

A Bayesian approach to Markov modelling in cost-effectiveness analyses: application to taxane use in advanced breast cancer

Summary. The paper demonstrates how cost-effectiveness decision analysis may be implemented from a Bayesian perspective, using Markov chain Monte Carlo simulation methods for both the synthesis of relevant evidence input into the model and the evaluation of the model itself. The desirable aspects of a Bayesian approach for this type of analysis include the incorporation of full parameter uncertainty, the ability to perform all the analysis, including each meta-analysis, in a single coherent model and the incorporation of expert opinion either directly or regarding the relative credibility of different data sources. The method is described, and its ease of implementation demonstrated, through a practical example to evaluate the cost-effectiveness of using taxanes for the second-line treatment of advanced breast cancer compared with conventional treatment. For completeness, the results from the Markov chain Monte Carlo simulation model are compared and contrasted with those from a classical Monte Carlo simulation model.