Biomedical subjects
Publications and source records attributed to J F Lawless.
We consider lifetime data involving pairs of study individuals with more than one possible cause of failure for each individual. Non-parametric estimation of cause-specific distribution functions is considered under independent censoring. Properties of the estimators are discussed and an illustration of their application is given.
Events that may occur repeatedly for individual subjects are of interest in many medical studies. We review methods of analysis for repeated events, emphasizing that the approach taken in a given study should allow clinical questions to be addressed as directly as possible. Methods based on full models for event processes as well as on simpler 'marginal' assumptions are considered. The treatment of dependent terminating events related to the recurrent events is also discussed. We apply various methods of analysis to studies involving pulmonary exacerbations in persons with cystic fibrosis, and the occurrence of bone metastases and skeletal events in cancer patients, respectively. Most of the methodology considered can be implemented with existing software.
We consider recurrent event data when the duration or gap times between successive event occurrences are of intrinsic interest. Subject heterogeneity not attributed to observed covariates is usually handled by random effects which result in an exchangeable correlation structure for the gap times of a subject. Recently, efforts have been put into relaxing this restriction to allow non-exchangeable correlation. Here we consider dynamic models where random effects can vary stochastically over the gap times. We extend the traditional Gaussian variance components models and evaluate a previously proposed proportional hazards model through a simulation study and some examples. Besides, semiparametric estimation of the proportional hazards models is considered. Both models are easily used. The Gaussian models are easily interpreted in terms of the variance structure. On the other hand, the proportional hazards models would be more appropriate in the context of survival analysis, particularly in the interpretation of the regression parameters. They can be sensitive to the choice of model for random effects but not to the choice of the baseline hazard function.
Many models have been proposed that relate failure times and stochastic time-varying covariates. In some of these models, failure occurs when a particular observable marker crosses a threshold level. We are interested in the more difficult, and often more realistic, situation where failure is not related deterministically to an observable marker. In this case, joint models for marker evolution and failure tend to lead to complicated calculations for characteristics such as the marginal distribution of failure time or the joint distribution of failure time and marker value at failure. This paper presents a model based on a bivariate Wiener process in which one component represents the marker and the second, which is latent (unobservable), determines the failure time. In particular, failure occurs when the latent component crosses a threshold level. The model yields reasonably simple expressions for the characteristics mentioned above and is easy to fit to commonly occurring data that involve the marker value at the censoring time for surviving cases and the marker value and failure time for failing cases. Parametric and predictive inference are discussed, as well as model checking. An extension of the model permits the construction of a composite marker from several candidate markers that may be available. The methodology is demonstrated by a simulated example and a case application.
Chronic medical conditions are often manifested by the incidence of recurrent adverse clinical events. In clinical trials designed to investigate therapeutic interventions for such conditions it is natural to make treatment comparisons on the basis of event occurrence. However, when there is a more serious, possibly related, event that terminates the occurrence of the recurrent events, the problem of dependent censoring arises. Here, we consider robust modelling strategies for expressing covariate effects on the recurrent event process that address the possible dependence between the recurrent and terminal events. The various methods differ in the way the dependence is addressed, and hence in the interpretation of covariate effects. The methods are applied to a data set from a kidney transplant study and simulated data chosen for illustrative purposes.
Robust nonparametric tests are considered for use in longitudinal studies in which the response of interest is a recurrent event. The tests are robust in the sense that they do not rely on distributional assumptions regarding the processes generating the events. The methods we describe are presented in the context of a clinical trial with attention initially directed at the two-sample problem in which a single experimental treatment is compared to a control. We investigate a family of generalized pseudo-score statistics (Lawless and Nadeau, 1995, Technometrics 37, 158-168) in which weight functions may be chosen to generate tests sensitive to various types of departure from the null hypothesis that the mean functions for the treatment and control groups are identical. All tests we consider are evaluated by simulation with respect to the type I error rate and power under a variety of practical scenarios. An application involving data from a kidney transplant study illustrates these procedures. For trials with multiple treatment arms, we generalize these approaches and indicate test statistics appropriate for unstructured alternatives and tests based on linear contrasts of the treatment-specific mean functions. Extensions of this methodology for stratified designs are also indicated.
A method of interim monitoring is described for longitudinal comparative studies in which the outcome of interest is a recurrent event and treatment comparisons are based on expected numbers of events. The nonparametric methods described by Cook, Lawless, and Nadeau (1996, Biometrics 52, 116-130) are generalized to provide a robust estimate of the covariance matrix for a sequence of test statistics calculated over time. The error spending function methodology of Lan and DeMets (1983, Biometrika 70, 659-663) is adopted to control the experimental type I error rate. A simulation study indicates satisfactory frequency properties of this procedure for the moderate to large scale trials for which it is intended. Extensions of this approach to handle stratified designs and studies with multitype recurrent events are indicated. Data from a kidney transplant study (Cole et al., 1994, Transplantation 57, 60-67) are used for illustrative purposes.
Multi-state Markov models can be useful in analysing disease history data. We apply the general estimation methods of Kalbfleisch and Lawless to panel data in which individuals are viewed over only a portion of their life history and complete information about transition times between states is unavailable. Methods to assess goodness-of-fit are proposed. To illustrate the methods, we consider models of HIV disease relating important immunological marker measurements to the onset of AIDS.
Toxicologists frequently conduct toxicity experiments in which different treatment conditions are applied to groups of animals and the resulting mortality in each group is measured at a number of discrete time points over the course of the experiment. Both survival analysis and generalized linear models have been proposed for analyzing this type of data. Whatever the approach taken, the model should allow for the presence of extra-multinomial variation arising from the use of groups of animals rather than individuals as the experimental units. We consider a number of models for overdispersion that can be incorporated into the generalized linear model framework for multinomial data. These models are extensions of ones proposed for binomial data by Williams (1982, Applied Statistics 31, 144-148) and Moore (1986, Biometrika 73, 583-588; 1987, Applied Statistics 36, 8-14). In addition, we examine robust asymptotic covariance matrix estimators for regression parameters, similar to those given in Liang and Zeger (1986, Biometrika 73, 13-22) and Zeger and Liang (1986, Biometrics 42, 121-130), and compare them to the model-based asymptotic estimators. Recommendations for analysis are given.
The number of cases of transfusion-associated acquired immune deficiency syndrome (TA-AIDS) that will be seen over the next few years is difficult to estimate, because of the uncertainty about the number of persons infected with the human immunodeficiency virus (HIV) via blood transfusion and about the duration of the incubation period from HIV infection via transfusion to diagnosis of AIDS. Presented here are a mathematical model and nonparametric and parametric statistical analyses of recent data on TA-AIDS that indicate clearly the existing estimability problems. The methods provide short-term projections of new TA-AIDS cases to be reported; the results suggest about 1100 new cases to be reported in the United States between July 1988 and June 1989 and about 1500 more between July 1989 and June 1990. Estimates of the number of eventual TA-AIDS cases to be seen are considerably more uncertain and require additional assumptions about the incubation distribution. Under the assumption that the probability of an infected person developing AIDS within 8 years of infection is 0.40 (an estimation derived from cohort studies in homosexual men and hemophiliacs), parametric and nonparametric analyses give, respectively, point estimates of 14,300 and 15,000 for the number of eventual cases of AIDS (in the age group 13-69) attributable to infection by blood transfusion prior to July 1985. The parametric analysis gives a corresponding 95 percent confidence interval.
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Regression and clustering methods have both been used to explore the effects of explanatory variables on survival times for patients with cancer or other chronic diseases. This paper discusses effective and computationally feasible approaches for this task in situations where there are fairly large and complex data sets; the techniques stressed are all-subsets regression and a kind of recursive partition clustering. We compare the two approaches in a rather general way, in part by examining some survival data for patients with ovarian carcinoma, and conclude that both have strong points to recommend them.
This paper describes a system written to carry out regression analyses under certain generalized linear models that are widely used in biomedical research. These include continuous response models such as the Weibull, log-logistic, log-normal and Cox proportional hazards models used in survival analysis, and also discrete Poisson, binomial and multinomial response regression models. The system fits models, generates residuals and other diagnostic output, and has an all-subsets regression feature. This paper describes the models implemented and gives statistical background; Part II describes the ISMOD system and presents examples of its application.
This paper describes a system written to carry out regression analyses under certain generalized linear models that are widely used in biomedical research. These include continuous response models such as the Weibull, log logistic, log normal and Cox proportional hazards models used in survival analysis, and also discrete Poisson, binomial and multinomial response regression models. The system fits models, generates residuals and other diagnostic output, and also has an all-subsets regression feature. This paper describes the ISMOD system and presents examples of its application; Part I describes the models implemented and gives statistical background.
In this paper, situations in which individuals move through a finite set of states according to a continuous-time Markov process are considered. Only aggregate data are available: these consist of the number of individuals in each state at specified observation times. We develop conditional least squares and approximate maximum-likelihood-estimation procedures for time-homogeneous models, and extend the methods so that they can handle immigration of individuals into the system during observation. Asymptotic covariance estimates are presented, and some problems for future study are noted.
Many studies in medicine involve conditions whereby subjects make transitions among a set of defined states over time. In such situations the durations of sojourns in specific states is frequently of interest. This article considers the modelling and analysis of sojourn times, beginning with semi-Markov models in which the durations of different sojourns are independent, and then considering extended models incorporating chronological time effects and random effects. Methodologic challenges for inference are discussed, and examples involving a relapse-remitting process and recurrent events are considered.
Data related to life histories of individuals can be obtained in many different ways, and the usefulness of multi-state models for statistical analysis is generally highly dependent on the type and nature of the data. In this paper, we focus on this, and present an approach to estimation for certain 'difficult' situations associated with retrospective or incomplete prospective observation. The paper begins with the identification of some problem areas in the analysis of data on life history processes. We discuss maximum likelihood estimation in some simple contexts and introduce a pseudo-likelihood which enables the simple analysis of some sampling procedures. This approach is illustrated on standard retrospective and case-cohort designs.