Current status data with two competing risks and missing failure types: a parametric approach.

Missing cause of failure is a common problem in competing risks data. Here we consider a general missing pattern in which one observes a set of possible causes containing the true cause. In this work, we focus on the parametric analysis of current status data with two competing risks and the above-mentioned missing pattern. We make some simpler assumptions on the conditional probability of observing a set of possible causes of failure given the true cause and carry out maximum-likelihood estimation of the model parameters. Asymptotic properties of the maximum-likelihood estimators are also discussed. Simulation studies are performed to study the finite sample properties of the estimators and also to investigate the role of the monitoring time distribution. Finally, the method is illustrated through the analysis of a real data set.

Optimal Timing for Cancer Screening and Adaptive Surveillance Using Mathematical Modeling.

Cancer screening and early detection efforts have been partially successful in reducing incidence and mortality, but many improvements are needed. Although current medical practice is informed by epidemiologic studies and experts, the decisions for guidelines are ultimately ad hoc. We propose here that quantitative optimization of protocols can potentially increase screening success and reduce overdiagnosis. Mathematical modeling of the stochastic process of cancer evolution can be used to derive and optimize the timing of clinical screens so that the probability is maximal that a patient is screened within a certain "window of opportunity" for intervention when early cancer development may be observable. Alternative to a strictly empirical approach or microsimulations of a multitude of possible scenarios, biologically based mechanistic modeling can be used for predicting when best to screen and begin adaptive surveillance. We introduce a methodology for optimizing screening, assessing potential risks, and quantifying associated costs to healthcare using multiscale models. As a case study in Barrett's esophagus, these methods were applied for a model of esophageal adenocarcinoma that was previously calibrated to U.S. cancer registry data. Optimal screening ages for patients with symptomatic gastroesophageal reflux disease were older (58 for men and 64 for women) than what is currently recommended (age > 50 years). These ages are in a cost-effective range to start screening and were independently validated by data used in current guidelines. Collectively, our framework captures critical aspects of cancer evolution within patients with Barrett's esophagus for a more personalized screening design. SIGNIFICANCE: This study demonstrates how mathematical modeling of cancer evolution can be used to optimize screening regimes, with the added potential to improve surveillance regimes. GRAPHICAL ABSTRACT: http://cancerres.aacrjournals.org/content/canres/81/4/1123/F1.large.jpg.

A validation sampling approach for consistent estimation of adverse drug reaction risk with misclassified right-censored survival data.

Patient electronic health records, viewed as continuous-time right-censored survival data, can be used to estimate adverse drug reaction risk. Temporal outcome misclassification may occur as a result of errors in follow-up. These errors can be due to a failure to observe the incidence time of the adverse event of interest (due to misdiagnosis or nonreporting, etc) or an actual misdiagnosis of a competing adverse event. As the misclassifying event is often unobservable in the original data, we apply an internal validation sampling approach to produce consistent estimation in the presence of such errors. We introduce a univariate survival model and a cause-specific hazards model in which misclassification may also manifest as a diagnosis of an alternate adverse health outcome other than that of interest. We develop a method of maximum likelihood estimation of the model parameters and establish consistency and asymptotic normality of the estimators using standard results. We also conduct simulation studies to numerically investigate the finite sample properties of these estimators and the impact of ignoring the misclassification error.

Sample size of the reference sample in a case-augmented study.

The case-augmented study, in which a case sample is augmented with a reference (random) sample from the source population with only covariates information known, is becoming popular in different areas of applied science such as pharmacovigilance, ecology, and econometrics. In general, the case sample is available from some source (for example, hospital database, case registry, etc.); however, the reference sample is required to be drawn from the corresponding source population. The required minimum size of the reference sample is an important issue in this regard. In this work, we address the minimum sample size calculation and discuss related issues. Copyright © 2017 John Wiley & Sons, Ltd.

Effect of reporting bias in the analysis of spontaneous reporting data.

It is well-known that a spontaneous reporting system suffers from significant under-reporting of adverse drug reactions from the source population. The existing methods do not adjust for such under-reporting for the calculation of measures of association between a drug and the adverse drug reaction under study. Often there is direct and/or indirect information on the reporting probabilities. This work incorporates the reporting probabilities into existing methodologies, specifically to Bayesian confidence propagation neural network and DuMouchel's empirical Bayesian methods, and shows how the two methods lead to biased results in the presence of under-reporting. Considering all the cases to be reported, the association measure for the source population can be estimated by using only exposure information through a reference sample from the source population.

Time-series analyses of air pollution and mortality in the United States: a subsampling approach.

BACKGROUND: Hierarchical Bayesian methods have been used in previous papers to estimate national mean effects of air pollutants on daily deaths in time-series analyses. OBJECTIVES: We obtained maximum likelihood estimates of the common national effects of the criteria pollutants on mortality based on time-series data from ≤ 108 metropolitan areas in the United States. METHODS: We used a subsampling bootstrap procedure to obtain the maximum likelihood estimates and confidence bounds for common national effects of the criteria pollutants, as measured by the percentage increase in daily mortality associated with a unit increase in daily 24-hr mean pollutant concentration on the previous day, while controlling for weather and temporal trends. We considered five pollutants [PM10, ozone (O3), carbon monoxide (CO), nitrogen dioxide (NO2), and sulfur dioxide (SO2)] in single- and multipollutant analyses. Flexible ambient concentration-response models for the pollutant effects were considered as well. We performed limited sensitivity analyses with different degrees of freedom for time trends. RESULTS: In single-pollutant models, we observed significant associations of daily deaths with all pollutants. The O3 coefficient was highly sensitive to the degree of smoothing of time trends. Among the gases, SO2 and NO2 were most strongly associated with mortality. The flexible ambient concentration-response curve for O3 showed evidence of nonlinearity and a threshold at about 30 ppb. CONCLUSIONS: Differences between the results of our analyses and those reported from using the Bayesian approach suggest that estimates of the quantitative impact of pollutants depend on the choice of statistical approach, although results are not directly comparable because they are based on different data. In addition, the estimate of the O3-mortality coefficient depends on the amount of smoothing of time trends.

Number and size distribution of colorectal adenomas under the multistage clonal expansion model of cancer.

Colorectal cancer (CRC) is believed to arise from mutant stem cells in colonic crypts that undergo a well-characterized progression involving benign adenoma, the precursor to invasive carcinoma. Although a number of (epi)genetic events have been identified as drivers of this process, little is known about the dynamics involved in the stage-wise progression from the first appearance of an adenoma to its ultimate conversion to malignant cancer. By the time adenomas become endoscopically detectable (i.e., are in the range of 1-2 mm in diameter), adenomas are already comprised of hundreds of thousands of cells and may have been in existence for several years if not decades. Thus, a large fraction of adenomas may actually remain undetected during endoscopic screening and, at least in principle, could give rise to cancer before they are detected. It is therefore of importance to establish what fraction of adenomas is detectable, both as a function of when the colon is screened for neoplasia and as a function of the achievable detection limit. To this end, we have derived mathematical expressions for the detectable adenoma number and size distributions based on a recently developed stochastic model of CRC. Our results and illustrations using these expressions suggest (1) that screening efficacy is critically dependent on the detection threshold and implicit knowledge of the relevant stem cell fraction in adenomas, (2) that a large fraction of non-extinct adenomas remains likely undetected assuming plausible detection thresholds and cell division rates, and (3), under a realistic description of adenoma initiation, growth and progression to CRC, the empirical prevalence of adenomas is likely inflated with lesions that are not on the pathway to cancer.

Analysis of spontaneous adverse drug reaction (ADR) reports using supplementary information.

Assessment of safety of newly marketed drugs is an important public health issue. Once the drug is in the market, clinicians and/or health professionals are responsible for recognizing and reporting suspected side effects known as adverse drug reaction (ADR). Such reports are collected in a so-called spontaneous reporting (SR) system. The primary purpose of spontaneous ADR reporting is to provide early warnings or suspicions, which have not been recognized prior to marketing of a drug because of limitations of clinical trials. We shall discuss the existing work to analyze the SR database and their drawbacks and also suggest methodologies to tackle these drawbacks by defining a source population and considering the problem of under-reporting, with the help of supplementary data. Unbiased estimate of population odds-ratio has been obtained and the corresponding asymptotic results are derived.

Parametric estimation of quality adjusted lifetime (QAL) distribution in progressive illness--death model.

In this work, we consider the parametric estimation of quality adjusted lifetime (QAL) distribution in progressive illness-death models. The main idea of this paper is to derive the theoretical distribution of QAL for the progressive illness-death models, under parametric models for the sojourn time distributions in different states, and then replace the model parameters by their estimates obtained by standard techniques of survival analysis. The method of estimation of the model parameters is also described. A data set of IBCSG Trial V has been analyzed for illustration. Extension to more general illness-death models is also discussed.

On the relationship between time-series studies, dynamic population studies, and estimating loss of life due to short-term exposure to environmental risks.

There is a growing concern that short-term exposure to combustion-related air pollution is associated with increased risk of death. This finding is based largely on time-series studies that estimate associations between daily variations in ambient air pollution concentrations and in the number of nonaccidental deaths within a community. Because these results are not based on cohort or dynamic population designs, where individuals are followed in time, it has been suggested that estimates of effect from these time-series studies cannot be used to determine the amount of life lost because of short-term exposures. We show that results from time-series studies are equivalent to estimates obtained from a dynamic population when each individual's survival experience can be summarized as the daily number of deaths. This occurs when the following conditions are satisfied: a) the environmental covariates vary in time and not between individuals; b) on any given day, the probability of death is small; c) on any given day and after adjusting for known risk factors for mortality such age, sex, smoking habits, and environmental exposures, each subject of the at-risk population has the same probability of death; d) environmental covariates have a common effect on mortality of all members of at-risk population; and e) the averages of individual risk factors, such as smoking habits, over the at-risk population vary smoothly with time. Under these conditions, the association between temporal variation in the environmental covariates and the survival experience of members of the dynamic population can be estimated by regressing the daily number of deaths on the daily value of the environmental covariates, as is done in time-series mortality studies. Issues in extrapolating risk estimates based on time-series studies in one population to estimate the amount of life lost in another population are also discussed.

Exploring heterogeneity in tumour data using Markov chain Monte Carlo.

We describe a Bayesian approach to incorporate between-individual heterogeneity associated with parameters of complicated biological models. We emphasize the use of the Markov chain Monte Carlo (MCMC) method in this context and demonstrate the implementation and use of MCMC by analysis of simulated overdispersed Poisson counts and by analysis of an experimental data set on preneoplastic liver lesions (their number and sizes) in the presence of heterogeneity. These examples show that MCMC-based estimates, derived from the posterior distribution with uniform priors, may agree well with maximum likelihood estimates (if available). However, with heterogeneous parameters, maximum likelihood estimates can be difficult to obtain, involving many integrations. In this case, the MCMC method offers substantial computational advantages.

Estimation of competing risks with general missing pattern in failure types.

In competing risks data, missing failure types (causes) is a very common phenomenon. In this work, we consider a general missing pattern in which, if a failure type is not observed, one observes a set of possible types containing the true type, along with the failure time. We first consider maximum likelihood estimation with missing-at-random assumption via the expectation maximization (EM) algorithm. We then propose a Nelson-Aalen type estimator for situations when certain information on the conditional probability of the true type given a set of possible failure types is available from the experimentalists. This is based on a least-squares type method using the relationships between hazards for different types and hazards for different combinations of missing types. We conduct a simulation study to investigate the performance of this method, which indicates that bias may be small, even for high proportion of missing data, for sufficiently large number of observations. The estimates are somewhat sensitive to misspecification of the conditional probabilities of the true types when the missing proportion is high. We also consider an example from an animal experiment to illustrate our methodology.

Choice of stratification in Poisson process analysis of recurrent event data with environmental covariates.

The Poisson process approach for studying the association between environmental covariates and recurrent events depends on the stratification of study period into intervals within which the baseline intensities are assumed constant. In this work we investigate the problem of bias and variance due to misspecification of this stratification. We suggest a cross-validation approach to choosing a stratification model to balance the trade-off between bias and variance. We also establish a connection between the Poisson process approach and case cross-over studies.