Impact of Undiagnosed Chronic Obstructive Pulmonary Disease and Asthma on Symptoms, Quality of Life, Healthcare Use, and Work Productivity

Rationale: A significant proportion of individuals with chronic obstructive pulmonary disease (COPD) and asthma remain undiagnosed. Objectives: The objective of this study was to evaluate symptoms, quality of life, healthcare use, and work productivity in subjects with undiagnosed COPD or asthma compared with those previously diagnosed, as well as healthy control subjects. Methods: This multicenter population-based case-finding study randomly recruited adults with respiratory symptoms who had no previous history of diagnosed lung disease from 17 Canadian centers using random digit dialing. Participants who exceeded symptom thresholds on the Asthma Screening Questionnaire or the COPD Diagnostic Questionnaire underwent pre- and post-bronchodilator spirometry to determine if they met diagnostic criteria for COPD or asthma. Two control groups, a healthy group without respiratory symptoms and a symptomatic group with previously diagnosed COPD or asthma, were similarly recruited. Measurements and Main Results: A total of 26,905 symptomatic individuals were interviewed, and 4,272 subjects were eligible. Of these, 2,857 completed pre- and post-bronchodilator spirometry, and 595 (21%) met diagnostic criteria for COPD or asthma. Individuals with undiagnosed COPD or asthma reported greater impact of symptoms on health status and daily activities, worse disease-specific and general quality of life, greater healthcare use, and poorer work productivity than healthy control subjects. Individuals with undiagnosed asthma had symptoms, quality of life, and healthcare use burden similar to those of individuals with previously diagnosed asthma, whereas subjects with undiagnosed COPD were less disabled than those with previously diagnosed COPD. Conclusions: Undiagnosed COPD or asthma imposes important, unmeasured burdens on the healthcare system and is associated with poor health status and negative effects on work productivity.

Semiparametric predictive inference for failure data using first-hitting-time threshold regression

The progression of disease for an individual can be described mathematically as a stochastic process. The individual experiences a failure event when the disease path first reaches or crosses a critical disease level. This happening defines a failure event and a first hitting time or time-to-event, both of which are important in medical contexts. When the context involves explanatory variables then there is usually an interest in incorporating regression structures into the analysis and the methodology known as threshold regression comes into play. To date, most applications of threshold regression have been based on parametric families of stochastic processes. This paper presents a semiparametric form of threshold regression that requires the stochastic process to have only one key property, namely, stationary independent increments. As this property is frequently encountered in real applications, this model has potential for use in many fields. The mathematical underpinnings of this semiparametric approach for estimation and prediction are described. The basic data element required by the model is a pair of readings representing the observed change in time and the observed change in disease level, arising from either a failure event or survival of the individual to the end of the data record. An extension is presented for applications where the underlying disease process is unobservable but component covariate processes are available to construct a surrogate disease process. Threshold regression, used in combination with a data technique called Markov decomposition, allows the methods to handle longitudinal time-to-event data by uncoupling a longitudinal record into a sequence of single records. Computational aspects of the methods are straightforward. An array of simulation experiments that verify computational feasibility and statistical inference are reported in an online supplement. Case applications based on longitudinal observational data from The Osteoarthritis Initiative (OAI) study are presented to demonstrate the methodology and its practical use.

Patient and physician factors associated with symptomatic undiagnosed asthma or COPD

BACKGROUND

It remains unclear why some symptomatic individuals with asthma or COPD remain undiagnosed. Here, we compare patient and physician characteristics between symptomatic individuals with obstructive lung disease (OLD) who are undiagnosed and individuals with physician-diagnosed OLD.

METHODS

Using random-digit dialling and population-based case finding, we recruited 451 participants with symptomatic undiagnosed OLD and 205 symptomatic control participants with physician-diagnosed OLD. Data on symptoms, quality of life and healthcare utilisation were analysed. We surveyed family physicians of participants in both groups to elucidate differences in physician practices that could contribute to undiagnosed OLD.

RESULTS

Participants with undiagnosed OLD had lower mean pre-bronchodilator forced expiratory volume in 1 s percentage predicted compared with those who were diagnosed (75.2% versus 80.8%; OR 0.975, 95% CI 0.963-0.987). They reported greater psychosocial impacts due to symptoms and worse energy and fatigue than those with diagnosed OLD. Undiagnosed OLD was more common in participants whose family physicians were practising for >15 years and in those whose physicians reported that they were likely to prescribe respiratory medications without doing spirometry. Undiagnosed OLD was more common among participants who had never undergone spirometry (OR 10.83, 95% CI 6.18-18.98) or who were never referred to a specialist (OR 5.92, 95% CI 3.58-9.77). Undiagnosed OLD was less common among participants who had required emergency department care (OR 0.44, 95% CI 0.20-0.97).

CONCLUSIONS

Individuals with symptomatic undiagnosed OLD have worse pre-bronchodilator lung function and present with greater psychosocial impacts on quality of life compared with their diagnosed counterparts. They were less likely to have received appropriate investigations and specialist referral for their respiratory symptoms.

Accounting for delayed entry into observational studies and clinical trials: length-biased sampling and restricted mean survival time

Individuals in many observational studies and clinical trials for chronic diseases are enrolled well after onset or diagnosis of their disease. Times to events of interest after enrollment are therefore residual or left-truncated event times. Individuals entering the studies have disease that has advanced to varying extents. Moreover, enrollment usually entails probability sampling of the study population. Finally, event times over a short to moderate time horizon are often of interest in these investigations, rather than more speculative and remote happenings that lie beyond the study period. This research report looks at the issue of delayed entry into these kinds of studies and trials. Time to event for an individual is modelled as a first hitting time of an event threshold by a latent disease process, which is taken to be a Wiener process. It is emphasized that recruitment into these studies often involves length-biased sampling. The requisite mathematics for this kind of sampling and delayed entry are presented, including explicit formulas needed for estimation and inference. Restricted mean survival time (RMST) is taken as the clinically relevant outcome measure. Exact parametric formulas for this measure are derived and presented. The results are extended to settings that involve study covariates using threshold regression methods. Methods adapted for clinical trials are presented. An extensive case illustration for a clinical trial setting is then presented to demonstrate the methods, the interpretation of results, and the harvesting of useful insights. The closing discussion covers a number of important issues and concepts.

Derivation and Validation of the UCAP-Q Case-finding Questionnaire to Detect Undiagnosed Asthma and COPD

BACKGROUND

Many people with asthma and COPD remain undiagnosed. We developed and validated a new case-finding questionnaire to identify symptomatic adults with undiagnosed obstructive lung disease.

METHODS

Adults in the community with no prior history of physician-diagnosed lung disease who self-reported respiratory symptoms were contacted via random-digit dialing. Pre- and post-bronchodilator spirometry was used to confirm asthma or COPD. Predictive questions were selected using multinomial logistic regression with backward elimination. Questionnaire performance was assessed using sensitivity, predictive values, and area under the receiver operating curve (AUC). The questionnaire was assessed for test-retest reliability, acceptability, and readability. External validation was prospectively conducted in an independent sample and predictive performance re-evaluated.

RESULTS

A 13-item UCAP-Q case-finding questionnaire to predict undiagnosed asthma or COPD was developed. The most appropriate risk cut-off was determined to be 6% for either disease. Applied to the derivation sample (N=1615), the questionnaire yielded a sensitivity of 92% for asthma and 97% for COPD, specificity of 17%, with an AUC of 0.69 (95% CI: 0.64-0.74) for asthma and 0.82 (95% CI: 0.78-0.86) for COPD. Prospective validation using an independent sample (n=471) showed sensitivities of 93% and 92% for asthma and COPD, respectively, specificity of 19%, with AUC's of 0.70 (95% CI: 0.62-0.79) for asthma and 0.81 (95% CI: 0.74-0.87) for COPD. AUC's for UCAP-Q were higher compared to AUC's for currently recommended case-finding questionnaires for asthma or COPD.Conclusions:The UCAP-Q demonstrated high sensitivities and AUC's for identifying undiagnosed asthma or COPD. A web-based calculator allows for easy calculation of risk probabilities for each disease.

Population-based case-finding to identify subjects with undiagnosed asthma or COPD

BACKGROUND

∼5-10% of adults may have undiagnosed airflow obstruction. The objective of this study was to develop a population-based case-finding strategy to assess the prevalence of undiagnosed airflow obstruction (asthma or COPD) amongst adults with respiratory symptoms in Canada.

METHODS

Adults without a previous history of asthma, COPD or lung disease were recruited using random digit-dialling and asked if they had symptoms of dyspnoea, cough, sputum or wheeze within the past 6 months. Those who answered affirmatively completed the Asthma Screening Questionnaire (ASQ), COPD-Diagnostic Questionnaire (COPD-DQ) and COPD Assessment Test (CAT). Those with an ASQ score of ≥6 or a COPD-DQ score of ≥20 underwent pre- and post-bronchodilator spirometry to diagnose asthma or COPD.

RESULTS

12 117 individuals were contacted at home and assessed for study eligibility. Of the 1260 eligible individuals, 910 (72%) enrolled and underwent spirometry. Ultimately, 184 subjects (20% of those enrolled) had obstructive lung disease (73 asthma and 111 COPD). Individuals found to have undiagnosed asthma or COPD had more severe respiratory symptoms and impaired quality of life compared with those without airflow obstruction. The ASQ, COPD-DQ, and CAT had ROC areas for predicting undiagnosed asthma or COPD of 0.49, 0.64 and 0.56, respectively. Four descriptive variables (age, BMI, sex and pack-years smoked) produced better receiver operating characteristic (ROC) values than the questionnaires (ROC area=0.68).

CONCLUSION

20% of randomly selected individuals who report respiratory symptoms in Canada have undiagnosed airflow obstruction due to asthma or COPD. Questionnaires could exclude subjects at low risk but lack the ability to accurately find subjects with undiagnosed disease.

Influence of country-level differences on COPD prevalence

Purpose

Studies suggest that COPD prevalence may vary between countries. We conducted an ecological study of data from COPD prevalence articles to assess the influence of differences in country-level risk factors on COPD prevalence.

Patients and methods

Our study covered English language articles published during 2003–2014. Qualified articles used spirometry to assess COPD prevalence and used representative samples from national or subnational populations. Stepwise binomial regression was used to analyze associations between study- and country-level factors and COPD prevalence.

Results

Eighty articles provided 1,583 measures of COPD prevalence for subjects in different sex, age, and smoking categories for 112 districts in 41 countries. Adjusted prevalence rates for COPD were significantly lower for Australia/New Zealand and the Mediterranean and significantly higher for Latin America, compared to North America, Southeast Asia, and Northern Europe. Country-level socioeconomic development variables had an uneven and mixed association with COPD prevalence. High elevation above sea level was shown to be a protective factor for COPD. Study-level variables for the established risk factors of sex, age, and smoking explained 64% of variability in COPD prevalence. Country-level risk factors raised the explanatory power to 72%. Approximately 28% of worldwide variability in COPD prevalence remained unexplained.

Conclusion

Our study suggests that COPD prevalence varies across world regions, even after adjustment for established risk factors. Major country-level risk factors contributing to the worldwide epidemic of COPD remain to be investigated.

Stochastic processes directed by randomized time

The paper investigates stochastic processes directed by a randomized time process. A new family of directing processes called Hougaard processes is introduced. Monotonicity properties preserved under subordination, and dependence among processes directed by a common randomized time are studied. Results for processes subordinated to Poisson and stable processes are presented. Potential applications to shock models and threshold models are also discussed. Only Markov processes are considered.

Recurrent first hitting times in Wiener diffusion under several observation schemes

Recurrent events are commonly encountered in the natural sciences, engineering, and medicine. The theory of renewal and regenerative processes provides an elegant mathematical foundation for idealized recurrent event processes. In real-world applications, however, the contexts tend to be complicated by a variety of practical intricacies, including observation schemes with different phase and data structures. This paper formulates a recurrent event process as a succession of independent and identically distributed first hitting times for a Wiener sample path as it passes through successive equally-spaced levels. We develop exact mathematical results for statistical inferences based on several observation schemes that include observation initiated at a renewal point, observation of a stationary process over a finite window, and other variants. We also consider inferences drawn from different data structures, including gap times between renewal points (or fragments thereof) and counts of renewal events occurring within an observation window. We explore the precision of estimates using simulated scenarios and develop empirical regression functions for planning the sample size of a recurrent event study. We demonstrate our results using data from a clinical trial for chronic obstructive pulmonary disease in which the recurrent events are successive exacerbations of the condition. The case study demonstrates how covariates can be incorporated into the analysis using threshold regression.

Constructing normalcy and discrepancy indexes for birth weight and gestational age using a threshold regression mixture model

Birth weight and gestational age are important measures of a newborn's intrinsic health, serving both as outcome measures and explanatory variables in health studies. The measures are highly correlated but occasionally inconsistent. We anticipate that health researchers and other scientists would be helped by summary indexes of birth weight and gestational age that give more precise indications of whether the birth outcome is healthy or not. We propose a pair of indexes that we refer to as the birth normalcy index or BNI and birth discrepancy index or BDI. Both indexes are simple functions of birth weight and gestational age and in logarithmic form are orthogonal by construction. The BNI gauges whether the birth weight and gestational age combination are in a normal range. The BDI gauges whether birth weight and gestational age are consistent. We present a three-component mixture model for BNI, with the components representing premature, at-risk, and healthy births. The BNI distribution is derived from a stochastic model of fetal development proposed by Whitmore and Su (2007, Lifetime Data Analysis 13, 161-190) and takes the form of a mixture of inverse Gaussian distributions. We present a noncentral t-distribution as a model for BDI. BNI and BDI are also well suited for making comparisons of birth outcomes in different reference populations. A simple z-score and t-score are proposed for such comparisons. The BNI and BDI distributions can be estimated for births in any reference population of interest using threshold regression.

A threshold regression model for recurrent exacerbations in chronic obstructive pulmonary disease

OBJECTIVE

Respiratory exacerbations are a major source of morbidity in patients with chronic obstructive pulmonary disease (COPD). In this article, we model COPD health status as a formal stochastic process. A successful model will provide a suitable statistical structure for analysis of the effects of medical interventions on a patient's health status, and, possibly, offer new insights into the underlying disease process.

STUDY DESIGN AND SETTING

Our approach uses a regression methodology for time-to-event data called threshold regression (TR). We test the methodology on COPD data from a randomized clinical trial. Two TR models are studied: one based on a Poisson process and the other, a Wiener diffusion process.

RESULTS

Both models provide reasonably accurate fits to the clinical trial data. The insights offered by the fitted models are interpreted. Analysis of the clinical trial data set using these TR models revealed that patients who experienced multiple exacerbations showed a progressive acceleration in rate of exacerbations, and successive shortening of stable intervals between exacerbations.

CONCLUSION

TR techniques allow for realistic modeling of the COPD health state. A hybrid Poisson/Wiener diffusion TR model that incorporates the causal determinants of disease operating in each patient may be preferable.

Threshold regression for survival data with time-varying covariates

Time-to-event data with time-varying covariates pose an interesting challenge for statistical modeling and inference, especially where the data require a regression structure but are not consistent with the proportional hazard assumption. Threshold regression (TR) is a relatively new methodology based on the concept that degradation or deterioration of a subject's health follows a stochastic process and failure occurs when the process first reaches a failure state or threshold (a first-hitting-time). Survival data with time-varying covariates consist of sequential observations on the level of degradation and/or on covariates of the subject, prior to the occurrence of the failure event. Encounters with this type of data structure abound in practical settings for survival analysis and there is a pressing need for simple regression methods to handle the longitudinal aspect of the data. Using a Markov property to decompose a longitudinal record into a series of single records is one strategy for dealing with this type of data. This study looks at the theoretical conditions for which this Markov approach is valid. The approach is called threshold regression with Markov decomposition or Markov TR for short. A number of important special cases, such as data with unevenly spaced time points and competing risks as stopping modes, are discussed. We show that a proportional hazards regression model with time-varying covariates is consistent with the Markov TR model. The Markov TR procedure is illustrated by a case application to a study of lung cancer risk. The procedure is also shown to be consistent with the use of an alternative time scale. Finally, we present the connection of the procedure to the concept of a collapsible survival model.

Proportional hazards and threshold regression: their theoretical and practical connections

Proportional hazards (PH) regression is a standard methodology for analyzing survival and time-to-event data. The proportional hazards assumption of PH regression, however, is not always appropriate. In addition, PH regression focuses mainly on hazard ratios and thus does not offer many insights into underlying determinants of survival. These limitations have led statistical researchers to explore alternative methodologies. Threshold regression (TR) is one of these alternative methodologies (see Lee and Whitmore, Stat Sci 21:501-513, 2006, for a review). The connection between PH regression and TR has been examined in previous published work but the investigations have been limited in scope. In this article, we study the connections between these two regression methodologies in greater depth and show that PH regression is, for most purposes, a special case of TR. We show two methods of construction by which TR models can yield PH functions for survival times, one based on altering the TR time scale and the other based on varying the TR boundary. We discuss how to estimate the TR time scale and boundary, with or without the PH assumption. A case demonstration is used to highlight the greater understanding of scientific foundations that TR can offer in comparison to PH regression. Finally, we discuss the potential benefits of positioning PH regression within the first-hitting-time context of TR regression.

Bayesian random-effects threshold regression with application to survival data with nonproportional hazards

In epidemiological and clinical studies, time-to-event data often violate the assumptions of Cox regression due to the presence of time-dependent covariate effects and unmeasured risk factors. An alternative approach, which does not require proportional hazards, is to use a first hitting time model which treats a subject's health status as a latent stochastic process that fails when it reaches a threshold value. Although more flexible than Cox regression, existing methods do not account for unmeasured covariates in both the initial state and the rate of the process. To address this issue, we propose a Bayesian methodology that models an individual's health status as a Wiener process with subject-specific initial state and drift. Posterior inference proceeds via a Markov chain Monte Carlo methodology with data augmentation steps to sample the final health status of censored observations. We apply our method to data from melanoma patients with nonproportional hazards and find interesting differences from a similar model without random effects. In a simulation study, we show that failure to account for unmeasured covariates can lead to inaccurate estimates of survival probabilities.

Modeling low birth weights using threshold regression: results for U.S. birth data

Babies born live under 2,500 g or with a gestational age under 37 weeks are often inadequately developed and have elevated risks of infant mortality, congenital malformations, mental retardation, and other physical and neurological impairments. In this paper, we model birth weight as a first hitting time (FHT) of a birthing boundary in a Wiener process representing fetal development. We associate the parameters of the process and boundary with covariates describing maternal characteristics and the birthing environment using a relatively new regression methodology called threshold regression. Two FHT models for birth weight are developed. One is a mixture model and the other a competing risks model. These models are tested in a case demonstration using a 4%-systematic sample of the more than four million live births in the United States in 2002. An extensive data set for these births was provided by the National Center for Health Statistics. The focus of this paper is on the conceptual framework, models and methodology. A full empirical study is deferred to a later occasion.

Nonparametric methods for microarray data based on exchangeability and borrowed power

This article proposes nonparametric inference procedures for analyzing microarray gene expression data that are reliable, robust, and simple to implement. They are conceptually transparent and require no special-purpose software. The analysis begins by normalizing gene expression data in a unique way. The resulting adjusted observations consist of gene-treatment interaction terms (representing differential expression) and error terms. The error terms are considered to be exchangeable, which is the only substantial assumption. Thus, under a family null hypothesis of no differential expression, the adjusted observations are exchangeable and all permutations of the observations are equally probable. The investigator may use the adjusted observations directly in a distribution-free test method or use their ranks in a rank-based method, where the ranking is taken over the whole data set. For the latter, the essential steps are as follows: (1) Calculate a Wilcoxon rank-sum difference or a corresponding Kruskal-Wallis rank statistic for each gene. (2) Randomly permute the observations and repeat the previous step. (3) Independently repeat the random permutation a suitable number of times. Under the exchangeability assumption, the permutation statistics are independent random draws from a null cumulative distribution function (c.d.f) approximated by the empirical c.d.f Reference to the empirical c.d.f tells if the test statistic for a gene is outlying and, hence, shows differential expression. This feature is judged by using an appropriate rejection region or computing a p-value for each test statistic, taking into account multiple testing. The distribution-free analog of the rank-based approach is also available and has parallel steps which are described in the article. The proposed nonparametric analysis tends to give good results with no additional refinement, although a few refinements are presented that may interest some investigators. The implementation is illustrated with a case application involving differential gene expression in wild-type and knockout mice of an E. coli lipopolysaccharide (LPS) endotoxin treatment, relative to a baseline untreated condition.

Assessing lung cancer risk in railroad workers using a first hitting time regression model

This article examines the application of a first hitting time (FHT) model, using an operational time scale, to assess mortality risk differentials of the work environment. A major case application is presented that applies the model to three job categories of railroad workers. The data set involves a study of more than 50 000 workers with mortality assessed from 1959 to 1996. Lung cancer mortality was assessed because of a suspected link to diesel exhaust exposure. Based on a model that stipulates that death occurs when the disease state of a subject first hits a threshold value, the FHT model provides insights into factors influencing disease progression. In this application, in particular, the findings suggest that a job category in 1959 alters the risk of death from lung cancer.

Power and sample size for DNA microarray studies

A microarray study aims at having a high probability of declaring genes to be differentially expressed if they are truly expressed, while keeping the probability of making false declarations of expression acceptably low. Thus, in formal terms, well-designed microarray studies will have high power while controlling type I error risk. Achieving this objective is the purpose of this paper. Here, we discuss conceptual issues and present computational methods for statistical power and sample size in microarray studies, taking account of the multiple testing that is generic to these studies. The discussion encompasses choices of experimental design and replication for a study. Practical examples are used to demonstrate the methods. The examples show forcefully that replication of a microarray experiment can yield large increases in statistical power. The paper refers to cDNA arrays in the discussion and illustrations but the proposed methodology is equally applicable to expression data from oligonucleotide arrays.

A statistical model for investigating binding probabilities of DNA nucleotide sequences using microarrays

There is considerable scientific interest in knowing the probability that a site-specific transcription factor will bind to a given DNA sequence. Microarray methods provide an effective means for assessing the binding affinities of a large number of DNA sequences as demonstrated by Bulyk et al. (2001, Proceedings of the National Academy of Sciences, USA 98, 7158-7163) in their study of the DNA-binding specificities of Zif268 zinc fingers using microarray technology. In a follow-up investigation, Bulyk, Johnson, and Church (2002, Nucleic Acid Research 30, 1255-1261) studied the interdependence of nucleotides on the binding affinities of transcription proteins. Our article is motivated by this pair of studies. We present a general statistical methodology for analyzing microarray intensity measurements reflecting DNA-protein interactions. The log probability of a protein binding to a DNA sequence on an array is modeled using a linear ANOVA model. This model is convenient because it employs familiar statistical concepts and procedures and also because it is effective for investigating the probability structure of the binding mechanism.

Models for microarray gene expression data

This paper describes a general methodology for the analysis of differential gene expression based on microarray data. First, we characterize the data by a linear statistical model that accounts for relevant sources of variation in the data and then we consider estimation of the model parameters. Because microarray studies typically involve thousands of genes, we propose a two-stage method for parameter estimation. The interaction terms for genes and experimental conditions in this model capture all relevant information about differential gene expression in the microarray data. We propose a mixture distribution model for a summary statistic of differential expression that consists of null and alternative component distributions. The mixture model suggests two methods for identifying genes exhibiting differential expression. One is a frequentist method that identifies distinguished genes and the other an empirical Bayes procedure that yields estimated posterior probabilities of differential expression, conditional on observed microarray readings.

Importance of replication in microarray gene expression studies: statistical methods and evidence from repetitive cDNA hybridizations

We present statistical methods for analyzing replicated cDNA microarray expression data and report the results of a controlled experiment. The study was conducted to investigate inherent variability in gene expression data and the extent to which replication in an experiment produces more consistent and reliable findings. We introduce a statistical model to describe the probability that mRNA is contained in the target sample tissue, converted to probe, and ultimately detected on the slide. We also introduce a method to analyze the combined data from all replicates. Of the 288 genes considered in this controlled experiment, 32 would be expected to produce strong hybridization signals because of the known presence of repetitive sequences within them. Results based on individual replicates, however, show that there are 55, 36, and 58 highly expressed genes in replicates 1, 2, and 3, respectively. On the other hand, an analysis by using the combined data from all 3 replicates reveals that only 2 of the 288 genes are incorrectly classified as expressed. Our experiment shows that any single microarray output is subject to substantial variability. By pooling data from replicates, we can provide a more reliable analysis of gene expression data. Therefore, we conclude that designing experiments with replications will greatly reduce misclassification rates. We recommend that at least three replicates be used in designing experiments by using cDNA microarrays, particularly when gene expression data from single specimens are being analyzed.

Statistical inference for serial dilution assay data

Serial dilution assays are widely employed for estimating substance concentrations and minimum inhibitory concentrations. The Poisson-Bernoulli model for such assays is appropriate for count data but not for continuous measurements that are encountered in applications involving substance concentrations. This paper presents practical inference methods based on a log-normal model and illustrates these methods using a case application involving bacterial toxins.

Failure inference from a marker process based on a bivariate Wiener model

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.

Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes

Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.

Modelling accelerated degradation data using Wiener diffusion with a time scale transformation

Engineering degradation tests allow industry to assess the potential life span of long-life products that do not fail readily under accelerated conditions in life tests. A general statistical model is presented here for performance degradation of an item of equipment. The degradation process in the model is taken to be a Wiener diffusion process with a time scale transformation. The model incorporates Arrhenius extrapolation for high stress testing. The lifetime of an item is defined as the time until performance deteriorates to a specified failure threshold. The model can be used to predict the lifetime of an item or the extent of degradation of an item at a specified future time. Inference methods for the model parameters, based on accelerated degradation test data, are presented. The model and inference methods are illustrated with a case application involving self-regulating heating cables. The paper also discusses a number of practical issues encountered in applications.

Estimating degradation by a Wiener diffusion process subject to measurement error

Most materials and components degrade physically before they fail. Engineering degradation tests are designed to measure these degradation processes. Measurements in the tests reflect the inherent randomness of degradation itself as well as measurement errors created by imperfect instruments, procedures and environments. This paper describes a statistical model for measured degradation data that takes both sources of variation into account. The degradation process in the model is taken to be a Wiener diffusion process. The measurement errors are assumed to be independent normal random outcomes that are independent of the degradation process. The paper describes inference procedures for the model and discusses some practical issues that must be considered in dealing with the statistical problem. A case study is presented.

The mortality component of health status indexes

The mortality component of contemporary health indexes is discussed. Since these indexes reduce to mortality indexes when only life and death states enter the analysis, they share the conceptual weaknesses of mortality indexes. Also, they do not incorporate consumption variables explicity and therefore provide no structure for relating health status and living standard. Some attention is devoted to methodological problems of assessing survival probabilities, either from survey or experimental data or from beliefs of experts or individuals who are affected directly. The final section deals with individual preferences for survival lotteries. Conceptual weaknesses of common indexes are discussed, several canonical models for survival preferences are presented, the interdependence of individual utilities is discussed, and methods for eliciting individual survival preferences are considered, along with some illustrative empirical results.

The inverse Gaussian distribution as a model of hospital stay

Properties of the inverse gaussian distribution are presented with comments on fitting the distribution to lentgh-of-stay data. A conceptual framework for the hospitalization process is described; it suggests that the inverse gaussian distribution has considerable potential as both a descriptive and prescriptive model of length of stay, especially in the setting of psychiatric hospitals.