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

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.

Development and external validation of 1- and 2-year mortality prediction models in cystic fibrosis

INTRODUCTION

We aimed to develop a clinical tool for predicting 1- and 2-year risk of death for patients with cystic fibrosis (CF). The model considers patients' overall health status as well as risk of intermittent shock events in calculating the risk of death.

METHODS

Canadian CF Registry data from 1982 to 2015 were used to develop a predictive risk model using threshold regression. A 2-year risk of death estimated conditional probability of surviving the second year given survival for the first year. UK CF Registry data from 2007 to 2013 were used to externally validate the model.

RESULTS

The combined effect of CF chronic health status and CF intermittent shock risk provided a simple clinical scoring tool for assessing 1-year and 2-year risk of death for an individual CF patient. At a threshold risk of death of ≥20%, the 1-year model had a sensitivity of 74% and specificity of 96%. The area under the receiver operating curve (AUC) for the 2-year mortality model was significantly greater than the AUC for a model that predicted survival based on forced expiratory volume in 1 s <30% predicted (AUC 0.95 versus 0.68 respectively, p<0.001). The Canadian-derived model validated well with the UK data and correctly identified 79% of deaths and 95% of survivors in a single year in the UK.

CONCLUSIONS

The prediction models provide an accurate risk of death over a 1- and 2-year time horizon. The models performed equally well when validated in an independent UK CF population.

Using threshold regression to analyze survival data from complex surveys: With application to mortality linked NHANES III Phase II genetic data

The Cox proportional hazards (PH) model is a common statistical technique used for analyzing time-to-event data. The assumption of PH, however, is not always appropriate in real applications. In cases where the assumption is not tenable, threshold regression (TR) and other survival methods, which do not require the PH assumption, are available and widely used. These alternative methods generally assume that the study data constitute simple random samples. In particular, TR has not been studied in the setting of complex surveys that involve (1) differential selection probabilities of study subjects and (2) intracluster correlations induced by multistage cluster sampling. In this paper, we extend TR procedures to account for complex sampling designs. The pseudo-maximum likelihood estimation technique is applied to estimate the TR model parameters. Computationally efficient Taylor linearization variance estimators that consider both the intracluster correlation and the differential selection probabilities are developed. The proposed methods are evaluated by using simulation experiments with various complex designs and illustrated empirically by using mortality-linked Third National Health and Nutrition Examination Survey Phase II genetic data.

Development of a Conceptual Model of Disease Progression for Use in Economic Modeling of Chronic Obstructive Pulmonary Disease

BACKGROUND

To develop and validate a new conceptual model (CM) of chronic obstructive pulmonary disease (COPD) for use in disease progression and economic modeling. The CM identifies and describes qualitative associations between disease attributes, progression and outcomes.

METHODS

A literature review was performed to identify any published CMs or literature reporting the impact and association of COPD disease attributes with outcomes. After critical analysis of the literature, a Steering Group of experts from the disciplines of health economics, epidemiology and clinical medicine was convened to develop a draft CM, which was refined using a Delphi process. The refined CM was validated by testing for associations between attributes using data from the Evaluation of COPD Longitudinally to Identify Predictive Surrogate Endpoints (ECLIPSE).

RESULTS

Disease progression attributes included in the final CM were history and occurrence of exacerbations, lung function, exercise capacity, signs and symptoms (cough, sputum, dyspnea), cardiovascular disease comorbidities, 'other' comorbidities (including depression), body composition (body mass index), fibrinogen as a biomarker, smoking and demographic characteristics (age, gender). Mortality and health-related quality of life were determined to be the most relevant final outcome measures for this model, intended to be the foundation of an economic model of COPD.

CONCLUSION

The CM is being used as the foundation for developing a new COPD model of disease progression and to provide a framework for the analysis of patient-level data. The CM is available as a reference for the implementation of further disease progression and economic models.

Estimating time to event characteristics via longitudinal threshold regression models - an application to cervical dilation progression

In longitudinal studies, it is sometimes of interest to estimate the distribution of the time a longitudinal process takes to traverse from one threshold to another. For example, the distribution of the time it takes a woman's cervical dilation to progress from 3 to 4 cm can aid the decision-making of obstetricians as to whether a stalled labor should be allowed to proceed or stopped in favor of other options. Often researchers treat this type of data structure as interval censored and employ traditional survival analysis methods. However, the traditional interval censoring approaches are inefficient in that they do not use all of the available data. In this paper, we propose utilizing a longitudinal threshold model to estimate the distribution of the elapsed time between two thresholds of the longitudinal process from repeated measurements. We extend this modeling framework to be used with multiple thresholds. A Wiener process under the first hitting time framework is used to represent survival distribution. We demonstrate our model through simulation studies and an analysis of data from the Consortium on Safe Labor study. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

A threshold regression model to predict return to work after traumatic limb injury

OBJECTIVE

The study aims to examine the severity of initial impairment and recovery rate of return-to-work (RTW) predictors among workers with traumatic limb injury.

METHODS

This 2-year prospective cohort study recruited 1124 workers with traumatic limb injury during the first 2 weeks of hospital admission. Baseline data were obtained by questionnaire and chart review. Patient follow-up occurred at 1, 3, 6, 12, 18, and 24 months post injury. The primary outcome was the time of first RTW. The impact of potential predictors on initial impairment and rate of recovery towards RTW was estimated by threshold regression (TR).

RESULTS

A total of 846 (75.27%) participants returned to work during the follow-up period. Our model revealed that the initial impairment level in elderly workers and lower limb injuries were 33% and 35% greater than their counterparts, respectively. Workers with >12 years of education, part-time job, and moderate and higher self-efficacy were less impaired at initial injury compared with their counterparts. In terms of the rate of recovery leading to RTW, workers with older age, part-time jobs, lower limbs, or combined injuries had a significantly slower recovery rate, while workers with 9-12 years of education and >12 years of education had a significantly faster recovery rate.

CONCLUSIONS

Our study provides researchers and clinicians with evidence to understand the baseline impairment and rate of recovery towards RTW by explaining the predictors of RTW among workers with traumatic limb injuries.

Factors associated with change in exacerbation frequency in COPD

BACKGROUND

Patients with chronic obstructive pulmonary disease (COPD) can be categorized as having frequent (FE) or infrequent (IE) exacerbations depending on whether they respectively experience two or more, or one or zero exacerbations per year. Although most patients do not change category from year to year, some will, and the factors associated with this behaviour have not been examined.

METHODS

1832 patients completing two year follow-up in the Evaluation of COPD Longitudinally to Identify Predictive Surrogate End-points (ECLIPSE) study were examined at baseline and then yearly. Exacerbations were defined by health care utilisation. Patient characteristics compared between those patients who did or did not change exacerbation category from year 1 to year 2.

FINDINGS

Between years 1 and 2, 221 patients (17%) changed from IE to FE and 210 patients (39%) from FE to IE. More severe disease was associated with changing from IE to FE and less severe disease from FE to IE. Over the preceding year, small falls in FEV1 and 6-minute walking distance were associated with changing from IE to FE, and small falls in platelet count associated with changing from FE to IE.

CONCLUSION

No parameter clearly predicts an imminent change in exacerbation frequency category.

TRIAL REGISTRATION

SCO104960, clinicaltrials.gov identifier NCT00292552.

Improving clinical reality in chronic obstructive pulmonary disease economic modelling : development and validation of a micro-simulation approach

BACKGROUND

Chronic obstructive pulmonary disease (COPD) is a progressive and irreversible disease responsible for the deaths of 3 million people worldwide in 2005, and predicted to be the third leading cause of death worldwide by 2030. Many COPD models developed to date have followed a Markov structure, in which patients or populations can move between defined health states over successive time periods or cycles. In COPD, health states are typically based on disease severity defined solely by lung function, as described by the Global Initiative for Chronic Obstructive Lung Disease (GOLD) guidelines. These current modelling methods may restrict the ability to reflect the disease progression/clinical pathway or clinical practice.

OBJECTIVES

Given these limitations in previous COPD models, the authors aimed to develop a more flexible model that could improve on the description of the clinical disease pathway. The overall objective of this model was to inform the development of policies, guidelines or cost-effectiveness analyses. A second objective was to validate the model in relation to existing epidemiology studies of COPD.

METHODS

A patient simulation model was developed in Microsoft Excel™. The predictability of the model was tested by populating it with data from natural history of disease studies as well as with clinical trial data. Each patient moves through the model with demographic characteristics randomly generated from a set distribution. These characteristics determine the risk of clinical events occurring in the model.

RESULTS

The validation with these studies found the model to have generally good predictive ability, yielding in this way a good degree of external validity.

CONCLUSIONS

The micro-simulation model is a flexible approach for modelling COPD that allows consideration of complex COPD treatment pathways. The model was found to be generally robust in terms of predicting clinical outcomes of published studies when tested against other studies. It has significant potential as a tool for supporting future COPD treatment positioning decisions as well as to inform the development of policies, guidelines or cost-effectiveness analyses.

New clinical insights into chronic obstructive pulmonary disease and their implications for pharmacoeconomic analyses

Chronic obstructive pulmonary disease (COPD) is one of the leading causes of death and disability worldwide, but before the development of several new pharmacological treatments little could be done for COPD patients. Recognition that these new treatments could significantly improve the prognosis for COPD patients has radically changed clinical management guidelines from a palliative philosophy to an aggressive approach intended to reduce chronic symptoms, improve quality of life and prolong survival. These new treatments have also sparked interest in COPD cost-effectiveness research. Most COPD cost-effectiveness studies have been based on clinical trial populations, limited to direct medical costs, and used standard analysis methods such as Markov modelling, and they have usually found that newer therapies have favourable cost effectiveness. However, new insights into the clinical progression of COPD bring into question some of the assumptions underlying older analyses. In this review, we examine clinical factors unique to COPD and recent changes in clinical perspectives that have important implications for pharmacoeconomic analyses. The main parameters explored include (i) the high indirect medical costs for COPD and their relevance in assessing the societal benefits of new therapy; (ii) the importance of acute deteriorations in COPD, known as exacerbations, and approaches to modelling the cost benefit of exacerbation reduction; (iii) quality/utility instruments for COPD; (iv) the prevalence of co-morbid conditions and confounding between COPD and co-morbid disease utilization; (v) the limitations of Markov modelling; and (vi) the problem of outliers.

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.