Continuous-time multistate models are widely used for categorical response data, particularly in the modeling of chronic diseases. However, inference is difficult when the process is only observed at discrete time points, with no information about the times or types of events between observation times, unless a Markov assumption is made. This assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state. Such a formulation results in a semi-Markov model. We show that the computational problems associated with fitting semi-Markov models to panel-observed data can be alleviated by considering a class of semi-Markov models with phase-type sojourn distributions. This allows methods for hidden Markov models to be applied. In addition, extensions to models where observed states are subject to classification error are given. The methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post-lung-transplantation patients.

Background Pancreatic cancer diagnosis and staging can be difficult in 10–20% of patients. Positron emission tomography (PET)/computed tomography (CT) adds precise anatomical localisation to functional data. The use of PET/CT may add further value to the diagnosis and staging of pancreatic cancer. Objective To determine the incremental diagnostic accuracy and impact of PET/CT in addition to standard diagnostic work-up in patients with suspected pancreatic cancer. Design A multicentre prospective diagnostic accuracy and clinical value study of PET/CT in suspected pancreatic malignancy. Participants Patients with suspected pancreatic malignancy. Interventions All patients to undergo PET/CT following standard diagnostic work-up. Main outcome measures The primary outcome was the incremental diagnostic value of PET/CT in addition to standard diagnostic work-up with multidetector computed tomography (MDCT). Secondary outcomes were (1) changes in patients’ diagnosis, staging and management as a result of PET/CT; (2) changes in the costs and effectiveness of patient management as a result of PET/CT; (3) the incremental diagnostic value of PET/CT in chronic pancreatitis; (4) the identification of groups of patients who would benefit most from PET/CT; and (5) the incremental diagnostic value of PET/CT in other pancreatic tumours. Results Between 2011 and 2013, 589 patients with suspected pancreatic cancer underwent MDCT and PET/CT, with 550 patients having complete data and in-range PET/CT. Sensitivity and specificity for the diagnosis of pancreatic cancer were 88.5% and 70.6%, respectively, for MDCT and 92.7% and 75.8%, respectively, for PET/CT. The maximum standardised uptake value (SUVmax.) for a pancreatic cancer diagnosis was 7.5. PET/CT demonstrated a significant improvement in relative sensitivity (p = 0.01) and specificity (p = 0.023) compared with MDCT. Incremental likelihood ratios demonstrated that PET/CT significantly improved diagnostic accuracy in all scenarios (p < 0.0002). PET/CT correctly changed the staging of pancreatic cancer in 56 patients (p = 0.001). PET/CT influenced management in 250 (45%) patients. PET/CT stopped resection in 58 (20%) patients who were due to have surgery. The benefit of PET/CT was limited in patients with chronic pancreatitis or other pancreatic tumours. PET/CT was associated with a gain in quality-adjusted life-years of 0.0157 (95% confidence interval –0.0101 to 0.0430). In the base-case model PET/CT was seen to dominate MDCT alone and is thus highly likely to be cost-effective for the UK NHS. PET/CT was seen to be most cost-effective for the subgroup of patients with suspected pancreatic cancer who were thought to be resectable. Conclusion PET/CT provided a significant incremental diagnostic benefit in the diagnosis of pancreatic cancer and significantly influenced the staging and management of patients. PET/CT had limited utility in chronic pancreatitis and other pancreatic tumours. PET/CT is likely to be cost-effective at current reimbursement rates for PET/CT to the UK NHS. This was not a randomised controlled trial and therefore we do not have any information from patients who would have undergone MDCT only for comparison. In addition, there were issues in estimating costs for PET/CT. Future work should evaluate the role of PET/CT in intraductal papillary mucinous neoplasm and prognosis and response to therapy in patients with pancreatic cancer. Study registration Current Controlled Trials ISRCTN73852054 and UKCRN 8166. Funding The National Institute for Health Research Health Technology Assessment programme.

Non-parametric estimation of the transition probabilities in multi-state models is considered for non-Markov processes. Firstly, a generalization of the estimator of Pepe et al., (1991) (Statistics in Medicine) is given for a class of progressive multi-state models based on the difference between Kaplan-Meier estimators. Secondly, a general estimator for progressive or non-progressive models is proposed based upon constructed univariate survival or competing risks processes which retain the Markov property. The properties of the estimators and their associated standard errors are investigated through simulation. The estimators are demonstrated on datasets relating to survival and recurrence in patients with colon cancer and prothrombin levels in liver cirrhosis patients.

No abstract

The lung transplantation candidate population is heterogeneous and survival benefit has not been established for all patient groups. UK data from a cohort of 1997 adult (aged ≥ 16), first lung transplant candidates (listed July 1995 to July 2006, follow-up to December 2007) were analyzed by diagnosis, to assess mortality relative to continued listing. Donor lungs were primarily allocated according to local criteria. Diagnosis groups studied were cystic fibrosis (430), bronchiectasis (123), pulmonary hypertension (74), diffuse parenchymal lung disease (564), chronic obstructive pulmonary disease (COPD, 647) and other (159). The proportion of patients in each group who died while listed varied significantly (respectively 37%, 48%, 41%, 49%, 19%, 38%). All groups had an increased risk of death at transplant, which fell below waiting list risk of death within 4.3 months. Thereafter, the hazard ratio for death relative to listing ranged from 0.34 for cystic fibrosis to 0.64 for COPD (p < 0.05 all groups except pulmonary hypertension). Mortality reduction was greater after bilateral lung transplantation in pulmonary fibrosis patients (p = 0.049), but not in COPD patients. Transplantation appeared to improve survival for all groups. Differential waiting list and posttransplant mortality by diagnosis suggest further use and development of algorithms to inform lung allocation.

Multi-state models are a popular method of describing medical processes that can be represented as discrete states or stages. They have particular use when the data are panel-observed, meaning they consist of discrete snapshots of disease status at irregular time points which may be unique to each patient. However, due to the difficulty of inference in more complicated cases, strong assumptions such as the Markov property, patient homogeneity and time homogeneity are applied. It is important that the validity of these assumptions is tested. A review of methods for diagnosing model fit for panel-observed continuous-time Markov and misclassification-type hidden Markov models is given, with illustrative application to a dataset on cardiac allograft vasculopathy progression in post-heart transplant patients.

No abstract

Methods for fitting nonhomogeneous Markov models to panel-observed data using direct numerical solution to the Kolmogorov Forward equations are developed. Nonhomogeneous Markov models occur most commonly when baseline transition intensities depend on calendar time, but may also occur with deterministic time-dependent covariates such as age. We propose transition intensities based on B-splines as a smooth alternative to piecewise constant intensities and also as a generalization of time transformation models. An expansion of the system of differential equations allows first derivatives of the likelihood to be obtained, which can be used in a Fisher scoring algorithm for maximum likelihood estimation. The method is evaluated through a small simulation study and demonstrated on data relating to the development of cardiac allograft vasculopathy in posttransplantation patients.