General tests of the Markov property in multi-state models.

Multi-state models for event history analysis most commonly assume the process is Markov. This article considers tests of the Markov assumption that are applicable to general multi-state models. Two approaches using existing methodology are considered; a simple method based on including time of entry into each state as a covariate in Cox models for the transition intensities and a method involving detecting a shared frailty through a stratified Commenges-Andersen test. In addition, using the principle that under a Markov process the future rate of transitions of the process at times $t > s$ should not be influenced by the state occupied at time $s$, a new class of general tests is developed by considering summaries from families of log-rank statistics where patients are grouped by the state occupied at varying initial time $s$. An extended form of the test applicable to models that are Markov conditional on observed covariates is also derived. The null distribution of the proposed test statistics are approximated by using wild bootstrap sampling. The approaches are compared in simulation and applied to a dataset on sleeping behavior. The most powerful test depends on the particular departure from a Markov process, although the Cox-based method maintained good power in a wide range of scenarios. The proposed class of log-rank statistic based tests are most useful in situations where the non-Markov behavior does not persist, or is not uniform in nature across patient time.

Salivary cortisol, cortisone and serum cortisol concentrations are related to age and body mass index in healthy children and young people.

BACKGROUND: Saliva is an ideal medium in which to measure cortisol in children. However, there are very few data reporting salivary cortisol or cortisone concentrations in healthy children since the introduction of liquid chromatography-mass spectrometry (LC-MS/MS) to routine laboratory practice. DESIGN: Early morning serum cortisol, salivary cortisol and cortisone were measured on fasting samples, and salivary hormones were measured in samples collected every 2 hours during waking hours, and 30 minutes after waking the following morning. PARTICIPANTS: 43 healthy paediatric volunteers (19 female), median age 11.5 years, range 6.2-18.7, participated. RESULTS: Early morning serum cortisol (265 nmol/L, 156-516) correlated strongly with salivary cortisol (4.7 nmol/L, 1.1-14.6) and cortisone (28.8 nmol/L, 11.7-56.6), P < .0001 for both. Serum cortisol, salivary cortisol and salivary cortisone correlated directly with age (P < .0001, P = .002 and P = .015, respectively), and salivary cortisone/cortisol ratio correlated indirectly with age (P = .007). Between 08.00 and 21.00, area under the curve for salivary cortisol (mean ± 1 SD) was 41.8 ± 19.1 and for cortisone 213.0 ± 61.2. Salivary cortisol was undetectable in 25/130 (19%) of samples collected after 13.00, while cortisone was always detectable. DISCUSSION: Salivary cortisol and cortisone concentrations are strongly related to serum cortisol concentrations; however, cortisone may be a preferable measure as cortisol is often undetectable. Age may be an important factor in the interpretation of early morning cortisol measurements made in serum and saliva.

Instrumental variable estimation in semi-parametric additive hazards models.

Instrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available. Two-stage least-squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data. The semi-parametric additive hazard model which can include time-independent and time-dependent covariate effects is particularly suited for the two-stage residual inclusion method, since it allows direct estimation of time-independent covariate effects without restricting the effect of the residual on the hazard. In this article, we prove asymptotic normality of two-stage residual inclusion estimators of regression coefficients in a semi-parametric additive hazard model with time-independent and time-dependent covariate effects. We consider the cases of continuous and binary exposure. Estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands. The new methods are compared to existing ones in a simulation study and are applied to a real data set. The proposed methods perform favorably especially in cases with exposure-dependent censoring.

Quantifying the association between progression-free survival and overall survival in oncology trials using Kendall's τ.

This paper considers methods for estimating the association between progression-free and overall survival in oncology trials. Copula-based, nonparametric, and illness-death model-based methods are reviewed. In addition, the approach based on an underlying illness-death model is generalized to allow general parametric models. The performance of these methods, in terms of bias and efficiency, is investigated through simulation and also illustrated using data from a clinical trial of treatments for colon cancer. The simulations suggest that the illness-death model-based method provides good estimates of Kendall's τ across several scenarios. In some situations, copula-based methods perform well but their performance is sensitive to the choice of copula. The Clayton copula is most appropriate in scenarios, which might realistically reflect an oncology trial, but the use of copula models in practice is questionable.

Estimation in multi-arm two-stage trials with treatment selection and time-to-event endpoint.

We consider estimation of treatment effects in two-stage adaptive multi-arm trials with a common control. The best treatment is selected at interim, and the primary endpoint is modeled via a Cox proportional hazards model. The maximum partial-likelihood estimator of the log hazard ratio of the selected treatment will overestimate the true treatment effect in this case. Several methods for reducing the selection bias have been proposed for normal endpoints, including an iterative method based on the estimated conditional selection biases and a shrinkage approach based on empirical Bayes theory. We adapt these methods to time-to-event data and compare the bias and mean squared error of all methods in an extensive simulation study and apply the proposed methods to reconstructed data from the FOCUS trial. We find that all methods tend to overcorrect the bias, and only the shrinkage methods can reduce the mean squared error. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Sample size re-estimation in paired comparative diagnostic accuracy studies with a binary response.

BACKGROUND: The sample size required to power a study to a nominal level in a paired comparative diagnostic accuracy study, i.e. studies in which the diagnostic accuracy of two testing procedures is compared relative to a gold standard, depends on the conditional dependence between the two tests - the lower the dependence the greater the sample size required. A priori, we usually do not know the dependence between the two tests and thus cannot determine the exact sample size required. One option is to use the implied sample size for the maximal negative dependence, giving the largest possible sample size. However, this is potentially wasteful of resources and unnecessarily burdensome on study participants as the study is likely to be overpowered. A more accurate estimate of the sample size can be determined at a planned interim analysis point where the sample size is re-estimated. METHODS: This paper discusses a sample size estimation and re-estimation method based on the maximum likelihood estimates, under an implied multinomial model, of the observed values of conditional dependence between the two tests and, if required, prevalence, at a planned interim. The method is illustrated by comparing the accuracy of two procedures for the detection of pancreatic cancer, one procedure using the standard battery of tests, and the other using the standard battery with the addition of a PET/CT scan all relative to the gold standard of a cell biopsy. Simulation of the proposed method illustrates its robustness under various conditions. RESULTS: The results show that the type I error rate of the overall experiment is stable using our suggested method and that the type II error rate is close to or above nominal. Furthermore, the instances in which the type II error rate is above nominal are in the situations where the lowest sample size is required, meaning a lower impact on the actual number of participants recruited. CONCLUSION: We recommend multinomial model maximum likelihood estimation of the conditional dependence between paired diagnostic accuracy tests at an interim to reduce the number of participants required to power the study to at least the nominal level. TRIAL REGISTRATION: ISRCTN ISRCTN73852054 . Registered 9th of January 2015. Retrospectively registered.

Estimation of time-shift models with application to survival calibration in health technology assessment.

The incremental life expectancy, defined as the difference in mean survival times between two treatment groups, is a crucial quantity of interest in cost-effectiveness analyses. Usually, this quantity is very difficult to estimate from censored survival data with a limited follow-up period. The paper develops estimation procedures for a time-shift survival model that, provided model assumptions are met, gives a reliable estimate of incremental life expectancy without extrapolation beyond the study period. Methods for inference are developed both for individual patient data and when only published Kaplan-Meier curves are available. Through simulation, the estimators are shown to be close to unbiased and constructed confidence intervals are shown to have close to nominal coverage for small to moderate sample sizes. Copyright © 2016 John Wiley & Sons, Ltd.

Transition probability estimates for non-Markov multi-state models.

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.

Long-term follow-up reveals low incidence of colorectal cancer, but frequent need for resection, among Australian patients with inflammatory bowel disease.

BACKGROUND & AIMS: Inflammatory bowel disease can require surgical resection and also lead to colorectal cancer (CRC). We investigated the cumulative incidence of resection surgeries and CRC among patients with ulcerative colitis (UC) or Crohn's disease (CD). METHODS: We analyzed data from a cohort of patients who participated in an inflammatory bowel disease study (504 with UC and 377 with CD) at 2 academic medical centers in Sydney, Australia from 1977 to 1992 (before the development of biologic therapies). We collected follow-up data on surgeries and development of CRC from hospital and community medical records or via direct contact with patients during a median time period of 14 years. Cumulative incidences of resection surgeries and CRC were calculated by competing risk survival analysis. RESULTS: Among patients with UC, CRC developed in 24, for a cumulative incidence of 1% at 10 years (95% confidence interval [CI], 0%-2%), 3% at 20 years (95% CI, 1%-5%), and 7% at 30 years (95% CI, 4%-10%). Their cumulative incidence of colectomy was 15% at 10 years (95% CI, 11%-19%), 26% at 20 years (95% CI, 21%-30%), and 31% at 30 years (95% CI, 25%-36%). Among patients with CD, 5 of 327 with colon disease developed CRC, with a cumulative incidence of CRC of 1% at 10 years (95% CI, 0%-2%), 1% at 20 years (95% CI, 0%-2%), and 2% at 30 years (95% CI, 0%-4%). Among all patients with CD, the cumulative incidence of resection was 32% at 5 years (95% CI, 27%-37%), 43% at 10 years (95% CI, 37%-49%), and 53% at 15 years (95% CI, 46%-58%). Of these 168 subjects, 42% required a second resection within 15 years of the first surgery (95% CI, 33%-50%). CONCLUSIONS: Patients with UC have a low incidence of CRC during a 30-year period (7% or less); the incidence among patients with CD is even lower. However, almost one-third of patients with UC and about 50% of those with CD will require surgery.

Early morning salivary cortisol and cortisone, and adrenal responses to a simplified low-dose short Synacthen test in children with asthma.

OBJECTIVE: To examine serum cortisol responses to a simplified low-dose short Synacthen test (LDSST) in children treated with inhaled corticosteroids (ICS) for asthma and to compare these to early morning salivary cortisol (EMSC) and cortisone (EMSCn) levels. DESIGN: Early morning salivary cortisol and EMSCn samples were collected for three consecutive days. On day three, Synacthen 500 ng/1·73 m(2) was administered intravenously. Samples were collected at 0, 15, 25, 35 min. RESULTS: A total of 269 subjects (160 M: 109 F), median (range) age 10·0 (5·1-15·2) years were studied. Peak cortisol in the LDSST was <500 nmol/l in 101 subjects (37·5%) and <350 nmol/l in 12 subjects (4·5%). Basal cortisol correlated with peak cortisol: r = 0·55, (95% CI: 0·46, 0·63, P < 0·0001). Time at which peak cortisol concentration was achieved was significantly related to the value of peak cortisol (P < 0·0001), with higher cortisol peaks occurring later in the test and lower cortisol peaks occurring earlier. EMSC and EMSCn had no predictive value for the identification of patients with a peak cortisol <500 nmol/l. EMSCn was superior to EMSC in identifying patients with a peak cortisol <350 nmol/l: a minimum EMSCn cut-off value of 12·5 nmol/l gave a negative predictive value of 99·2% and positive predictive value of 30·1%. CONCLUSION: Our data illustrate that basal measures of cortisol are likely to be of value in screening populations for patients at greatest risk of adrenal crisis. EMSCn shows promise as a screening tool for the identification of patients with severe adrenal insufficiency.

Development and psychometric testing of the online Adolescent Diabetes Needs Assessment Tool (ADNAT).

AIM: To report on the development and psychometric testing of the Adolescent Diabetes Needs Assessment Tool. BACKGROUND: The UK has the fifth largest paediatric diabetes population in the world, but one of the poorest levels of diabetes control, highlighting the need for intervention development. DESIGN: Mixed methods following recommendations for questionnaire design and validation. METHODS: A total of 171 young people (12-18 years) participated between 2008- 2011. Methods included item selection using secondary framework analysis, item review, pre-testing, piloting and online transfer. Statistical tests assessed reliability using item-total correlations, interitem consistency and test-retest reliability; and validity using blood glucose (HbA1c) levels and the Self-Management of type 1 Diabetes in Adolescence questionnaire. RESULTS: The Adolescent Diabetes Needs Assessment Tool consists of 117 questions divided between six domains of educational and psychosocial support needs. It combines reflective questioning with needs assessment to raise self-awareness to support adolescent decision-making in relation to diabetes self-care. Thirty-six of the questions provide self-care and psychosocial health assessment scores. Face and content validity of the scoring items were all positively evaluated in terms of appropriateness and readability and tests for validity found significant correlations with Self-Management of type 1 Diabetes in Adolescence and weak correlation with HbA1c , which compared favourably with Self-Management of type 1 Diabetes in Adolescence, the only comparable (USA) tool. Item response analysis validated the use of simple additive scores. CONCLUSIONS: The Adolescent Diabetes Needs Assessment Tool combines reflective learning with needs assessment to support patient-centred clinical consultations.

Measurement of flood peak effects as a result of soil and land management, with focus on experimental issues and scale.

As a result of several serious flood events which have occurred since 2000, flooding across Europe is now receiving considerable public and media attention. The impact of land use on hydrology and flood response is significantly under-researched, and the links between land use change and flooding are still unclear. This study considers runoff data available from studies of arable in-field land use management options, applied with the aim of reducing diffuse pollution from arable land, in order to investigate whether these treatments also have potential to reduce downstream flooding. Intensive monitoring of 17 hillslope treatment areas produced a record of flood peak data covering different mitigation treatments for runoff which occurred in the winter of 2007-2008. We investigated event total runoff responses to rainfall, peak runoff, and timing of the runoff peaks from replicates of different treatments, in order to assess whether there is a significant difference in flood peak response between different mitigation options which could be used to mitigate downstream flood risk. A mixed-modelling approach was adopted in order to determine whether differences observed in runoff response were significant. The results of this study suggest that changes in land use management using arable in-field mitigation treatments can affect local-scale runoff generation, with differences observed in the size, duration and timing of flood peaks as a result of different management practices, but the study was unable to allow significant treatment effects to be determined. We suggest that further field studies of the effects of changes in land use and land use management need to upscale towards farm and catchment scale experiments which consider high quality before-and-after data over longer temporal timescales. This type of data collection is essential in order to allow appropriate land use management decisions to be made.

A pool-adjacent-violators type algorithm for non-parametric estimation of current status data with dependent censoring.

A likelihood based approach to obtaining non-parametric estimates of the failure time distribution is developed for the copula based model of Wang et al. (Lifetime Data Anal 18:434-445, 2012) for current status data under dependent observation. Maximization of the likelihood involves a generalized pool-adjacent violators algorithm. The estimator coincides with the standard non-parametric maximum likelihood estimate under an independence model. Confidence intervals for the estimator are constructed based on a smoothed bootstrap. It is also shown that the non-parametric failure distribution is only identifiable if the copula linking the observation and failure time distributions is fully-specified. The method is illustrated on a previously analyzed tumorigenicity dataset.

A Systematic Review of Methodologies Used in Models of the Treatment of Diabetes Mellitus.

BACKGROUND: Diabetes mellitus is a chronic and complex disease, increasing in prevalence and consequent health expenditure. Cost-effectiveness models with long time horizons are commonly used to perform economic evaluations of diabetes' treatments. As such, prediction accuracy and structural uncertainty are important features in cost-effectiveness models of chronic conditions. OBJECTIVES: The aim of this systematic review is to identify and review published cost-effectiveness models of diabetes treatments developed between 2011 and 2022 regarding their methodological characteristics. Further, it also appraises the quality of the methods used, and discusses opportunities for further methodological research. METHODS: A systematic literature review was conducted in MEDLINE and Embase to identify peer-reviewed papers reporting cost-effectiveness models of diabetes treatments, with time horizons of more than 5 years, published in English between 1 January 2011 and 31 of December 2022. Screening, full-text inclusion, data extraction, quality assessment and data synthesis using narrative synthesis were performed. The Philips checklist was used for quality assessment of the included studies. The study was registered in PROSPERO (CRD42021248999). RESULTS: The literature search identified 30 studies presenting 29 unique cost-effectiveness models of type 1 and/or type 2 diabetes treatments. The review identified 26 type 2 diabetes mellitus (T2DM) models, 3 type 1 DM (T1DM) models and one model for both types of diabetes. Fifteen models were patient-level models, whereas 14 were at cohort level. Parameter uncertainty was assessed thoroughly in most of the models, whereas structural uncertainty was seldom addressed. All the models where validation was conducted performed well. The methodological quality of the models with respect to structure was high, whereas with respect to data modelling it was moderate. CONCLUSIONS: Models developed in the past 12 years for health economic evaluations of diabetes treatments are of high-quality and make use of advanced methods. However, further developments are needed to improve the statistical modelling component of cost-effectiveness models and to provide better assessment of structural uncertainty.

Baseline and Peak Cortisol Response to the Low-Dose Short Synacthen Test Relates to Indication for Testing, Age, and Sex.

Context: Meta-analyses report that the low dose short Synacthen test (LDSST) is more sensitive but less specific than the standard dose test for the diagnosis of adrenal insufficiency, and there are concerns regarding the accuracy of dosing in the LDSST. Objective: Perform a retrospective, observational study to review the outcomes of LDSSTs performed in a tertiary endocrine service from 2008 to 2014 (N = 335) and 2016 to 2020 (N = 160), and examine for relationships between cortisol measurements and indication for testing, age and sex. Methods: LDSST were performed by endocrine nurses. Synacthen 500 ng/1.73m2 administered as IV bolus, sampling at 0, 15, 25, and 35 minutes. Results: Mean (± 1SD) baseline cortisol was 221 ± 120 nmol/L, peak 510 ± 166 nmol/L and increment 210 ± 116 nmol/L. 336 (70%) patients had a normal response (baseline cortisol >100 nmol/L, peak >450 nmol/L), 78 (16%) a suboptimal response (peak cortisol 350-450 nmol/L) and were prescribed hydrocortisone to during periods of stress only, 67 (14%) an abnormal response (baseline <100nmol/L or peak <350nmol/L) and were prescribed daily hydrocortisone. Basal, peak, and incremental increases in cortisol were higher in females (P = .03, P < .001, P = .03, respectively). Abnormal results occurred most frequently in patients treated previously with pharmacological doses of glucocorticoids or structural brain abnormalities (P < .001). Conclusion: The low prevalence and strong association of abnormal results with indication for testing, suggests that over diagnosis occurred infrequently in this clinical setting.

Flexible nonhomogeneous markov models for panel observed data.

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.

Accounting for bias due to a non-ignorable tracing mechanism in a retrospective breast cancer cohort study.

We consider the analysis of competing risks in a retrospective breast cancer cohort study where tracing of patients is dependent on survival to a pre-specified truncation time. We demonstrate that if ignored, the observed cause-specific hazards will become distorted before the truncation time. Two approaches to account for the tracing bias are considered. First, a likelihood-based method using piecewise constant transition intensities under a Markov assumption. Second, a pseudo-likelihood method using inverse probability of tracing weights. For the breast cancer example, both methods improve the precision of estimates compared with a conventional approach based on excluding patients.

Incidence and risk factors of long COVID in the UK: a single-centre observational study.

BACKGROUND: Studies to evaluate long COVID symptoms and their risk factors are limited. We evaluated the presence of long COVID and its risk factors in patients discharged from a hospital with COVID-19 illness. METHODS: This observational study included 271 COVID-19 patients admitted between February and July 2020 in a hospital in the UK. The primary outcome measure was to assess the duration and severity of long COVID and its predictors at 3, 6 and 9 months. Logistic regression was performed to assess the potential risk factors for long COVID. RESULTS: Out of 89 patients interviewed, 55 (62%) had long COVID for 3 months, 46 (52%) for 6 months and 37 of the 75 patients admitted to the hospital with acute COVID-19 had long COVID for 9 months (49%). The most common long COVID symptoms were fatigue and breathlessness. CONCLUSION: Nearly two-thirds of patients at 3 months and a half at 9 months had long COVID. COVID-19 pneumonia was the strongest predictor of long COVID in Caucasians at 3 months.

Semi-Markov models with phase-type sojourn distributions.

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.