Modeling the multi-state natural history of rare diseases with heterogeneous individual patient data: A simulation study.

Multi-state survival models are used to represent the natural history of a disease, forming the basis of a health technology assessment comparing a novel treatment to current practice. Constructing such models for rare diseases is problematic, since evidence sources are typically much sparser and more heterogeneous. This simulation study investigated different one-stage and two-stage approaches to meta-analyzing individual patient data (IPD) in a multi-state survival setting when the number and size of studies being meta-analyzed are small. The objective was to assess methods of different complexity to see when they are accurate, when they are inaccurate and when they struggle to converge due to the sparsity of data. Biologically plausible multi-state IPD were simulated from study- and transition-specific hazard functions. One-stage frailty and two-stage stratified models were estimated, and compared to a base case model that did not account for study heterogeneity. Convergence and the bias/coverage of population-level transition probabilities to, and lengths of stay in, each state were used to assess model performance. A real-world application to Duchenne Muscular Dystrophy, a neuromuscular rare disease, was conducted, and a software demonstration is provided. Models not accounting for study heterogeneity were consistently out-performed by two-stage models. Frailty models struggled to converge, particularly in scenarios of low heterogeneity, and predictions from models that did converge were also subject to bias. Stratified models may be better suited to meta-analyzing disparate sources of IPD in rare disease natural history/economic modeling, as they converge more consistently and produce less biased predictions of lengths of stay.

Multiple imputation strategies for missing event times in a multi-state model analysis.

In clinical studies, multi-state model (MSM) analysis is often used to describe the sequence of events that patients experience, enabling better understanding of disease progression. A complicating factor in many MSM studies is that the exact event times may not be known. Motivated by a real dataset of patients who received stem cell transplants, we considered the setting in which some event times were exactly observed and some were missing. In our setting, there was little information about the time intervals in which the missing event times occurred and missingness depended on the event type, given the analysis model covariates. These additional challenges limited the usefulness of some missing data methods (maximum likelihood, complete case analysis, and inverse probability weighting). We show that multiple imputation (MI) of event times can perform well in this setting. MI is a flexible method that can be used with any complete data analysis model. Through an extensive simulation study, we show that MI by predictive mean matching (PMM), in which sampling is from a set of observed times without reliance on a specific parametric distribution, has little bias when event times are missing at random, conditional on the observed data. Applying PMM separately for each sub-group of patients with a different pathway through the MSM tends to further reduce bias and improve precision. We recommend MI using PMM methods when performing MSM analysis with Markov models and partially observed event times.

An augmented illness-death model for semi-competing risks with clinically immediate terminal events.

Preeclampsia is a pregnancy-associated condition posing risks of both fetal and maternal mortality and morbidity that can only resolve following delivery and removal of the placenta. Because in its typical form preeclampsia can arise before delivery, but not after, these two events exemplify the time-to-event setting of "semi-competing risks" in which a non-terminal event of interest is subject to the occurrence of a terminal event of interest. The semi-competing risks framework presents a valuable opportunity to simultaneously address two clinically meaningful risk modeling tasks: (i) characterizing risk of developing preeclampsia, and (ii) characterizing time to delivery after onset of preeclampsia. However, some people with preeclampsia deliver immediately upon diagnosis, while others are admitted and monitored for an extended period before giving birth, resulting in two distinct trajectories following the non-terminal event, which we call "clinically immediate" and "non-immediate" terminal events. Though such phenomena arise in many clinical contexts, to-date there have not been methods developed to acknowledge the complex dependencies between such outcomes, nor leverage these phenomena to gain new insight into individualized risk. We address this gap by proposing a novel augmented frailty-based illness-death model with a binary submodel to distinguish risk of immediate terminal event following the non-terminal event. The model admits direct dependence of the terminal event on the non-terminal event through flexible regression specification, as well as indirect dependence via a shared frailty term linking each submodel. We develop an efficient Bayesian sampler for estimation and corresponding model fit metrics, and derive formulae for dynamic risk prediction. In an extended example using pregnancy outcome data from an electronic health record, we demonstrate the proposed model's direct applicability to address a broad range of clinical questions.

Fresh fruit, dried fruit, raw vegetables, and cooked vegetables consumption associated with progression trajectory of type 2 diabetes: a multi-state analysis of a prospective cohort.

PURPOSE: To examine the effects of fresh fruit, dried fruit, raw vegetables, and cooked vegetables on type 2 diabetes (T2D) progression trajectory. METHODS: We included 429,886 participants in the UK Biobank who were free of diabetes and diabetes complications at baseline. Food groups were determined using a validated food frequency questionnaire. Outcomes were T2D incidence, complications, and mortality. Multi-state model was used to analyze the effects of food groups on T2D progression. RESULTS: During a follow-up of 12.6 years, 10,333 incident T2D cases were identified, of whom, 3961 (38.3%) developed T2D complications and 1169 (29.5%) died. We found that impacts of four food groups on T2D progression varied depending on disease stage. For example, compared to participants who ate less than one piece of dried fruit per day, the hazard ratios and 95% confidence intervals for those who ate ≥ 2 pieces of dried fruit per day were 0.82 (0.77, 0.87), 0.88 (0.85, 0.92), and 0.86 (0.78, 0.95) for transitions from diabetes-free state to incident T2D, from diabetes-free state to total death, and from incident T2D to T2D complications, respectively. Higher intake of fresh fruit was significantly associated with lower risk of disease progression from diabetes-free state to all-cause death. Higher intake of raw and cooked vegetables was significantly associated with lower risks of disease progression from diabetes-free state to incident T2D and to total death. CONCLUSIONS: These findings indicate that higher intake of fresh fruit, dried fruit, raw vegetables, and cooked vegetables could be beneficial for primary and secondary prevention of T2D.

Association of cigarette smoking, smoking cessation with the risk of cardiometabolic multimorbidity in the UK Biobank.

BACKGROUND: To investigate the association between cigarette smoking, smoking cessation and the trajectory of cardiometabolic multimorbidity (CMM), and further to examine the association of age at smoking initiation and smoking cessation with CMM. METHODS: This study included 298,984 UK Biobank participants without cardiometabolic diseases (CMDs) (including type 2 diabetes, coronary heart diseases, stroke, and hypertension) at baseline. Smoking status was categorized into former, current, and never smokers, with age at smoking initiation and smoking cessation as a proxy for current and former smokers. The multi-state model was performed to evaluate the association between cigarette smoking, smoking cessation and CMM. RESULTS: During a median follow-up of 13.2 years, 59,193 participants developed first cardiometabolic disease (FCMD), 14,090 further developed CMM, and 16,487 died. Compared to former smokers, current smokers had higher risk at all transitions, with hazard ratio (95% confidence interval) = 1.59 (1.55 ∼ 1.63) vs. 1.18 (1.16 ∼ 1.21) (P = 1.48 × 10- 118) from health to FCMD, 1.40 (1.33 ∼ 1.47) vs. 1.09 (1.05 ∼ 1.14) (P = 1.50 × 10- 18) from FCMD to CMM, and 2.87 (2.72 ∼ 3.03) vs. 1.38 (1.32 ∼ 1.45) (P < 0.001) from health, 2.16 (1.98 ∼ 2.35) vs. 1.25 (1.16 ∼ 1.34) (P = 1.18 × 10- 46) from FCMD, 2.02 (1.79 ∼ 2.28) vs. 1.22 (1.09 ∼ 1.35) (P = 3.93 × 10- 17) from CMM to death; whereas quitting smoking reduced the risk attributed to cigarette smoking by approximately 76.5% across all transitions. Reduced risks of smoking cessation were also identified when age at quitting smoking was used as a proxy for former smokers. CONCLUSIONS: Cigarette smoking was associated with a higher risk of CMM across all transitions; however, smoking cessation, especially before the age of 35, was associated with a significant decrease in CMM risk attributed to cigarette smoking.

Penalized estimation of frailty-based illness-death models for semi-competing risks.

Semi-competing risks refer to the time-to-event analysis setting, where the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical contexts, including studies of preeclampsia, a condition that may arise during pregnancy and for which delivery is a terminal event. Models that acknowledge semi-competing risks enable investigation of relationships between covariates and the joint timing of the outcomes, but methods for model selection and prediction of semi-competing risks in high dimensions are lacking. Moreover, in such settings researchers commonly analyze only a single or composite outcome, losing valuable information and limiting clinical utility-in the obstetric setting, this means ignoring valuable insight into timing of delivery after preeclampsia has onset. To address this gap, we propose a novel penalized estimation framework for frailty-based illness-death multi-state modeling of semi-competing risks. Our approach combines non-convex and structured fusion penalization, inducing global sparsity as well as parsimony across submodels. We perform estimation and model selection via a pathwise routine for non-convex optimization, and prove statistical error rate results in this setting. We present a simulation study investigating estimation error and model selection performance, and a comprehensive application of the method to joint risk modeling of preeclampsia and timing of delivery using pregnancy data from an electronic health record.

Real-time analysis of hospital length of stay in a mixed SARS-CoV-2 Omicron and Delta epidemic in New South Wales, Australia.

BACKGROUND: The distribution of the duration that clinical cases of COVID-19 occupy hospital beds (the 'length of stay') is a key factor in determining how incident caseloads translate into health system burden. Robust estimation of length of stay in real-time requires the use of survival methods that can account for right-censoring induced by yet unobserved events in patient progression (e.g. discharge, death). In this study, we estimate in real-time the length of stay distributions of hospitalised COVID-19 cases in New South Wales, Australia, comparing estimates between a period where Delta was the dominant variant and a subsequent period where Omicron was dominant. METHODS: Using data on the hospital stays of 19,574 individuals who tested positive to COVID-19 prior to admission, we performed a competing-risk survival analysis of COVID-19 clinical progression. RESULTS: During the mixed Omicron-Delta epidemic, we found that the mean length of stay for individuals who were discharged directly from ward without an ICU stay was, for age groups 0-39, 40-69 and 70 +, respectively, 2.16 (95% CI: 2.12-2.21), 3.93 (95% CI: 3.78-4.07) and 7.61 days (95% CI: 7.31-8.01), compared to 3.60 (95% CI: 3.48-3.81), 5.78 (95% CI: 5.59-5.99) and 12.31 days (95% CI: 11.75-12.95) across the preceding Delta epidemic (1 July 2021-15 December 2021). We also considered data on the stays of individuals within the Hunter New England Local Health District, where it was reported that Omicron was the only circulating variant, and found mean ward-to-discharge length of stays of 2.05 (95% CI: 1.80-2.30), 2.92 (95% CI: 2.50-3.67) and 6.02 days (95% CI: 4.91-7.01) for the same age groups. CONCLUSIONS: Hospital length of stay was substantially reduced across all clinical pathways during a mixed Omicron-Delta epidemic compared to a prior Delta epidemic, contributing to a lessened health system burden despite a greatly increased infection burden. Our results demonstrate the utility of survival analysis in producing real-time estimates of hospital length of stay for assisting in situational assessment and planning of the COVID-19 response.

What is the role of puberty in the development of islet autoimmunity and progression to type 1 diabetes?

In many populations, the peak period of incidence of type 1 diabetes (T1D) has been observed to be around 10-14 years of age, coinciding with puberty, but direct evidence of the role of puberty in the development of T1D is limited. We therefore aimed to investigate whether puberty and the timing of its onset are associated with the development of islet autoimmunity (IA) and subsequent progression to T1D. A Finnish population-based cohort of children with HLA-DQB1-conferred susceptibility to T1D was followed from 7 years of age until 15 years of age or until a diagnosis of T1D (n = 6920). T1D-associated autoantibodies and growth were measured at 3- to 12-month intervals, and pubertal onset timing was assessed based on growth. The analyses used a three-state survival model. IA was defined as being either positive for islet cell antibodies plus at least one biochemical autoantibody (ICA + 1) or as being repeatedly positive for at least one biochemical autoantibody (BC1). Depending on the IA definition, either 303 (4.4%, ICA + 1) or 435 (6.3%, BC1) children tested positive for IA by the age of 7 years, and 211 (3.2%, ICA + 1)) or 198 (5.3%, BC1) developed IA during follow-up. A total of 172 (2.5%) individuals developed T1D during follow-up, of whom 169 were positive for IA prior to the clinical diagnosis. Puberty was associated with an increase in the risk of progression to T1D, but only from ICA + 1-defined IA (hazard ratio 1.57; 95% confidence interval 1.14, 2.16), and the timing of pubertal onset did not affect the association. No association between puberty and the risk of IA was detected. In conclusion, puberty may affect the risk of progression but is not a risk factor for IA.

Estimating distribution of length of stay in a multi-state model conditional on the pathway, with an application to patients hospitalised with Covid-19.

Multi-state models are used to describe how individuals transition through different states over time. The distribution of the time spent in different states, referred to as 'length of stay', is often of interest. Methods for estimating expected length of stay in a given state are well established. The focus of this paper is on the distribution of the time spent in different states conditional on the complete pathway taken through the states, which we call 'conditional length of stay'. This work is motivated by questions about length of stay in hospital wards and intensive care units among patients hospitalised due to Covid-19. Conditional length of stay estimates are useful as a way of summarising individuals' transitions through the multi-state model, and also as inputs to mathematical models used in planning hospital capacity requirements. We describe non-parametric methods for estimating conditional length of stay distributions in a multi-state model in the presence of censoring, including conditional expected length of stay (CELOS). Methods are described for an illness-death model and then for the more complex motivating example. The methods are assessed using a simulation study and shown to give unbiased estimates of CELOS, whereas naive estimates of CELOS based on empirical averages are biased in the presence of censoring. The methods are applied to estimate conditional length of stay distributions for individuals hospitalised due to Covid-19 in the UK, using data on 42,980 individuals hospitalised from March to July 2020 from the COVID19 Clinical Information Network.

Bivariate pseudo-observations for recurrent event analysis with terminal events.

The analysis of recurrent events in the presence of terminal events requires special attention. Several approaches have been suggested for such analyses either using intensity models or marginal models. When analysing treatment effects on recurrent events in controlled trials, special attention should be paid to competing deaths and their impact on interpretation. This paper proposes a method that formulates a marginal model for recurrent events and terminal events simultaneously. Estimation is based on pseudo-observations for both the expected number of events and survival probabilities. Various relevant hypothesis tests in the framework are explored. Theoretical derivations and simulation studies are conducted to investigate the behaviour of the method. The method is applied to two real data examples. The bivariate marginal pseudo-observation model carries the strength of a two-dimensional modelling procedure and performs well in comparison with available models. Finally, an extension to a three-dimensional model, which decomposes the terminal event per death cause, is proposed and exemplified.

Ambient air pollution associated with incidence and dynamic progression of type 2 diabetes: a trajectory analysis of a population-based cohort.

BACKGROUND: Though the association between air pollution and incident type 2 diabetes (T2D) has been well documented, evidence on the association with development of subsequent diabetes complications and post-diabetes mortality is scarce. We investigate whether air pollution is associated with different progressions and outcomes of T2D. METHODS: Based on the UK Biobank, 398,993 participants free of diabetes and diabetes-related events at recruitment were included in this analysis. Exposures to particulate matter with a diameter ≤ 10 µm (PM10), PM2.5, nitrogen oxides (NOx), and NO2 for each transition stage were estimated at each participant's residential addresses using data from the UK's Department for Environment, Food and Rural Affairs. The outcomes were incident T2D, diabetes complications (diabetic kidney disease, diabetic eye disease, diabetic neuropathy disease, peripheral vascular disease, cardiovascular events, and metabolic events), all-cause mortality, and cause-specific mortality. Multi-state model was used to analyze the impact of air pollution on different progressions of T2D. Cumulative transition probabilities of different stages of T2D under different air pollution levels were estimated. RESULTS: During the 12-year follow-up, 13,393 incident T2D patients were identified, of whom, 3791 developed diabetes complications and 1335 died. We observed that air pollution was associated with different progression stages of T2D with different magnitudes. In a multivariate model, the hazard ratios [95% confidence interval (CI)] per interquartile range elevation in PM2.5 were 1.63 (1.59, 1.67) and 1.08 (1.03, 1.13) for transitions from healthy to T2D and from T2D to complications, and 1.50 (1.47, 1.53), 1.49 (1.36, 1.64), and 1.54 (1.35, 1.76) for mortality risk from baseline, T2D, and diabetes complications, respectively. Generally, we observed stronger estimates of four air pollutants on transition from baseline to incident T2D than those on other transitions. Moreover, we found significant associations between four air pollutants and mortality risk due to cancer and cardiovascular diseases from T2D or diabetes complications. The cumulative transition probability was generally higher among those with higher levels of air pollution exposure. CONCLUSIONS: This study indicates that ambient air pollution exposure may contribute to increased risk of incidence and progressions of T2D, but to diverse extents for different progressions.

Effect of heparin treatment on pulmonary embolism and in-hospital death in unvaccinated COVID-19 patients without overt deep vein thrombosis.

BACKGROUND: Pulmonary embolism (PE) without overt deep vein thrombosis (DVT) was common in hospitalized coronavirus-induced disease (COVID)-19 patients and represented a diagnostic, prognostic, and therapeutic challenge. The aim of this study was to analyze the prognostic role of PE on mortality and the preventive effect of heparin on PE and mortality in unvaccinated COVID-19 patients without overt DVT. METHODS: Data from 401 unvaccinated patients (age 68 ± 13 years, 33% females) consecutively admitted to the intensive care unit or the medical ward were included in a retrospective longitudinal study. PE was documented by computed tomography scan and DVT by compressive venous ultrasound. The effect of PE diagnosis and any heparin use on in-hospital death (primary outcome) was analyzed by a classical survival model. The preventive effect of heparin on either PE diagnosis or in-hospital death (secondary outcome) was analyzed by a multi-state model after having reclassified patients who started heparin after PE diagnosis as not treated. RESULTS: Median follow-up time was 8 days (range 1-40 days). PE cumulative incidence and in-hospital mortality were 27% and 20%, respectively. PE was predicted by increased D-dimer levels and COVID-19 severity. Independent predictors of in-hospital death were age (hazards ratio (HR) 1.05, 95% confidence interval (CI) 1.03-1.08, p < 0.001), body mass index (HR 0.93, 95% CI 0.89-0.98, p = 0.004), COVID-19 severity (severe versus mild/moderate HR 3.67, 95% CI 1.30-10.4, p = 0.014, critical versus mild/moderate HR 12.1, 95% CI 4.57-32.2, p < 0.001), active neoplasia (HR 2.58, 95% CI 1.48-4.50, p < 0.001), chronic obstructive pulmonary disease (HR 2.47; 95% CI 1.15-5.27, p = 0.020), respiratory rate (HR 1.06, 95% CI 1.02-1.11, p = 0.008), heart rate (HR 1.03, 95% CI 1.01-1.04, p < 0.001), and any heparin treatment (HR 0.35, 95% CI 0.18-0.67, p = 0.001). In the multi-state model, preventive heparin at prophylactic or intermediate/therapeutic dose, compared with no treatment, reduced PE risk and in-hospital death, but it did not influence mortality of patients with a PE diagnosis. CONCLUSIONS: PE was common during the first waves pandemic in unvaccinated patients, but it was not a negative prognostic factor for in-hospital death. Heparin treatment at any dose prevented mortality independently of PE diagnosis, D-dimer levels, and disease severity.

Inference for transition probabilities in non-Markov multi-state models.

Multi-state models are frequently used when data come from subjects observed over time and where focus is on the occurrence of events that the subjects may experience. A convenient modeling assumption is that the multi-state stochastic process is Markovian, in which case a number of methods are available when doing inference for both transition intensities and transition probabilities. The Markov assumption, however, is quite strict and may not fit actual data in a satisfactory way. Therefore, inference methods for non-Markov models are needed. In this paper, we review methods for estimating transition probabilities in such models and suggest ways of doing regression analysis based on pseudo observations. In particular, we will compare methods using land-marking with methods using plug-in. The methods are illustrated using simulations and practical examples from medical research.

Strong survival selection on seasonal migration versus residence induced by extreme climatic events.

Elucidating the full eco-evolutionary consequences of climate change requires quantifying the impact of extreme climatic events (ECEs) on selective landscapes of key phenotypic traits that mediate responses to changing environments. Episodes of strong ECE-induced selection could directly alter population composition, and potentially drive micro-evolution. However, to date, few studies have quantified ECE-induced selection on key traits, meaning that immediate and longer-term eco-evolutionary implications cannot yet be considered. One widely expressed trait that allows individuals to respond to changing seasonal environments, and directly shapes spatio-seasonal population dynamics, is seasonal migration versus residence. Many populations show considerable among-individual phenotypic variation, resulting in 'partial migration'. However, variation in the magnitude of direct survival selection on migration versus residence has not been rigorously quantified, and empirical evidence of whether seasonal ECEs induce, intensify, weaken or reverse such selection is lacking. We designed full annual cycle multi-state capture-recapture models that allow estimation of seasonal survival probabilities of migrants and residents from spatio-temporally heterogeneous individual resightings. We fitted these models to 9 years of geographically extensive year-round resighting data from partially migratory European shags Phalacrocorax aristotelis. We thereby quantified seasonal and annual survival selection on migration versus residence across benign and historically extreme non-breeding season (winter) conditions, and tested whether selection differed between females and males. We show that two of four observed ECEs, defined as severe winter storms causing overall low survival, were associated with very strong seasonal survival selection against residence. These episodes dwarfed the weak selection or neutrality evident otherwise, and hence caused selection through overall annual survival. The ECE that caused highest overall mortality and strongest selection also caused sex-biased mortality, but there was little overall evidence of sex-biased selection on migration versus residence. Our results imply that seasonal ECEs and associated mortality can substantially shape the landscape of survival selection on migration versus residence. Such ECE-induced phenotypic selection will directly alter migrant and resident frequencies, and thereby alter immediate spatio-seasonal population dynamics. Given underlying additive genetic variation, such ECEs could potentially cause micro-evolutionary changes in seasonal migration, and thereby cause complex eco-evolutionary population responses to changing seasonal environments.

Risk factors associated with severe hospital burden of COVID-19 disease in Regione Lombardia: a cohort study.

BACKGROUND: Understanding the risk factors associated with hospital burden of COVID-19 is crucial for healthcare planning for any future waves of infection. METHODS: An observational cohort study is performed, using data on all PCR-confirmed cases of COVID-19 in Regione Lombardia, Italy, during the first wave of infection from February-June 2020. A multi-state modelling approach is used to simultaneously estimate risks of progression through hospital to final outcomes of either death or discharge, by pathway (via critical care or not) and the times to final events (lengths of stay). Logistic and time-to-event regressions are used to quantify the association of patient and population characteristics with the risks of hospital outcomes and lengths of stay respectively. RESULTS: Risks of severe outcomes such as ICU admission and mortality have decreased with month of admission (for example, the odds ratio of ICU admission in June vs March is 0.247 [0.120-0.508]) and increased with age (odds ratio of ICU admission in 45-65 vs 65 + age group is 0.286 [0.201-0.406]). Care home residents aged 65 + are associated with increased risk of hospital mortality and decreased risk of ICU admission. Being a healthcare worker appears to have a protective association with mortality risk (odds ratio of ICU mortality is 0.254 [0.143-0.453] relative to non-healthcare workers) and length of stay. Lengths of stay decrease with month of admission for survivors, but do not appear to vary with month for non-survivors. CONCLUSIONS: Improvements in clinical knowledge, treatment, patient and hospital management and public health surveillance, together with the waning of the first wave after the first lockdown, are hypothesised to have contributed to the reduced risks and lengths of stay over time.

Instrumental variable estimation of early treatment effect in randomized screening trials.

The primary analysis of randomized screening trials for cancer typically adheres to the intention-to-screen principle, measuring cancer-specific mortality reductions between screening and control arms. These mortality reductions result from a combination of the screening regimen, screening technology and the effect of the early, screening-induced, treatment. This motivates addressing these different aspects separately. Here we are interested in the causal effect of early versus delayed treatments on cancer mortality among the screening-detectable subgroup, which under certain assumptions is estimable from conventional randomized screening trial using instrumental variable type methods. To define the causal effect of interest, we formulate a simplified structural multi-state model for screening trials, based on a hypothetical intervention trial where screening detected individuals would be randomized into early versus delayed treatments. The cancer-specific mortality reductions after screening detection are quantified by a cause-specific hazard ratio. For this, we propose two estimators, based on an estimating equation and a likelihood expression. The methods extend existing instrumental variable methods for time-to-event and competing risks outcomes to time-dependent intermediate variables. Using the multi-state model as the basis of a data generating mechanism, we investigate the performance of the new estimators through simulation studies. In addition, we illustrate the proposed method in the context of CT screening for lung cancer using the US National Lung Screening Trial data.

The impact of generic aromatase inhibitors on initiation, adherence, and persistence among women with breast cancer: Applying multi-state models to understand the dynamics of adherence.

PURPOSE: Clinical trials have clearly documented the survival benefit of aromatase inhibitors (AIs); however, many women fail to initiate (primary nonadherence) or remain adherent to AIs (secondary nonadherence). Prior studies have found that costs impact secondary nonadherence to medications but have failed to examine primary nonadherence. The purpose of this study is to examine primary and secondary adherence following the reduction in copays due to the introduction of generic AIs. METHODS: Using Surveillance, Epidemiology, and End Results-Medicare data, we identified 50 054 women diagnosed with incident breast cancer between 2008 and 2013. We compare women whose copays would change and those whose would not, due to the receipt of cost-sharing subsidies before and after generics were introduced using a difference-in-difference (DinD) analysis. To examine primary and secondary nonadherence, we rely on a multistate model with four states (Not yet initiated, User, Not Using, and Death). We adjusted for baseline factors using inverse probability treatment weights and then simulated adherence for 36 months following diagnosis. RESULTS: The generic introduction of AIs resulted in patients initiating AIs faster (DinD = -4.7%, 95%CI = -7.0, -2.3; patients not yet initiating treatment at 6-months), being more adherent (DinD ranging in absolute increase of 8.1%-10.4%) and being less likely to not be using the therapy (DinD range in absolute decrease of 1.2% at 6 months to 8.8% at 24 months) for women that do not receive a subsidy after generics were available. CONCLUSIONS: Introduction of generic alternatives to AIs significantly reduced primary and secondary nonadherence.

Evaluating the effect of healthcare providers on the clinical path of heart failure patients through a semi-Markov, multi-state model.

BACKGROUND: Investigating similarities and differences among healthcare providers, on the basis of patient healthcare experience, is of interest for policy making. Availability of high quality, routine health databases allows a more detailed analysis of performance across multiple outcomes, but requires appropriate statistical methodology. METHODS: Motivated by analysis of a clinical administrative database of 42,871 Heart Failure patients, we develop a semi-Markov, illness-death, multi-state model of repeated admissions to hospital, subsequent discharge and death. Transition times between these health states each have a flexible baseline hazard, with proportional hazards for patient characteristics (case-mix adjustment) and a discrete distribution for frailty terms representing clusters of providers. Models were estimated using an Expectation-Maximization algorithm and the number of clusters was based on the Bayesian Information Criterion. RESULTS: We are able to identify clusters of providers for each transition, via the inclusion of a nonparametric discrete frailty. Specifically, we detect 5 latent populations (clusters of providers) for the discharge transition, 3 for the in-hospital to death transition and 4 for the readmission transition. Out of hospital death rates are similar across all providers in this dataset. Adjusting for case-mix, we could detect those providers that show extreme behaviour patterns across different transitions (readmission, discharge and death). CONCLUSIONS: The proposed statistical method incorporates both multiple time-to-event outcomes and identification of clusters of providers with extreme behaviour simultaneously. In this way, the whole patient pathway can be considered, which should help healthcare managers to make a more comprehensive assessment of performance.

Seasonal movements and tributary-specific fidelity of blue sucker Cycleptus elongatus in a Southern Plains riverscape.

This study used acoustic telemetry and a multistate Cormack-Jolly-Seber model to determine the seasonal movement patterns of blue sucker Cycleptus elongatus from 2015 to 2017. Several hypotheses were ranked using AICc , and it was determined that the movement patterns of blue suckers in a mainstem reach below a hydropower dam (i.e., tailwater) differed from those of blue suckers tagged in the major tributaries (perennial with stream order >3). This study estimated a low probability (≤0.13) blue suckers would leave the tailwater reach at any time during the study. Conversely, blue suckers tagged in the major tributaries had a high probability (≥0.88) of leaving after the spawning season (February-May). Blue suckers tagged in the major tributaries displayed a high probability (0.83) of returning to the tributaries in the spawning season of 2016 when discharges were high. Blue suckers also had a higher probability of fidelity to the tributary where they were tagged (0.65) rather than straying to different tributaries (0.18). The majority of tagged blue suckers that strayed selected the only undammed tributary in the study area. In 2017, spring discharges were low, and the probability of blue suckers returning to any major tributary was low (0.19), with little difference in the probability of displaying site fidelity (0.10) vs. straying (0.09).

Estimation for an accelerated failure time model with intermediate states as auxiliary information.

The accelerated failure time (AFT) model is a common method for estimating the effect of a covariate directly on a patient's survival time. In some cases, death is the final (absorbing) state of a progressive multi-state process, however when the survival time for a subject is censored, traditional AFT models ignore the intermediate information from the subject's most recent disease state despite its relevance to the mortality process. We propose a method to estimate an AFT model for survival time to the absorbing state that uses the additional data on intermediate state transition times as auxiliary information when a patient is right censored. The method extends the Gehan AFT estimating equation by conditioning on each patient's censoring time and their disease state at their censoring time. With simulation studies, we demonstrate that the estimator is empirically unbiased, and can improve efficiency over commonly used estimators that ignore the intermediate states.