Refracture and mortality risk in the elderly with osteoporotic fractures: the AGES-Reykjavik study.

There is imminent refracture risk in elderly individuals for up to six years, with a decline thereafter except in women below 75 who face a constant elevated risk. Elderly men with fractures face the highest mortality risk, particularly those with hip and vertebral fractures. Targeted monitoring and treatment strategies are recommended. PURPOSE: Current management and interventions for osteoporotic fractures typically focus on bone mineral density loss, resulting in suboptimal evaluation of fracture risk. The aim of the study is to understand the progression of fractures to refractures and mortality in the elderly using multi-state models to better target those at risk. METHODS: This prospective, observational study analysed data from the AGES-Reykjavik cohort of Icelandic elderly, using multi-state models to analyse the evolution of fractures into refractures and mortality, and to estimate the probability of future events in subjects based on prognostic factors. RESULTS: At baseline, 4778 older individuals aged 65 years and older were included. Elderly men, and elderly women above 80 years of age, had a distinct imminent refracture risk that lasted between 2-6 years, followed by a sharp decline. However, elderly women below 75 continued to maintain a nearly constant refracture risk profile for ten years. Hip (30-63%) and vertebral (24-55%) fractures carried the highest 5-year mortality burden for elderly men and women, regardless of age, and for elderly men over 80, lower leg fractures also posed a significant mortality risk. CONCLUSION: The risk of refracture significantly increases in the first six years following the initial fracture. Elderly women, who experience fractures at a younger age, should be closely monitored to address their long-term elevated refracture risk. Elderly men, especially those with hip and vertebral fractures, face substantial mortality risk and require prioritized monitoring and treatment.

The dynamics and outcomes of AKI progression during the COVID-19 pandemic.

PURPOSE: Acute kidney injury (AKI) associated with COVID-19 is associated with poor prognosis. This study assessed the hitherto uninvestigated impact of COVID-19 on the progression and clinical outcomes of patients with AKI. METHODS: Data from 576 patients with AKI admitted between 13/3/20 and 13/5/20 were studied. Increasingly complex analyses, from logistic regressions to competing-risk and multi-state models, have revealed insights into AKI progression dynamics associated with PCR-confirmed COVID-19 acquisition and death. Meta-analyses of case fatality ratios among patients with AKI were also conducted. RESULTS: The overall case-fatality ratio was 0.33 [95% CI (0.20-0.36)]; higher in COVID-19 positive (COVID+) patients 0.52 [95% CI (0.46-0.58)] than in their negative (COVID-) counterparts 0.16 [95% CI (0.12-0.20)]. In AKI Stage-3 patients, that was 0.71 [95% CI (0.64-0.79)] among COVID+ patients with 45% dead within 14 days and 0.35 [95% CI (0.25-0.44)] in the COVID- group and 28% died within 14 days. Among patients diagnosed with AKI Stage-1 within 24 h, the probability of progression to AKI Stage-3 on day 7 post admission was 0.22 [95% CI (0.17-0.27)] among COVID+ patients, and 0.06 [95% CI (0.03, 0.09)] among those who tested negative. The probability of discharge by day 7 was 0.71 [95% CI (0.66, 0.75)] in COVID- patients, and 0.27 [95% CI (0.21, 0.32)] in COVID+ patients. By day 14, in AKI Stage-3 COVID+ patients, that was 0.35 [95% CI (0.25, 0.44)] with little change by day 10, that is, 0.38 [95% CI (0.29, 0.47)]. CONCLUSION: These results are consistent with either a rapid progression in severity, prolonged hospital care, or high case fatality ratio among AKI Stage-3 patients, significantly exacerbated by COVID-19 infection.

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.

Multi-state network meta-analysis of progression and survival data.

Multiple randomized controlled trials, each comparing a subset of competing interventions, can be synthesized by means of a network meta-analysis to estimate relative treatment effects between all interventions in the evidence base. Here we focus on estimating relative treatment effects for time-to-event outcomes. Cancer treatment effectiveness is frequently quantified by analyzing overall survival (OS) and progression-free survival (PFS). We introduce a method for the joint network meta-analysis of PFS and OS that is based on a time-inhomogeneous tri-state (stable, progression, and death) Markov model where time-varying transition rates and relative treatment effects are modeled with parametric survival functions or fractional polynomials. The data needed to run these analyses can be extracted directly from published survival curves. We demonstrate use by applying the methodology to a network of trials for the treatment of non-small-cell lung cancer. The proposed approach allows the joint synthesis of OS and PFS, relaxes the proportional hazards assumption, extends to a network of more than two treatments, and simplifies the parameterization of decision and cost-effectiveness analyses.

Target trial emulation with multi-state model analysis to assess treatment effectiveness using clinical COVID-19 data.

BACKGROUND: Real-world observational data are an important source of evidence on the treatment effectiveness for patients hospitalized with coronavirus disease 2019 (COVID-19). However, observational studies evaluating treatment effectiveness based on longitudinal data are often prone to methodological biases such as immortal time bias, confounding bias, and competing risks. METHODS: For exemplary target trial emulation, we used a cohort of patients hospitalized with COVID-19 (n = 501) in a single centre. We described the methodology for evaluating the effectiveness of a single-dose treatment, emulated a trial using real-world data, and drafted a hypothetical study protocol describing the main components. To avoid immortal time and time-fixed confounding biases, we applied the clone-censor-weight technique. We set a 5-day grace period as a period of time when treatment could be initiated. We used the inverse probability of censoring weights to account for the selection bias introduced by artificial censoring. To estimate the treatment effects, we took the multi-state model approach. We considered a multi-state model with five states. The primary endpoint was defined as clinical severity status, assessed by a 5-point ordinal scale on day 30. Differences between the treatment group and standard of care treatment group were calculated using a proportional odds model and shown as odds ratios. Additionally, the weighted cause-specific hazards and transition probabilities for each treatment arm were presented. RESULTS: Our study demonstrates that trial emulation with a multi-state model analysis is a suitable approach to address observational data limitations, evaluate treatment effects on clinically heterogeneous in-hospital death and discharge alive endpoints, and consider the intermediate state of admission to ICU. The multi-state model analysis allows us to summarize results using stacked probability plots that make it easier to interpret results. CONCLUSIONS: Extending the emulated target trial approach to multi-state model analysis complements treatment effectiveness analysis by gaining information on competing events. Combining two methodologies offers an option to address immortal time bias, confounding bias, and competing risk events. This methodological approach can provide additional insight for decision-making, particularly when data from randomized controlled trials (RCTs) are unavailable.

Exploring different research questions via complex multi-state models when using registry-based repeated prescriptions of antidepressants in women with breast cancer and a matched population comparison group.

BACKGROUND: Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be applied. We aim to explore different research questions using a series of multi-state models of increasing complexity when studying repeated prescriptions data, while also evaluating different modelling choices. METHODS: We develop a series of research questions regarding the probability of being under antidepressant medication across time using multi-state models, among Swedish women diagnosed with breast cancer (n = 18,313) and an age-matched population comparison group of cancer-free women (n = 92,454) using a register-based database (Breast Cancer Data Base Sweden 2.0). Research questions were formulated ranging from simple to more composite ones. Depending on the research question, multi-state models were built with structures ranging from simpler ones, like single-event survival analysis and competing risks, up to complex bidirectional and recurrent multi-state structures that take into account the recurring start and stop of medication. We also investigate modelling choices, such as choosing a time-scale for the transition rates and borrowing information across transitions. RESULTS: Each structure has its own utility and answers a specific research question. However, the more complex structures (bidirectional, recurrent) enable accounting for the intermittent nature of prescribed medication data. These structures deliver estimates of the probability of being under medication and total time spent under medication over the follow-up period. Sensitivity analyses over different definitions of the medication cycle and different choices of timescale when modelling the transition intensity rates show that the estimates of total probabilities of being in a medication cycle over follow-up derived from the complex structures are quite stable. CONCLUSIONS: Each research question requires the definition of an appropriate multi-state structure, with more composite ones requiring such an increase in the complexity of the multi-state structure. When a research question is related with an outcome of interest that repeatedly changes over time, such as the medication status based on prescribed medication, the use of novel multi-state models of adequate complexity coupled with sensible modelling choices can successfully address composite, more realistic research questions.

Similarity of competing risks models with constant intensities in an application to clinical healthcare pathways involving prostate cancer surgery.

The recent availability of routine medical data, especially in a university-clinical context, may enable the discovery of typical healthcare pathways, that is, typical temporal sequences of clinical interventions or hospital readmissions. However, such pathways are heterogeneous in a large provider such as a university hospital, and it is important to identify similar care pathways that can still be considered typical pathways. We understand the pathway as a temporal process with possible transitions from a single initial treatment state to hospital readmission of different types, which constitutes a competing risks setting. In this article, we propose a multi-state model-based approach to uncover pathway similarity between two groups of individuals. We describe a new bootstrap procedure for testing the similarity of constant transition intensities from two competing risk models. In a large simulation study, we investigate the performance of our similarity approach with respect to different sample sizes and different similarity thresholds. The studies are motivated by an application from urological clinical routine and we show how the results can be transferred to the application example.

Role of socioeconomic, lifestyle, and clinical factors in the progression of cardiometabolic multimorbidity in China: A 10-year prospective cohort study.

BACKGROUND AND AIMS: Cardiometabolic multimorbidity has become increasingly common over the past few decades. Little is known about how risk factors affect temporal progression of cardiometabolic multimorbidity. We aim to explore the role of socioeconomic, lifestyle, and clinical risk factors in the progression of cardiometabolic multimorbidity. METHODS AND RESULTS: This prospective cohort study included 56,587 participants aged ≥45 years who were free of diabetes, stroke, and heart disease. Three clusters of risk factors were assessed and each on a 5-point scale: socioeconomic, lifestyle, and clinical factors. We used multi-state models (MSMs) to examine the roles of risk factors in five transitions of multimorbidity trajectory: from healthy to first cardiometabolic disease, first cardiometabolic disease to cardiometabolic multimorbidity, health to mortality, first cardiometabolic disease to mortality, and cardiometabolic multimorbidity to mortality. In MSMs, socioeconomic (HR: 1.21; 95% CI: 1.19-1.25) and clinical (HR: 1.53; 95% CI: 1.51-1.56) scales were associated with the transition from health to first cardiometabolic. Socioeconomic (HR: 2.39; 95% CI: 2.24-2.54) and lifestyle (HR: 1.22; 95% CI: 1.18-1.26) scales were associated with the transitions from first disease to cardiometabolic multimorbidity. In addition, socioeconomic and lifestyle scales were associated with increased risk of mortality in people without cardiometabolic disease, with first cardiometabolic disease, and with cardiometabolic multimorbidity. CONCLUSIONS: Socioeconomic and lifestyle factors were not only important predictors of multimorbidity in those with existing cardiometabolic disease, but also important in shaping risk of mortality. However, clinical factors were the only key determinants of incidence of a first cardiometabolic disease.

Cyclic attractors of nonexpanding q-ary networks.

Discrete dynamical systems in which model components take on categorical values have been successfully applied to biological networks to study their global dynamic behavior. Boolean models in particular have been used extensively. However, multi-state models have also emerged as effective computational tools for the analysis of complex mechanisms underlying biological networks. Models in which variables assume more than two discrete states provide greater resolution, but this scheme introduces discontinuities. In particular, variables can increase or decrease by more than one unit in one time step. This can be corrected, without changing fixed points of the system, by applying an additional rule to each local activation function. On the other hand, if one is interested in cyclic attractors of their system, then this rule can potentially introduce new cyclic attractors that were not observed previously. This article makes some advancements in understanding the state space dynamics of multi-state network models with synchronous, sequential, or block-sequential update schedules and establishes conditions under which no new cyclic attractors are added to networks when the additional rule is applied. Our analytical results have the potential to be incorporated into modeling software and aid researchers in their analyses of biological multi-state networks.

Confirmatory adaptive group sequential designs for single-arm phase II studies with multiple time-to-event endpoints.

Existing methods concerning the assessment of long-term survival outcomes in one-armed trials are commonly restricted to one primary endpoint. Corresponding adaptive designs suffer from limitations regarding the use of information from other endpoints in interim design changes. Here we provide adaptive group sequential one-sample tests for testing hypotheses on the multivariate survival distribution derived from multi-state models, while making provision for data-dependent design modifications based on all involved time-to-event endpoints. We explicitly elaborate application of the methodology to one-sample tests for the joint distribution of (i) progression-free survival (PFS) and overall survival (OS) in the context of an illness-death model, and (ii) time to toxicity and time to progression while accounting for death as a competing event. Large sample distributions are derived using a counting process approach. Small sample properties are studied by simulation. An already established multi-state model for non-small cell lung cancer is used to illustrate the adaptive procedure.

Informed breeding dispersal following stochastic changes to patch quality in a pond-breeding amphibian.

The unidirectional movement of animals between breeding patches (i.e. breeding dispersal) has profound implications for the ecological and evolutionary dynamics of spatially structured populations. In spatiotemporally variable environments, individuals are expected to adjust their dispersal decisions according to information gathered on the environmental and/or social cues that reflect the fitness prospects in a given breeding patch (i.e. informed dispersal). A paucity of empirical work limited our understanding of the ability of animals to depart from low-quality breeding patches and settle in high-quality breeding patches. We examined the capacity of individuals to respond to stochastic changes in habitat quality via informed breeding dispersal in a pond-breeding amphibian. We conducted a 5-year (2015-2019) capture-recapture study of boreal toads Anaxyrus boreas boreas (n = 1,100) that breed in beaver ponds in western Wyoming, USA. During early spring of 2017, an extreme flooding event destroyed several beaver dams and resulted in the loss of breeding habitat. We used multi-state models to investigate how temporal changes in pond characteristics influenced breeding dispersal, and determine whether movement decisions were in accordance with prospects for reproductive fitness. Boreal toads more often departed from low-quality breeding ponds (without successful metamorphosis) and settled in high-quality breeding ponds (with successful metamorphosis). Movement decisions were context-dependent and associated with pond characteristics altered by beaver dam destruction. Individuals were more likely to depart from shallow ponds with high vegetation cover and settle in deep ponds with low vegetation cover. The probability of metamorphosis was related to the same environmental cues, suggesting that boreal toads assess the fitness prospects of a breeding patch and adjust movement decisions accordingly (i.e. informed breeding dispersal). We demonstrated that stochastic variability in environmental conditions and habitat quality can underpin dispersal behaviour in amphibians. Our study highlighted the mechanistic linkages between habitat change, movement behaviour and prospects for reproductive performance, which is critical for understanding how wild animals respond to rapid environmental change.

Development of a dynamic interactive web tool to enhance understanding of multi-state model analyses: MSMplus.

BACKGROUND: Multi-state models are used in complex disease pathways to describe a process where an individual moves from one state to the next, taking into account competing states during each transition. In a multi-state setting, there are various measures to be estimated that are of great epidemiological importance. However, increased complexity of the multi-state setting and predictions over time for individuals with different covariate patterns may lead to increased difficulty in communicating the estimated measures. The need for easy and meaningful communication of the analysis results motivated the development of a web tool to address these issues. RESULTS: MSMplus is a publicly available web tool, developed via the Shiny R package, with the aim of enhancing the understanding of multi-state model analyses results. The results from any multi-state model analysis are uploaded to the application in a pre-specified format. Through a variety of user-tailored interactive graphs, the application contributes to an improvement in communication, reporting and interpretation of multi-state analysis results as well as comparison between different approaches. The predicted measures that can be supported by MSMplus include, among others, the transition probabilities, the transition intensity rates, the length of stay in each state, the probability of ever visiting a state and user defined measures. Representation of differences, ratios and confidence intervals of the aforementioned measures are also supported. MSMplus is a useful tool that enhances communication and understanding of multi-state model analyses results. CONCLUSIONS: Further use and development of web tools should be encouraged in the future as a means to communicate scientific research.

Relaxing the assumption of constant transition rates in a multi-state model in hospital epidemiology.

BACKGROUND: Multi-state models are being increasingly used to capture complex disease pathways. The convenient formula of the exponential multi-state model can facilitate a quick and accessible understanding of the data. However, assuming time constant transition rates is not always plausible. On the other hand, obtaining predictions from a fitted model with time-dependent transitions can be challenging. One proposed solution is to utilise a general simulation algorithm to calculate predictions from a fitted multi-state model. METHODS: Predictions obtained from an exponential multi-state model were compared to those obtained from two different parametric models and to non-parametric Aalen-Johansen estimates. The first comparative approach fitted a multi-state model with transition-specific distributions, chosen separately based on the Akaike Information Criterion. The second approach was a Royston-Parmar multi-state model with 4 degrees of freedom, which was chosen as a reference model flexible enough to capture complex hazard shapes. All quantities were obtained analytically for the exponential and Aalen-Johansen approaches. The transition rates for the two comparative approaches were also obtained analytically, while all other quantities were obtained from the fitted models via a general simulation algorithm. Metrics investigated were: transition probabilities, attributable mortality (AM), population attributable fraction (PAF) and expected length of stay. This work was performed on previously analysed hospital acquired infection (HAI) data. By definition, a HAI takes three days to develop and therefore selected metrics were also predicted from time 3 (delayed entry). RESULTS: Despite clear deviations from the constant transition rates assumption, the empirical estimates of the transition probabilities were approximated reasonably well by the exponential model. However, functions of the transition probabilities, e.g. AM and PAF, were not well approximated and the comparative models offered considerable improvements for these metrics. They also provided consistent predictions with the empirical estimates in the case of delayed entry time, unlike the exponential model. CONCLUSION: We conclude that methods and software are readily available for obtaining predictions from multi-state models that do not assume constant transition rates. The multistate package in Stata facilitates a range of predictions with confidence intervals, which can provide a more comprehensive understanding of the data. User-friendly code is provided.

A hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models.

Multi-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. It is common to assume that the models are Markov, but the assumption can often be unrealistic. The Markov assumption is seldomly checked and violations can lead to biased estimation of many parameters of interest. This is a well known problem for the standard Aalen-Johansen estimator of transition probabilities and several alternative estimators, not relying on the Markov assumption, have been suggested. A particularly simple approach known as landmarking have resulted in the Landmark-Aalen-Johansen estimator. Since landmarking is a stratification method a disadvantage of landmarking is data reduction, leading to a loss of power. This is problematic for "less traveled" transitions, and undesirable when such transitions indeed exhibit Markov behaviour. Introducing the concept of partially non-Markov multi-state models, we suggest a hybrid landmark Aalen-Johansen estimator for transition probabilities. We also show how non-Markov transitions can be identified using a testing procedure. The proposed estimator is a compromise between regular Aalen-Johansen and landmark estimation, using transition specific landmarking, and can drastically improve statistical power. We show that the proposed estimator is consistent, but that the traditional variance estimator can underestimate the variance of both the hybrid and landmark estimator. Bootstrapping is therefore recommended. The methods are compared in a simulation study and in a real data application using registry data to model individual transitions for a birth cohort of 184 951 Norwegian men between states of sick leave, disability, education, work and unemployment.

The association between type 2 diabetes mellitus, hip fracture, and post-hip fracture mortality: a multi-state cohort analysis.

Type 2 diabetes mellitus (T2DM) is associated with an excess risk of fractures and overall mortality. This study compared hip fracture and post-hip fracture mortality in T2DM and non-diabetic subjects. The salient findings are that subjects in T2DM are at higher risk of dying after suffering a hip fracture. INTRODUCTION: Previous research suggests that individuals with T2DM are at an excess risk of both fractures and overall mortality, but their combined effect is unknown. Using multi-state cohort analyses, we estimate the association between T2DM and the transition to hip fracture, post-hip fracture mortality, and hip fracture-free all-cause death. METHODS: Population-based cohort from Catalonia, Spain, including all individuals aged 65 to 80 years with a recorded diagnosis of T2DM on 1 January 2006; and non-T2DM matched (up to 2:1) by year of birth, gender, and primary care practice. RESULTS: A total of 44,802 T2DM and 81,233 matched controls (53% women, mean age 72 years old) were followed for a median of 8 years: 23,818 died without fracturing and 3317 broke a hip, of whom 838 subsequently died. Adjusted HRs for hip fracture-free mortality were 1.32 (95% CI 1.28 to 1.37) for men and 1.72 (95% CI 1.65 to 1.79) for women. HRs for hip fracture were 1.24 (95% CI 1.08 to 1.43) and 1.48 (95% CI 1.36 to 1.60), whilst HRs for post-hip fracture mortality were 1.28 (95% CI 1.02 to 1.60) and 1.57 (95% CI 1.31 to 1.88) in men and women, respectively. CONCLUSION: T2DM individuals are at increased risk of hip fracture, post-hip fracture mortality, and hip fracture-free death. After adjustment, T2DM men were at a 28% higher risk of dying after suffering a hip fracture and women had 57% excess risk of post-hip fracture mortality.

Partially hidden multi-state modelling of a prolonged disease state defined by a composite outcome.

For rheumatic diseases, Minimal Disease Activity (MDA) is usually defined as a composite outcome which is a function of several individual outcomes describing symptoms or quality of life. There is ever increasing interest in MDA but relatively little has been done to characterise the pattern of MDA over time. Motivated by the aim of improving the modelling of MDA in psoriatic arthritis, the use of a two-state model to estimate characteristics of the MDA process is illustrated when there is particular interest in prolonged periods of MDA. Because not all outcomes necessary to define MDA are measured at all clinic visits, a partially hidden multi-state model with latent states is used. The defining outcomes are modelled as conditionally independent given these latent states, enabling information from all visits, even those with missing data on some variables, to be used. Data from the Toronto Psoriatic Arthritis Clinic are analysed to demonstrate improvements in accuracy and precision from the inclusion of data from visits with incomplete information on MDA. An additional benefit of this model is that it can be extended to incorporate explanatory variables, which allows process characteristics to be compared between groups. In the example, the effect of explanatory variables, modelled through the use of relative risks, is also summarised in a potentially more clinically meaningful manner by comparing times in states, and probabilities of visiting states, between patient groups.

Landmark estimation of transition probabilities in non-Markov multi-state models with covariates.

In non-Markov multi-state models, the traditional Aalen-Johansen (AJ) estimator for state transition probabilities is generally not valid. An alternative, suggested by Putter and Spitioni, is to analyse a subsample of the full data, consisting of the individuals present in a specific state at a given landmark time-point. The AJ estimator of occupation probabilities is then applied to the landmark subsample. Exploiting the result by Datta and Satten, that the AJ estimator is consistent for state occupation probabilities even in non-Markov models given that censoring is independent of state occupancy and times of transition between states, the landmark Aalen-Johansen (LMAJ) estimator provides consistent estimates of transition probabilities. So far, this approach has only been studied for non-parametric estimation without covariates. In this paper, we show how semi-parametric regression models and inverse probability weights can be used in combination with the LMAJ estimator to perform covariate adjusted analyses. The methods are illustrated by a simulation study and an application to population-wide registry data on work, education and health-related absence in Norway. Results using the traditional AJ estimator and the LMAJ estimator are compared, and show large differences in estimated transition probabilities for highly non-Markov multi-state models.

Nonparametric estimation of transition probabilities for a general progressive multi-state model under cross-sectional sampling.

Nonparametric estimation of the transition probability matrix of a progressive multi-state model is considered under cross-sectional sampling. Two different estimators adapted to possibly right-censored and left-truncated data are proposed. The estimators require full retrospective information before the truncation time, which, when exploited, increases efficiency. They are obtained as differences between two survival functions constructed for sub-samples of subjects occupying specific states at a certain time point. Both estimators correct the oversampling of relatively large survival times by using the left-truncation times associated with the cross-sectional observation. Asymptotic results are established, and finite sample performance is investigated through simulations. One of the proposed estimators performs better when there is no censoring, while the second one is strongly recommended with censored data. The new estimators are applied to data on patients in intensive care units (ICUs).

Population sensitivity of acute flaccid paralysis and environmental surveillance for serotype 1 poliovirus in Pakistan: an observational study.

BACKGROUND: To support poliomyelitis eradication in Pakistan, environmental surveillance (ES) of wastewater has been expanded alongside surveillance for acute flaccid paralysis (AFP). ES is a relatively new method of surveillance, and the population sensitivity of detecting poliovirus within endemic settings requires estimation. METHODS: Data for wild serotype 1 poliovirus from AFP and ES from January 2011 to September 2015 from 14 districts in Pakistan were analysed using a multi-state model framework. This framework was used to estimate the sensitivity of poliovirus detection from each surveillance source and parameters such as the duration of infection within a community. RESULTS: The location and timing of poliomyelitis cases showed spatial and temporal variability. The sensitivity of AFP surveillance to detect serotype 1 poliovirus infection in a district and its neighbours per month was on average 30.0% (95% CI 24.8-35.8) and increased with the incidence of poliomyelitis cases. The average population sensitivity of a single environmental sample was 59.4% (95% CI 55.4-63.0), with significant variation in site-specific estimates (median varied from 33.3-79.2%). The combined population sensitivity of environmental and AFP surveillance in a given month was on average 98.1% (95% CI 97.2-98.7), assuming four samples per month for each site. CONCLUSIONS: ES can be a highly sensitive supplement to AFP surveillance in areas with converging sewage systems. As ES for poliovirus is expanded, it will be important to identify factors associated with variation in site sensitivity, leading to improved site selection and surveillance system performance.

A multi-state approach to patients affected by chronic heart failure : The value added by administrative data.

Healthcare administrative databases are becoming more and more important and reliable sources of clinical and epidemiological information. They are able to track several interactions between a patient and the public healthcare system. In the present study, we make use of data extracted from the administrative data warehouse of Regione Lombardia, a region located in the northern part of Italy whose capital is Milan. Data are within a project aiming at providing a description of the epidemiology of Heart Failure (HF) patients at regional level, to profile health service utilization over time, and to investigate variations in patient care according to geographic area, socio-demographic characteristic and other clinical variables. We use multi-state models to estimate the probability of transition from (re)admission to discharge and death adjusting for covariates which are state dependent. To the best of our knowledge, this is the first Italian attempt of investigating which are the effects of pharmacological and outpatient cares covariates on patient's readmissions and death. This allows to better characterise disease progression and possibly identify what are the main determinants of a hospital admission and death in patients with Heart Failure.