Stacked probability plots of the extended illness-death model using constant transition hazards - an easy to use shiny app.

BACKGROUND: Extended illness-death models (a specific class of multistate models) are a useful tool to analyse situations like hospital-acquired infections, ventilation-associated pneumonia, and transfers between hospitals. The main components of these models are hazard rates and transition probabilities. Calculation of different measures and their interpretation can be challenging due to their complexity. METHODS: By assuming time-constant hazards, the complexity of these models becomes manageable and closed mathematical forms for transition probabilities can be derived. Using these forms, we created a tool in R to visualize transition probabilities via stacked probability plots. RESULTS: In this article, we present this tool and give some insights into its theoretical background. Using published examples, we give guidelines on how this tool can be used. Our goal is to provide an instrument that helps obtain a deeper understanding of a complex multistate setting. CONCLUSION: While multistate models (in particular extended illness-death models), can be highly complex, this tool can be used in studies to both understand assumptions, which have been made during planning and as a first step in analysing complex data structures. An online version of this tool can be found at https://eidm.imbi.uni-freiburg.de/ .

Surveillance Strategy after Curative Resection for Oesophageal Squamous Cell Cancer Using the Hazard Function.

BACKGROUND: The optimal surveillance period and frequency after curative resection for oesophageal squamous cell carcinoma (OSCC) remain unclear, and current guidelines are mainly based on traditional Kaplan-Meier analyses of cumulative incidence rather than risk analysis. The aim of this study was to determine a suitable follow-up surveillance program following oesophagectomy for OSCC using the hazard function. METHODS: A total of 1187 patients who underwent curative resection for OSCC between 2000 and 2014 were retrospectively analyzed. The changes in the estimated hazard rates (HRs) of recurrence over time were analyzed according to tumour-node-metastasis stage. RESULTS: Four hundred seventy-eight (40.2%) patients experienced recurrence during the follow-up period (median, 116.5 months). The risk of recurrence peaked at 9.2 months after treatment (HR = 0.0219) and then decreased to half the peak value at 24 months post-surgery. The HRs for Stage I and II patients were low (< 0.007) post-treatment. The HR for Stage III patients peaked at 9.9 months (HR = 0.031) and the hazard curve declined to a plateau at 30 months. Furthermore, the HR peaked at 10.8 months (HR = 0.052) in Stage IV patients and then gradually declined from 50 months. CONCLUSIONS: According to tumour-node-metastasis stage, changes in the HRs of postoperative recurrence in OSCC varied significantly. Intensive surveillance should be undertaken for 3 years in Stage III patients and for 4 years in Stage IV patients, followed by annual screening. For Stage I OSCC patients, a reduction in the surveillance intensity could be taken into consideration.

Partitioning mortality into growth-dependent and growth-independent hazards across 203 tropical tree species.

Tree death drives population dynamics, nutrient cycling, and evolution within plant communities. Mortality variation across species is thought to be influenced by different factors relative to variation within species. The unified model provided here separates mortality rates into growth-dependent and growth-independent hazards. This model creates the opportunity to simultaneously estimate these hazards both across and within species. Moreover, it provides the ability to examine how species traits affect growth-dependent and growth-independent hazards. We derive this unified mortality model using cross-validated Bayesian methods coupled with mortality data collected over three census intervals for 203 tropical rainforest tree species at Barro Colorado Island (BCI), Panama. We found that growth-independent mortality tended to be higher in species with lower wood density, higher light requirements, and smaller maximum diameter at breast height (dbh). Mortality due to marginal carbon budget as measured by near-zero growth rate tended to be higher in species with lower wood density and higher light demand. The total mortality variation attributable to differences among species was large relative to variation explained by these traits, emphasizing that much remains to be understood. This additive hazards model strengthens our capacity to parse and understand individual-level mortality in highly diverse tropical forests and hence to predict its consequences.

On null hypotheses in survival analysis.

The conventional nonparametric tests in survival analysis, such as the log-rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby, we can test hypotheses based on survival parameters that solve differential equations driven by cumulative hazards, and it is easy to implement the tests on a computer. We present simulations, suggesting that our tests perform well for several hypotheses in a range of scenarios. As an illustration, we apply our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomized controlled trial.

Evaluation of the treatment time-lag effect for survival data.

Medical treatments often take a period of time to reveal their impact on subjects, which is the so-called time-lag effect in the literature. In the survival data analysis literature, most existing methods compare two treatments in the entire study period. In cases when there is a substantial time-lag effect, these methods would not be effective in detecting the difference between the two treatments, because the similarity between the treatments during the time-lag period would diminish their effectiveness. In this paper, we develop a novel modeling approach for estimating the time-lag period and for comparing the two treatments properly after the time-lag effect is accommodated. Theoretical arguments and numerical examples show that it is effective in practice.

Systematic Review and Meta-analysis of Factors Influencing Survival Following Abdominal Aortic Aneurysm Repair.

BACKGROUND: Predicting long-term survival following repair is essential to clinical decision making when offering abdominal aortic aneurysm (AAA) treatment. A systematic review and a meta-analysis of pre-operative non-modifiable prognostic risk factors influencing patient survival following elective open AAA repair (OAR) and endovascular aneurysm repair (EVAR) was performed. METHODS: MEDLINE, Embase and Cochrane electronic databases were searched to identify all relevant articles reporting risk factors influencing long-term survival (≥1 year) following OAR and EVAR, published up to April 2015. Studies with <100 patients and those involving primarily ruptured AAA, complex repairs (supra celiac/renal clamp), and high risk patients were excluded. Primary risk factors were increasing age, sex, American Society of Anaesthesiologist (ASA) score, and comorbidities such as ischaemic heart disease (IHD), cardiac failure, hypertension, chronic obstructive pulmonary disease (COPD), renal impairment, cerebrovascular disease, peripheral vascular disease (PVD), and diabetes. Estimated risks were expressed as hazard ratio (HR). RESULTS: A total of 5,749 study titles/abstracts were retrieved and 304 studies were thought to be relevant. The systematic review included 51 articles and the meta-analysis 45. End stage renal disease and COPD requiring supplementary oxygen had the worst long-term survival, HR 3.15 (95% CI 2.45-4.04) and HR 3.05 (95% CI 1.93-4.80) respectively. An increase in age was associated with HR of 1.05 (95% CI 1.04-1.06) for every one year increase and females had a worse survival than men HR 1.15 (95% CI 1.07-1.27). An increase in ASA score and the presence of IHD, cardiac failure, hypertension, COPD, renal impairment, cerebrovascular disease, PVD, and diabetes were also factors associated with poor long-term survival. CONCLUSION: The result of this meta-analysis summarises and quantifies unmodifiable risk factors that influence late survival following AAA repair from the best available published evidence. The presence of these factors might assist in clinical decision making during discussion with patients regarding repair.

Does the diameter of abdominal aortic aneurysm influence late survival following abdominal aortic aneurysm repair? A systematic review and meta-analysis.

BACKGROUND: Studies reporting the influence of preoperative abdominal aortic aneurysm diameter on late survival following abdominal aortic aneurysm repair have not been consistent. AIM: To report the influence of abdominal aortic aneurysm diameter on overall long-term survival following abdominal aortic aneurysm repair. METHODS: Embase, Medline and the Cochrane electronic databases were searched to identify articles reporting the influence of abdominal aortic aneurysm diameter on late survival following open aneurysm repair and endovascular aneurysm repair published up to April 2015. Data were extracted from multivariate analysis; estimated risks were expressed as hazard ratio. RESULTS: A total of 2167 titles/abstracts were retrieved, of which 76 studies were fully assessed; 19 studies reporting on 22,104 patients were included. Preoperative larger abdominal aortic aneurysm size was associated with a worse survival compared to smaller aneurysms with a pooled hazard ratio of 1.14 (95% CI: 1.09-1.18), per 1 cm increase in abdominal aortic aneurysm diameter. Subgroup analysis of the different types of repair was performed and the hazard ratio (95% CI), for open aneurysm repair and endovascular aneurysm repair were 1.08 (1.03-1.12) and 1.20 (1.15-1.25), respectively, per 1 cm increase. There was a significant difference between the groups p < 0.02. CONCLUSIONS: This meta-analysis suggests that preoperative large abdominal aortic aneurysm independently influences overall late survival following abdominal aortic aneurysm repair, and this association was greater in abdominal aortic aneurysm repaired with endovascular aneurysm repair.

Model selection and diagnostics for joint modeling of survival and longitudinal data with crossing hazard rate functions.

Comparison of two hazard rate functions is important for evaluating treatment effect in studies concerning times to some important events. In practice, it may happen that the two hazard rate functions cross each other at one or more unknown time points, representing temporal changes of the treatment effect. Also, besides survival data, there could be longitudinal data available regarding some time-dependent covariates. When jointly modeling the survival and longitudinal data in such cases, model selection and model diagnostics are especially important to provide reliable statistical analysis of the data, which are lacking in the literature. In this paper, we discuss several criteria for assessing model fit that have been used for model selection and apply them to the joint modeling of survival and longitudinal data for comparing two crossing hazard rate functions. We also propose hypothesis testing and graphical methods for model diagnostics of the proposed joint modeling approach. Our proposed methods are illustrated by a simulation study and by a real-data example concerning two early breast cancer treatments.

Competing Risks Analysis of Kidney Transplant Waitlist Outcomes: Two Important Statistical Perspectives.

Modern competing risks analysis has 2 primary goals in clinical epidemiology as follows: (i) to maximize the clinician's knowledge of etiologic associations existing between potential predictor variables and various cause-specific outcomes via cause-specific hazard models, and (ii) to maximize the clinician's knowledge of noteworthy differences existing in cause-specific patient risk via cause-specific subdistribution hazard models (cumulative incidence functions [CIFs]). A perfect application exists in analyzing the following 4 distinct outcomes after listing for a deceased donor kidney transplant (DDKT): (i) receiving a DDKT, (ii) receiving a living donor kidney transplant (LDKT), (iii) waitlist removal due to patient mortality or a deteriorating medical condition, and (iv) waitlist removal due to other reasons. It is important to realize that obtaining a complete understanding of subdistribution hazard ratios (HRs) is simply not possible without first having knowledge of the multivariable relationships existing between the potential predictor variables and the cause-specific hazards (perspective #1), because the cause-specific hazards form the "building blocks" of CIFs. In addition, though we believe that a worthy and practical alternative to estimating the median waiting-time-to DDKT is to ask, "what is the conditional probability of the patient receiving a DDKT, given that he or she would not previously experience one of the competing events (known as the cause-specific conditional failure probability)," only an appropriate estimator of this conditional type of cumulative incidence should be used (perspective #2). One suggested estimator, the well-known "one minus Kaplan-Meier" approach (censoring competing events), simply does not represent any probability in the presence of competing risks and will almost always produce biased estimates (thus, it should never be used).

Regression Models and Multivariate Life Tables.

Semiparametric, multiplicative-form regression models are specified for marginal single and double failure hazard rates for the regression analysis of multivariate failure time data. Cox-type estimating functions are specified for single and double failure hazard ratio parameter estimation, and corresponding Aalen-Breslow estimators are specified for baseline hazard rates. Generalization to allow classification of failure times into a smaller set of failure types, with failures of the same type having common baseline hazard functions, is also included. Asymptotic distribution theory arises by generalization of the marginal single failure hazard rate estimation results of Danyu Lin, L.J. Wei and colleagues. The Péano series representation for the bivariate survival function in terms of corresponding marginal single and double failure hazard rates leads to novel estimators for pairwise bivariate survival functions and pairwise dependency functions, at specified covariate history. Related asymptotic distribution theory follows from that for the marginal single and double failure hazard rates and the continuity, compact differentiability of the Péano series transformation and bootstrap applicability. Simulation evaluation of the proposed estimation procedures are presented, and an application to multiple clinical outcomes in the Women's Health Initiative Dietary Modification Trial is provided. Higher dimensional marginal hazard rate regression modeling is briefly mentioned.

The channel capacity of visual awareness divided among multiple moving objects.

If attention is distributed among multiple moving objects, how does this divided attention affect the temporal process for detecting a specific target motion? Well-trained observers in three experiments monitored ongoing random motions of multiple objects, trying to rapidly detect non-random target motions. Response time hazard rates revealed a simple lawful structure of the detection processes. Target detection rates (hazard rates, in bits /s) were inversely proportional to the number of observed objects. Detection rates at any response time and in any condition equaled a product of two parallel (functionally independent and concurrent) visual processes: visual awareness and motion integration. The rate of visual awareness was inversely proportional to Set Size (n = 1-12), constant over time, and invariant with integrated motion information. Thus, a single rate parameter, indicating a constant channel capacity of visual awareness, described detection rates over a wide range of conditions and response times. During an initial interval of roughly 0.5 s, detection rates increased proportionally with the duration and length of motion; but after this initial integration, detection rates were constant, independent of the time the target remained undetected. The relationship between the quantity of visual information and detection rates was simpler than anticipated by contemporary theories of attention, perception, and performance.

Disaggregating activities of daily living limitations for predicting nursing home admission.

OBJECTIVE: To examine whether disaggregated activities of daily living (ADL) limitations better predict the risk of nursing home admission compared to conventionally used ADL disability counts. DATA SOURCES: We used panel data from the Health and Retirement Study (HRS) for years 1998-2010. The HRS is a nationally representative survey of adults older than 50 years (n = 18,801). STUDY DESIGN: We fitted Cox regressions in a continuous time survival model with age at first nursing home admission as the outcome. Time-varying ADL disability types were the key explanatory variables. PRINCIPAL FINDINGS: Of the six ADL limitations, bathing difficulty emerged as the strongest predictor of subsequent nursing home placement across cohorts. Eating and dressing limitations were also influential in driving admissions among more recent cohorts. Using simple ADL counts for analysis yielded similar adjusted R(2) s; however, the amount of explained variance doubled when we allowed the ADL disability measures to time-vary rather than remain static. CONCLUSIONS: Looking beyond simple ADL counts can provide health professionals insights into which specific disability types trigger long-term nursing home use. Functional disabilities measured closer in time carry more prognostic power than static measures.