Survival Analysis

2009 ◽  
Author(s):  
Jonathan Golub
Keyword(s):  
Time Series ◽  
Survival Analysis ◽  
Proportional Hazards ◽  
Temporal Information ◽  
Parametric Models ◽  
Cox Models ◽  
Standard Practice ◽  
Baseline Hazard ◽  
Political Processes ◽  
Proportional Hazards Assumption

This article provides a discussion of survival analysis that presents another way to incorporate temporal information into analysis in ways that give advantages similar to those from using time series. It describes the main choices researchers face when conducting survival analysis and offers a set of methodological steps that should become standard practice. After introducing the basic terminology, it shows that there is little to lose and much to gain by employing Cox models instead of parametric models. Cox models are superior to parametric models in three main respects: they provide more reliable treatment of the baseline hazard and superior handling of the proportional hazards assumption, and they are the best for handling tied data. Moreover, the illusory benefits of parametric models are presented. The greater use of Cox models enables researchers to elicit more useful information from their data, and allows for more reliable substantive inferences about important political processes.

It’s Déjà Vu All Over Again: Using Multiple-Spell Discrete-Time Survival Analysis

1995 ◽  
Vol 20 (1) ◽  
pp. 41-67 ◽  
Author(s):  
John B. Willett ◽  
Judith D. Singer
Keyword(s):  
Survival Analysis ◽  
Discrete Time ◽  
Proportional Hazards ◽  
Suicide Attempts ◽  
Teaching Profession ◽  
Single Event ◽  
Cognitive Reasoning ◽  
Proportional Hazards Assumption ◽  
Discrete Time Survival Analysis ◽  
Time Invariant

Multiple-spell discrete-time survival analysis can be used to investigate the repeated occurrence of a single event, or the sequential occurrence of disparate events, including: students’ and teachers’ entries into, and exits from, school; childrens’ progress through stages of cognitive reasoning; disturbed adolescents’ repeated suicide attempts; and so forth. In this article, we introduce and illustrate the method using longitudinal data on exit from, and reentry into, the teaching profession. The advantages of the approach include: (a) applicability to many educational problems; (b) easy inclusion of time-invariant and time-varying predictors; (c) minimal assumptions—no proportional-hazards assumption is invoked and so the effects of predictors can vary over time within, and across, spells; and (d) all statistical models can be fit with a standard logistic regression package.

scholarly journals A Review of Survival Analysis Methods Used in NICE Technology Appraisals of Cancer Treatments: Consistency, Limitations, and Areas for Improvement

2019 ◽  
Vol 39 (8) ◽  
pp. 899-909 ◽  
Author(s):  
Helen Bell Gorrod ◽  
Ben Kearns ◽  
John Stevens ◽  
Praveen Thokala ◽  
Alexander Labeit ◽  
...  
Keyword(s):  
Survival Analysis ◽  
Model Selection ◽  
Proportional Hazards ◽  
Survival Function ◽  
Progression Free Survival ◽  
Parametric Models ◽  
Survival Functions ◽  
Cancer Treatments ◽  
Hazard Functions ◽  
Support Unit

Objectives. In June 2011, the National Institute for Health and Care Excellence (NICE) Decision Support Unit published a Technical Support Document (TSD) providing recommendations on survival analysis for NICE technology appraisals (TAs). Survival analysis outputs are influential inputs into economic models estimating the cost-effectiveness of new cancer treatments. Hence, it is important that systematic and justifiable model selection approaches are used. This study investigates the extent to which the TSD recommendations have been followed since its publication. Methods. We reviewed NICE cancer TAs completed between July 2011 and July 2017. Information on survival analyses undertaken and associated critiques for overall survival (OS) and progression-free survival were extracted from the company submissions, Evidence Review Group (ERG) reports, and final appraisal determination documents. Results. Information was extracted from 58 TAs. Only 4 (7%) followed all TSD recommendations for OS outcomes. The vast majority (91%) compared a range of common parametric models and assessed their fit to the data (86%). Only a minority of TAs included an assessment of the shape of the hazard function (38%) or proportional hazards assumption (40%). Validation of the extrapolated portion of the survival function using external data was attempted in a minority of TAs (40%). Extrapolated survival functions were frequently criticized by ERGs (71%). Conclusions. Survival analysis within NICE TAs remains suboptimal, despite publication of the TSD. Model selection is not undertaken in a systematic way, resulting in inconsistencies between TAs. More attention needs to be given to assessing hazard functions and validation of extrapolated survival functions. Novel methods not described in the TSD have been used, particularly in the context of immuno-oncology, suggesting that an updated TSD may be of value.

scholarly journals Survival Following Road Traffic Accidents in a Level-I Trauma Center, Parametric versus Semi-Parametric Survival Models

2021 ◽  
Keyword(s):  
Multivariate Analysis ◽  
Survival Analysis ◽  
Statistical Models ◽  
Trauma Center ◽  
Proportional Hazards ◽  
Road Traffic ◽  
Weibull Model ◽  
Parametric Models ◽  
Level I ◽  
Parametric Survival

Background: Simulation studies present an important statistical tool to investigate the performance, properties, and adequacy of statistical models in pre-specified situations. The proportional hazards model of survival analysis is one of the most important statistical models in medical studies. This study aimed to investigate the underlying one-month survival of road traffic accident (RTA) victims in a Level 1 Trauma Center in Iran using parametric and semi-parametric survival analysis models from the viewpoint of post-crash care-provider in 2017. Materials and Methods: This retrospective cohort study (restudy) was conducted at Level-I Trauma Center of Shiraz, Iran, from January to December 2017. Considering the fact that certain covariates acting on survival may take a non-homogenous risk pattern leading to the violation of proportional hazards assumption in Cox-PH, the parametric survival modeling was employed to inspect the multiplicative effect of all covariates on the hazard. Distributions of choice were Exponential, Weibull and Lognormal. Parameters were estimated using the Akaike Results: Survival analysis was conducted on 8,621 individuals for whom the length of stay (observation period) was between 1 and 89 days. In total, 141 death occurred during this time. The log-rank test revealed inequality of survival functions across various categories of age, injury mechanism, injured body region, injury severity score, and nosocomial infections. Although the risk level in the Cox model is almost the same as that in the results of the parametric models, the Weibull model in the multivariate analysis yields better results, according to the Akaike criterion. Conclusion: In multivariate analysis, parametric models were more efficient than other models. Some results were similar in both parametric and semi-parametric models. In general, parametric models and among them the Weibull model was more efficient than other models.

scholarly journals Adapting the Default Weighted Survival Analysis Modelling Approach to Model IFRS 9 LGD

Risks ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 103
Author(s):  
Morne Joubert ◽  
Tanja Verster ◽  
Helgard Raubenheimer ◽  
Willem D. Schutte
Keyword(s):  
Survival Analysis ◽  
Financial Reporting ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Survival Curve ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Reporting Standard ◽  
International Financial Reporting Standard ◽  
Ifrs 9

Survival analysis is one of the techniques that could be used to predict loss given default (LGD) for regulatory capital (Basel) purposes. When using survival analysis to model LGD, a proposed methodology is the default weighted survival analysis (DWSA) method. This paper is aimed at adapting the DWSA method (used to model Basel LGD) to estimate the LGD for International Financial Reporting Standard (IFRS) 9 impairment requirements. The DWSA methodology allows for over recoveries, default weighting and negative cashflows. For IFRS 9, this methodology should be adapted, as the estimated LGD is a function of in the expected credit losses (ECL). Our proposed IFRS 9 LGD methodology makes use of survival analysis to estimate the LGD. The Cox proportional hazards model allows for a baseline survival curve to be adjusted to produce survival curves for different segments of the portfolio. The forward-looking LGD values are adjusted for different macro-economic scenarios and the ECL is calculated for each scenario. These ECL values are probability weighted to produce a final ECL estimate. We illustrate our proposed IFRS 9 LGD methodology and ECL estimation on a dataset from a retail portfolio of a South African bank.

Reporting of Multivariable Methods in the Medical Literature

2008 ◽  
Vol 56 (7) ◽  
pp. 954-957 ◽  
Author(s):  
Jeanette M. Tetrault ◽  
Maor Sauler ◽  
Carolyn K. Wells ◽  
John Concato
Keyword(s):  
Logistic Regression ◽  
New England ◽  
Proportional Hazards ◽  
Medical Literature ◽  
Multivariable Analysis ◽  
Cox Proportional Hazards ◽  
Primary Method ◽  
Primary Analysis ◽  
Proportional Hazards Assumption ◽  
Complete Reporting

BackgroundMultivariable models are frequently used in the medical literature, but many clinicians have limited training in these analytic methods. Our objective was to assess the prevalence of multivariable methods in medical literature, quantify reporting of methodological criteria applicable to most methods, and determine if assumptions specific to logistic regression or proportional hazards analysis were evaluated.MethodsWe examined all original articles in Annals of Internal Medicine, British Medical Journal, Journal of the American Medical Association, Lancet, and New England Journal of Medicine, from January through June 2006. Articles reporting multivariable methods underwent a comprehensive review; reporting of methodological criteria was based on each article's primary analysis.ResultsAmong 452 articles, 272 (60%) used multivariable analysis; logistic regression (89 [33%] of 272) and proportional hazards (76 [28%] of 272) were most prominent. Reporting of methodological criteria, when applicable, ranged from 5% (12/265) for assessing influential observations to 84% (222/265) for description of variable coding. Discussion of interpreting odds ratios occurred in 13% (12/89) of articles reporting logistic regression as the primary method and discussion of the proportional hazards assumption occurred in 21% (16/76) of articles using Cox proportional hazards as the primary method.ConclusionsMore complete reporting of multivariable analysis in the medical literature can improve understanding, interpretation, and perhaps application of these methods.

scholarly journals Testing the proportional hazards assumption in cox regression and dealing with possible non-proportionality in total joint arthroplasty research: methodological perspectives and review

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Ilari Kuitunen ◽  
Ville T. Ponkilainen ◽  
Mikko M. Uimonen ◽  
Antti Eskelinen ◽  
Aleksi Reito
Keyword(s):  
Survival Analysis ◽  
Regression Model ◽  
Total Joint Arthroplasty ◽  
Full Text ◽  
Proportional Hazards ◽  
Cox Regression ◽  
Joint Arthroplasty ◽  
Central Research ◽  
Cox Regression Model ◽  
Pubmed Database

Abstract Background Survival analysis and effect of covariates on survival time is a central research interest. Cox proportional hazards regression remains as a gold standard in the survival analysis. The Cox model relies on the assumption of proportional hazards (PH) across different covariates. PH assumptions should be assessed and handled if violated. Our aim was to investigate the reporting of the Cox regression model details and testing of the PH assumption in survival analysis in total joint arthroplasty (TJA) studies. Methods We conducted a review in the PubMed database on 28th August 2019. A total of 1154 studies were identified. The abstracts of these studies were screened for words “cox and “hazard*” and if either was found the abstract was read. The abstract had to fulfill the following criteria to be included in the full-text phase: topic was knee or hip TJA surgery; survival analysis was used, and hazard ratio reported. If all the presented criteria were met, the full-text version of the article was then read. The full-text was included if Cox method was used to analyze TJA survival. After accessing the full-texts 318 articles were included in final analysis. Results The PH assumption was mentioned in 114 of the included studies (36%). KM analysis was used in 281 (88%) studies and the KM curves were presented graphically in 243 of these (87%). In 110 (45%) studies, the KM survival curves crossed in at least one of the presented figures. The most common way to test the PH assumption was to inspect the log-minus-log plots (n = 59). The time-axis division method was the most used corrected model (n = 30) in cox analysis. Of the 318 included studies only 63 (20%) met the following criteria: PH assumption mentioned, PH assumption tested, testing method of the PH assumption named, the result of the testing mentioned, and the Cox regression model corrected, if required. Conclusions Reporting and testing of the PH assumption and dealing with non-proportionality in hip and knee TJA studies was limited. More awareness and education regarding the assumptions behind the used statistical models among researchers, reviewers and editors are needed to improve the quality of TJA research. This could be achieved by better collaboration with methodologists and statisticians and introducing more specific reporting guidelines for TJA studies. Neglecting obvious non-proportionality undermines the overall research efforts since causes of non-proportionality, such as possible underlying pathomechanisms, are not considered and discussed.

scholarly journals Evaluation of Changes on World Stock Exchanges in Connection with the SARS-CoV-2 Pandemic. Survival Analysis Methods

Risks ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 121
Author(s):  
Beata Bieszk-Stolorz ◽  
Krzysztof Dmytrów
Keyword(s):  
Survival Analysis ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Stock Exchange ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Stock Exchanges ◽  
Analysis Methods ◽  
Hazards Model ◽  
Kaplan Meier

The aim of our research was to compare the intensity of decline and then increase in the value of basic stock indices during the SARS-CoV-2 coronavirus pandemic in 2020. The survival analysis methods used to assess the risk of decline and chance of rise of the indices were: Kaplan–Meier estimator, logit model, and the Cox proportional hazards model. We observed the highest intensity of decline in the European stock exchanges, followed by the American and Asian plus Australian ones (after the fourth and eighth week since the peak). The highest risk of decline was in America, then in Europe, followed by Asia and Australia. The lowest risk was in Africa. The intensity of increase was the highest in the fourth and eleventh week since the minimal value had been reached. The highest odds of increase were in the American stock exchanges, followed by the European and Asian (including Australia and Oceania), and the lowest in the African ones. The odds and intensity of increase in the stock exchange indices varied from continent to continent. The increase was faster than the initial decline.

scholarly journals Systematic Water Fraction Estimation for a Global and Daily Surface Water Time-Series

2021 ◽  
Vol 13 (14) ◽  
pp. 2675
Author(s):  
Stefan Mayr ◽  
Igor Klein ◽  
Martin Rutzinger ◽  
Claudia Kuenzer
Keyword(s):  
Time Series ◽  
Surface Water ◽  
Spatial Resolution ◽  
Pure Water ◽  
Feature Space ◽  
Observation Time ◽  
Temporal Information ◽  
Landsat 8 ◽  
Water Fraction ◽  
Classification Probability

Fresh water is a vital natural resource. Earth observation time-series are well suited to monitor corresponding surface dynamics. The DLR-DFD Global WaterPack (GWP) provides daily information on globally distributed inland surface water based on MODIS (Moderate Resolution Imaging Spectroradiometer) images at 250 m spatial resolution. Operating on this spatiotemporal level comes with the drawback of moderate spatial resolution; only coarse pixel-based surface water quantification is possible. To enhance the quantitative capabilities of this dataset, we systematically access subpixel information on fractional water coverage. For this, a linear mixture model is employed, using classification probability and pure pixel reference information. Classification probability is derived from relative datapoint (pixel) locations in feature space. Pure water and non-water reference pixels are located by combining spatial and temporal information inherent to the time-series. Subsequently, the model is evaluated for different input sets to determine the optimal configuration for global processing and pixel coverage types. The performance of resulting water fraction estimates is evaluated on the pixel level in 32 regions of interest across the globe, by comparison to higher resolution reference data (Sentinel-2, Landsat 8). Results show that water fraction information is able to improve the product’s performance regarding mixed water/non-water pixels by an average of 11.6% (RMSE). With a Nash-Sutcliffe efficiency of 0.61, the model shows good overall performance. The approach enables the systematic provision of water fraction estimates on a global and daily scale, using only the reflectance and temporal information contained in the input time-series.

scholarly journals On the Connection between the GEP Performances and the Time Series Properties

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1853
Author(s):  
Alina Bărbulescu ◽  
Cristian Ștefan Dumitriu
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Functional Form ◽  
Financial Time Series ◽  
Gene Expression Programming ◽  
Parametric Models ◽  
Statistical Characteristics ◽  
Data Series ◽  
Financial Time ◽  
Data Generating Process

Artificial intelligence (AI) methods are interesting alternatives to classical approaches for modeling financial time series since they relax the assumptions imposed on the data generating process by the parametric models and do not impose any constraint on the model’s functional form. Even if many studies employed these techniques for modeling financial time series, the connection of the models’ performances with the statistical characteristics of the data series has not yet been investigated. Therefore, this research aims to study the performances of Gene Expression Programming (GEP) for modeling monthly and weekly financial series that present trend and/or seasonality and after the removal of each component. It is shown that series normality and homoskedasticity do not influence the models’ quality. The trend removal increases the models’ performance, whereas the seasonality elimination results in diminishing the goodness of fit. Comparisons with ARIMA models built are also provided.

scholarly journals Relating Spatiotemporal Patterns of Forest Fires Burned Area and Duration to Diurnal Land Surface Temperature Anomalies

2018 ◽  
Vol 10 (11) ◽  
pp. 1777 ◽  
Author(s):  
Carmine Maffei ◽  
Silvia Alfieri ◽  
Massimo Menenti
Keyword(s):  
Remote Sensing ◽  
Time Series ◽  
Surface Temperature ◽  
Land Surface Temperature ◽  
Forest Fires ◽  
Land Surface ◽  
Fire Danger ◽  
Parametric Models ◽  
Burned Area ◽  
Informative Content

Forest fires are a major source of ecosystem disturbance. Vegetation reacts to meteorological factors contributing to fire danger by reducing stomatal conductance, thus leading to an increase of canopy temperature. The latter can be detected by remote sensing measurements in the thermal infrared as a deviation of observed land surface temperature (LST) from climatological values, that is as an LST anomaly. A relationship is thus expected between LST anomalies and forest fires burned area and duration. These two characteristics are indeed controlled by a large variety of both static and dynamic factors related to topography, land cover, climate, weather (including those affecting LST) and anthropic activity. To investigate the predicting capability of remote sensing measurements, rather than constructing a comprehensive model, it would be relevant to determine whether anomalies of LST affect the probability distributions of burned area and fire duration. This research approached the outlined knowledge gap through the analysis of a dataset of forest fires in Campania (Italy) covering years 2003–2011 against estimates of LST anomaly. An LST climatology was first computed from time series of daily Aqua-MODIS LST data (product MYD11A1, collection 6) over the longest available sequence of complete annual datasets (2003–2017), through the Harmonic Analysis of Time Series (HANTS) algorithm. HANTS was also used to create individual annual models of LST data, to minimize the effect of varying observation geometry and cloud contamination on LST estimates while retaining its seasonal variation. LST anomalies where thus quantified as the difference between LST annual models and LST climatology. Fire data were intersected with LST anomaly maps to associate each fire with the LST anomaly value observed at its position on the day previous to the event. Further to this step, the closest probability distribution function describing burned area and fire duration were identified against a selection of parametric models through the maximization of the Anderson-Darling goodness-of-fit. Parameters of the identified distributions conditional to LST anomaly where then determined along their confidence intervals. Results show that in the study area log-transformed burned area is described by a normal distribution, whereas log-transformed fire duration is closer to a generalized extreme value (GEV) distribution. The parameters of these distributions conditional to LST anomaly show clear trends with increasing LST anomaly; significance of this observation was verified through a likelihood ratio test. This confirmed that LST anomaly is a covariate of both burned area and fire duration. As a consequence, it was observed that conditional probabilities of extreme events appear to increase with increasing positive deviations of LST from its climatology values. This confirms the stated hypothesis that LST anomalies affect forest fires burned area and duration and highlights the informative content of time series of LST with respect to fire danger.

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