Exploratory data analysis and the use of the hazard function for interpreting survival data: an investigator's primer.

1985 ◽  
Vol 3 (10) ◽  
pp. 1418-1431 ◽  
Author(s):  
R J Simes ◽  
M Zelen

This report discusses how one can use the hazard function to gain important insights on the patterns of failure in clinical studies when the principal endpoint is a time metric. These new insights may help gain increased understanding into the pathogenesis of a chronic disease and how it is affected by treatment intervention. The qualitative behavior of the hazard function can reveal whether mortality is increasing, decreasing, or is constant over time. Simple graphic plots are all that is necessary to show characteristic failure patterns. These informal procedures are in the spirit of carrying out exploratory analyses on the data. This report discusses the organization of clinical data using a "branch and leaf" plot, outlines the calculation of the hazard function and life table, and uses examples from lung cancer and uveal melanoma to illustrate calculations and ways of interpreting hazard functions.

2017 ◽  
Author(s):  
Sophie K. Herbst ◽  
Lorenz Fiedler ◽  
Jonas Obleser

AbstractHuman observers automatically extract temporal contingencies from the environment and predict the onset of future events. Temporal predictions are modelled by the hazard function, which describes the instantaneous probability for an event to occur given it has not occurred yet. Here, we tackle the question of whether and how the human brain tracks continuous temporal hazard on a moment-to-moment basis, and how flexibly it adjusts to strictly implicit variations in the hazard function. We applied an encoding-model approach to human electroencephalographic (EEG) data recorded during a pitch-discrimination task, in which we implicitly manipulated temporal predictability of the target tones by varying the interval between cue and target tone (the foreperiod). Critically, temporal predictability was either solely driven by the passage of time (resulting in a monotonic hazard function), or was modulated to increase at intermediate foreperiods (resulting in a modulated hazard function with a peak at the intermediate foreperiod). Forward encoding models trained to predict the recorded EEG signal from different temporal hazard functions were able to distinguish between experimental conditions, showing that implicit variations of temporal hazard bear tractable signatures in the human electroencephalogram. Notably, this tracking signal was reconstructed best from the supplementary motor area (SMA), underlining this area’s link to cognitive processing of time. Our results underline the relevance of temporal hazard to cognitive processing, and show that the predictive accuracy of the encoding-model approach can be utilised to track abstract time-resolved stimuli.Significance StatementExtracting temporal predictions from sensory input allows to process future input more efficiently and to prepare responses in time. In mathematical terms, temporal predictions can be described by the hazard function, modelling the probability of an event to occur over time. Here, we show that the human EEG tracks temporal hazard in an implicit foreperiod paradigm. Forward encoding models trained to predict the recorded EEG signal from different temporal-hazard functions were able to distinguish between experimental conditions that differed in their build-up of hazard over time. These neural signatures of tracking temporal hazard converge with the extant literature on temporal processing and provide new evidence that the supplementary motor area tracks hazard under strictly implicit timing conditions.


2020 ◽  
Author(s):  
Nádia P. Kozievitch ◽  
Tatiana M. C. Gadda ◽  
Keiko V. O. Fonseca ◽  
Marcelo O. Rosa ◽  
Luiz C. Gomes Jr. ◽  
...  

Smart transportation systems have been providing more data over time (such as bus routes, users, smartphones, etc.). Such data provides a number of opportunities to identify various facets of user behavior and traffic trends. In this paper we address some of the urban mobility challenges (already discussed by the Brazilian Computer Society), from a number of different perspectives, including (i) pattern discovery, (ii) statistical analysis, (iii) data integration, and (iv) open and connected data. In particular, we present an exploratory data analysis with GIS for public transportation toward a case study in Curitiba, Brazil.


2019 ◽  
Vol 151 ◽  
pp. 1004-1009 ◽  
Author(s):  
Hicham Hammouchi ◽  
Othmane Cherqi ◽  
Ghita Mezzour ◽  
Mounir Ghogho ◽  
Mohammed El Koutbi

2002 ◽  
Vol 33 (2) ◽  
pp. 173-190 ◽  
Author(s):  
I. W. McKeague ◽  
M. Tighiouart

In this article, we analyse right censored survival data by modelling their common hazard function nonparametrically. The hazard rate is assumed to be a stochastic process, with sample paths taking the form of step functions. This process jumps at times that form a time-homogeneous Poisson process, and a class of Markov random fields is used to model the values of these sample paths. Features of the posterior distribution, such as the mean hazard rate and survival probabilities, are evaluated using the Metropolis--Hastings--Green algorithm. We illustrate our methodology by simulation examples.


Author(s):  
H Rehman ◽  
Navin Chandra ◽  
Fatemeh Sadat Hosseini-Baharanchi ◽  
Ahmad Reza Baghestani

In the analysis of survival data, cause specific quantities of competing risks get considerable attention as compared to latent failure time approach. This article focuses on parametric regression analysis of survival data using cause specific hazard function with Burr type XII distribution as a baseline model. We obtained maximum likelihood and Bayes estimates of cumulative cause specific hazard functions under competing risk setup. For Bayesian point of view we proposed a class of informative priors for parameters to observe the comprehensive compatibility and their effectiveness under two different loss functions. The appropriateness of model is measured by the simulation study. Finally, we illustrate the proposed methodologies using bone marrow transplant data from the Princess Margaret Hospital Ontario, Canada.


2001 ◽  
Vol 09 (03) ◽  
pp. 221-233 ◽  
Author(s):  
A. V. ZORIN ◽  
A. D. TSODIKOV ◽  
G. M. ZHARINOV ◽  
A. Y. YAKOVLEV

The shape of the hazard function is of great interest in studies of the efficacy of cancer treatment and post-treatment cancer surveillance. We present estimates of the hazard rates obtained from data on survival of patients with cervical cancer and discuss associated methodological problems. Our study was carried out on survival data for 1826 women with cancer of the cervix uteri stratified by clinical stage and tumor growth pattern. We used nonparametric and various smoothing techniques for estimating the hazard function from the data; these were a nonparametric estimator based on the Nelson-Aalen method and its kernel counterparts, the kernel local likelihood estimator with a data-adaptive bandwidth, and a parametric estimator specifically designed for two-component hazards. For all categories of patients, the estimated hazard functions pass through a clear-cut maximum, tending to zero as the follow-up time becomes sufficiently long. In one stratum of patients we observed a bimodal shape of the hazard function. There are two alternative models that provide equally plausible explanations of this observation; one of them attributes the observed pattern of the hazard function to a certain heterogeneity of tumor cell population, while the competing model refers to a heterogeneity of the subsample of patients under study. Providing the probability of cure is high, as is the case in our setting, there is no way to discriminate between the two models on the basis of survival data.


2013 ◽  
Author(s):  
Stephen J. Tueller ◽  
Richard A. Van Dorn ◽  
Georgiy Bobashev ◽  
Barry Eggleston

Author(s):  
Jayesh S

UNSTRUCTURED Covid-19 outbreak was first reported in Wuhan, China. The deadly virus spread not just the disease, but fear around the globe. On January 2020, WHO declared COVID-19 as a Public Health Emergency of International Concern (PHEIC). First case of Covid-19 in India was reported on January 30, 2020. By the time, India was prepared in fighting against the virus. India has taken various measures to tackle the situation. In this paper, an exploratory data analysis of Covid-19 cases in India is carried out. Data namely number of cases, testing done, Case Fatality ratio, Number of deaths, change in visits stringency index and measures taken by the government is used for modelling and visual exploratory data analysis.


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