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Van Wijk RC, Simonsson USH. Finding the right hazard function for time‐to‐event modeling: A tutorial and Shiny application. CPT Pharmacometrics Syst Pharmacol 2022; 11:991-1001. [PMID: 35467083 PMCID: PMC9381898 DOI: 10.1002/psp4.12797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Revised: 03/15/2022] [Accepted: 03/21/2022] [Indexed: 11/28/2022] Open
Abstract
Parametric time‐to‐event analysis is an important pharmacometric method to predict the probability of an event up until a certain time as a function of covariates and/or drug exposure. Modeling is performed at the level of the hazard function describing the instantaneous rate of an event occurring at that timepoint. We give an overview of the parametric time‐to‐event analysis starting with graphical exploration by Kaplan–Meier plotting for the event data including censoring and nonparametric hazard estimators such as the kernel‐based visual hazard comparison for the underlying hazard. The most common hazard functions including the exponential, Gompertz, Weibull, log‐normal, log‐logistic, and circadian functions are described in detail. A Shiny application was developed to graphically guide the modeler which of the most common hazard functions presents a similar shape compared to the data in order to guide which hazard functions to test in the parametric time‐to‐event analysis. For the chosen hazard function(s), the Shiny application can additionally be used to explore corresponding parameter values to inform on suitable initial estimates for parametric modeling as well as on possible covariate or treatment relationships to certain parameters. Moreover, it can be used for the dissemination of results as well as communication, training, and workshops on time‐to‐event analysis. By guiding the modeler on which functions and what parameter values to test and compare as well as to assist in dissemination, the Shiny application developed here greatly supports the modeler in complicated parametric time‐to‐event modeling.
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Affiliation(s)
- Rob C. Van Wijk
- Department of Pharmaceutical Biosciences Uppsala University Uppsala Sweden
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Balakrishnan N, Mathew DC, Kattumannil SK. An exact test for exponentiality against renewal increasing mean residual life class. STATISTICS-ABINGDON 2022. [DOI: 10.1080/02331888.2022.2044328] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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dos Santos DT, Arroyo LH, Alves YM, Alves LS, Berra TZ, Crispim JDA, Alves JD, Ramos DAC, Alonso JB, de Assis IS, Ramos AV, Dessunti EM, Carvalho Pinto I, Palha PF, Arcêncio RA, Nunes C. Survival time among patients who were diagnosed with tuberculosis, the precocious deaths and associated factors in southern Brazil. Trop Med Health 2021; 49:31. [PMID: 33883022 PMCID: PMC8058757 DOI: 10.1186/s41182-021-00320-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 04/12/2021] [Indexed: 01/06/2023] Open
Abstract
BACKGROUND A diagnosis of tuberculosis (TB) does not mean that the disease will be treated successfully, since death may occur even among those who are known to the health services. Here, we aimed to analyze patient survival time from the diagnosis of TB to death, precocious deaths, and associated factors in southern Brazil. METHODS We conducted a longitudinal study with patients who were diagnosed with TB and who died due to the disease between 2008 and 2015 in southern Brazil. The starting point for measuring survival time was the patient's diagnosis date. Techniques for survival analysis were employed, including the Kaplan-Meier test and Cox's regression. A mixed-effect model was applied for identifying the associated factors to precocious deaths. Hazard ratio (HR) and odds ratio (OR) with 95% confidence intervals (95% CI) were estimated. We defined p value <0.05 as statistically significant for all statistics applied. RESULTS One hundred forty-six patients were included in the survival analysis, observing a median survival time of 23.5 days. We observed that alcoholism (HR=1.55, 95% CI=1.04-2.30) and being male (HR=6.49, 95% CI=1.03-2.68) were associated with death. The chance of precocious death within 60 days was 10.48 times greater than the chance of early death within 30 days. CONCLUSION Most of the deaths occurred within 2 months after the diagnosis, during the intensive phase of the treatment. The use of alcohol and gender were associated with death, revealing inequality between men and women. This study advanced knowledge regarding the vulnerability associated with mortality. These findings must be addressed to fill a gap in the care cascades for active TB and ensure equity in health.
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Affiliation(s)
- Danielle Talita dos Santos
- Ribeirão Preto College of Nursing (EERP/USP), University of São Paulo, Avenida dos Bandeirantes, 3900, Monte Alegre, Ribeirão Preto, São Paulo 14040-902 Brazil
| | - Luiz Henrique Arroyo
- Ribeirão Preto College of Nursing (EERP/USP), University of São Paulo, Avenida dos Bandeirantes, 3900, Monte Alegre, Ribeirão Preto, São Paulo 14040-902 Brazil
| | - Yan Mathias Alves
- Postgraduate in the Public Health Nursing Program, Ribeirão Preto College of Nursing at University of São Paulo, Ribeirão Preto, São Paulo Brazil
| | - Luana Seles Alves
- Postgraduate in the Public Health Nursing Program, Ribeirão Preto College of Nursing at University of São Paulo, Ribeirão Preto, São Paulo Brazil
| | - Thais Zamboni Berra
- Postgraduate in the Public Health Nursing Program, Ribeirão Preto College of Nursing at University of São Paulo, Ribeirão Preto, São Paulo Brazil
| | - Juliane de Almeida Crispim
- Inter-institucional Doctoral Program in Nursing, Ribeirão Preto College of Nursing at University of São Paulo, Ribeirão Preto, São Paulo Brazil
| | - Josilene Dália Alves
- Nursing Department, Federal University of Mato Grosso, Barra do Garças, Cuiabá, Brazil
| | | | - Jonas Bodini Alonso
- Ribeirão Preto College of Nursing (EERP/USP), University of São Paulo, Avenida dos Bandeirantes, 3900, Monte Alegre, Ribeirão Preto, São Paulo 14040-902 Brazil
| | | | - Antônio Vieira Ramos
- Postgraduate in the Public Health Nursing Program, Ribeirão Preto College of Nursing at University of São Paulo, Ribeirão Preto, São Paulo Brazil
| | | | - Ione Carvalho Pinto
- Postgraduate in the Public Health Nursing Program, Ribeirão Preto College of Nursing at University of São Paulo, Ribeirão Preto, São Paulo Brazil
| | - Pedro Fredemir Palha
- Postgraduate in the Public Health Nursing Program, Ribeirão Preto College of Nursing at University of São Paulo, Ribeirão Preto, São Paulo Brazil
| | - Ricardo Alexandre Arcêncio
- Ribeirão Preto College of Nursing (EERP/USP), University of São Paulo, Avenida dos Bandeirantes, 3900, Monte Alegre, Ribeirão Preto, São Paulo 14040-902 Brazil
| | - Carla Nunes
- NOVA National School of Public Health, Universidade NOVA de Lisboa, Lisbon, Portugal
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Matsouaka RA, Atem FD. Regression with a right-censored predictor using inverse probability weighting methods. Stat Med 2020; 39:4001-4015. [PMID: 32779274 DOI: 10.1002/sim.8704] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2019] [Revised: 06/27/2020] [Accepted: 06/29/2020] [Indexed: 12/23/2022]
Abstract
In a longitudinal study, measures of key variables might be incomplete or partially recorded due to drop-out, loss to follow-up, or early termination of the study occurring before the advent of the event of interest. In this paper, we focus primarily on the implementation of a regression model with a randomly censored predictor. We examine, particularly, the use of inverse probability weighting methods in a generalized linear model (GLM), when the predictor of interest is right-censored, to adjust for censoring. To improve the performance of the complete-case analysis and prevent selection bias, we consider three different weighting schemes: inverse censoring probability weights, Kaplan-Meier weights, and Cox proportional hazards weights. We use Monte Carlo simulation studies to evaluate and compare the empirical properties of different weighting estimation methods. Finally, we apply these methods to the Framingham Heart Study data as an illustrative example to estimate the relationship between age of onset of a clinically diagnosed cardiovascular event and low-density lipoprotein among cigarette smokers.
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Affiliation(s)
- Roland A Matsouaka
- Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina, USA.,Program for Comparative Effectiveness Methodology, Duke Clinical Research Institute, Durham, North Carolina, USA
| | - Folefac D Atem
- Department of Biostatistics and Data Science, University of Texas Health Science Center at Houston Houston, Houston, Texas, USA
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Ferraz RDO, Moreira-Filho DDC. Análise de sobrevivência de mulheres com câncer de mama: modelos de riscos competitivos. CIENCIA & SAUDE COLETIVA 2017; 22:3743-3754. [DOI: 10.1590/1413-812320172211.05092016] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2015] [Accepted: 03/26/2016] [Indexed: 11/22/2022] Open
Abstract
Resumo O objetivo deste estudo foi estimar os efeitos de fatores prognósticos na sobrevida do câncer de mama, como idade, estadiamento e extensão do tumor, utilizando modelos de riscos proporcionais de Cox e de riscos competitivos de Fine-Gray. É um estudo de coorte retrospectiva de base-populacional referente a 524 mulheres diagnosticadas com câncer de mama no período de 1993 a 1995, acompanhadas até 2011, residentes no município de Campinas, São Paulo, Brasil. O ponto de corte (cutoff) da variável idade foi definido utilizando-se modelos simples de Cox. Nos ajustes de modelos simples e múltiplo de Fine-Gray, a idade não foi significativa na presença de riscos competitivos e nem nos modelos de Cox, considerando-se, para ambas as modelagens, óbito por câncer de mama como desfecho de interesse. As curvas de sobrevidas estimadas por Kaplan-Meier evidenciaram diferenças expressivas para óbitos por câncer de mama e por riscos competitivos. As curvas de sobrevida por câncer de mama não apresentaram diferenças significativas quando comparados os grupos de idades, segundo teste de log rank. Os modelos de Cox e de Fine-Gray identificaram os mesmos fatores prognósticos que influenciavam na sobrevida do câncer de mama.
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Wu RF, Zheng M, Yu W. Subgroup Analysis with Time-to-Event Data Under a Logistic-Cox Mixture Model. Scand Stat Theory Appl 2016. [DOI: 10.1111/sjos.12213] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ruo-fan Wu
- Department of Statistics, School of Management; Fudan University
| | - Ming Zheng
- Department of Statistics, School of Management; Fudan University
| | - Wen Yu
- Department of Statistics, School of Management; Fudan University
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