An overview of semiparametric models in survival analysis

Finding the right hazard function for time‐to‐event modeling: A tutorial and Shiny application

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.

Survival time among patients who were diagnosed with tuberculosis, the precocious deaths and associated factors in southern Brazil

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.

Regression with a right-censored predictor using inverse probability weighting methods

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.

Análise de sobrevivência de mulheres com câncer de mama: modelos de riscos competitivos

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.