Abstract
Survival analysis is one of the most common methods of statistical analysis in medicine. The statistical analysis of the transplantation (or death) probability dependent on the waiting time on the "waiting list" is a rare case when the survival analysis is used to estimate the time before the event rather than to indirectly assess the risks. However, for an assessment to be adequate, the reason for censoringmust be independent of the outcome of interest. Patients on the waiting list are not only at risk of dying, they can be excluded from the waiting list due to deterioration of the comorbid background or as a result of kidney transplantation. Kaplan – Meier, Nelson – Aalen estimates, as well as a cause-specific Cox proportional hazards regression model, are consciously biased estimates of survival in the presence of competing risks. Since competing events are censored, it is impossible to directly assess the impact of covariates on their frequency, because there is no direct relationship between the regression coefficients and the intensity of these events. The determination of the median waiting time on the basis of such analysis generates a selection bias, which inevitably leads to a biased assessment. Thus, in presence of competing risks, these methods allow us to investigate the features of cause-and-effect relationships, but do not allow us to make a prediction of the individual probability of a particular event based on the value of its covariates. In the regression model of competing risks, the regression coefficients are monotonically related to the cumulative incidence function and the competing events have a direct impact on the regression coefficients. Its significant advantage is the additive nature of the cumulative incidence functions of all possible events. In the study of etiological associations, it is better to use Cox regression model, which allows to estimate the size of the effect of various factors. The regression model of competing risks, in turn, has a greater prognostic value and allows to estimate the probability of a specific outcome within a certain time in a single patient.
Highlights
In presence of competing risks, these methods allow us to investigate the features of cause-and-effect relationships, but do not allow us to make a prediction of the individual probability of a particular event based on the value of its covariates
In the regression model of competing risks, the regression coefficients are monotonically related to the cumulative incidence function and the competing events have a direct impact on the regression coefficients
Its significant advantage is the additive nature of the cumulative incidence functions of all possible events
Summary
Статистический анализ вероятности трансплантации (или смерти) в зависимости от времени ожидания в «листе ожидания» – редкий случай, когда анализ выживаемости применяется действительно для оценки времени до наступления события, а не для косвенной оценки рисков. Оценки Каплана – Мейера, Нельсона – Аалена, как и причинно-специфическая регрессионная модель пропорциональных рисков Кокса, являются заведомо предвзятыми оценками выживаемости в условиях наличия конкурирующих рисков. Регрессионная модель конкурирующих рисков, в свою очередь, имеет бóльшую прогностическую ценность и позволяет оценить вероятность конкретного исхода в течение определенного времени у отдельно взятого пациента. Ключевые слова: анализ выживаемости, статистика, причинно-специфический риск, метод Каплана – Мейера, модель пропорциональных рисков Кокса, регрессионная модель Файна и Грея, конкурирующий риск. Особенности анализа выживаемости на примере пациентов в «листе ожидания» трансплантации почки.
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