In this paper, we discuss the bivariate Birnbaum-Saunders accelerated lifetime model, in which we have modeled the dependence structure of bivariate survival data through the use of frailty models. Specifically, we propose the bivariate model Birnbaum-Saunders with the following frailty distributions: gamma, positive stable and logarithmic series. We present a study of inference and diagnostic analysis for the proposed model, more concisely, are proposed a diagnostic analysis based in local influence and residual analysis to assess the fit model, as well as, to detect influential observations. In this regard, we derived the normal curvatures of local influence under different perturbation schemes and we performed some simulation studies for assessing the potential of residuals to detect misspecification in the systematic component, the presence in the stochastic component of the model and to detect outliers. Finally, we apply the methodology studied to real data set from recurrence in times of infections of 38 kidney patients using a portable dialysis machine, we analyzed these data considering independence within the pairs and using the bivariate Birnbaum-Saunders accelerated lifetime model, so that we could make a comparison and verify the importance of modeling dependence within the times of infection associated with the same patient.

在本文中，我们讨论了双变量 Birnbaum-Saunders 加速寿命模型，其中我们通过使用脆弱模型对双变量生存数据的依赖结构进行了建模。具体来说，我们提出了具有以下脆弱分布的双变量模型 Birnbaum-Saunders：伽马、正稳定和对数级数。我们对所提出的模型进行了推理和诊断分析的研究，更简洁地说，提出了一种基于局部影响和残差分析的诊断分析，以评估拟合模型，以及检测有影响的观察结果。在这方面，我们推导出了不同扰动方案下局部影响的法向曲率，并进行了一些模拟研究，以评估残差检测系统组件中错误指定的潜力，模型的随机分量中的存在并检测异常值。最后，我们将所研究的方法应用于使用便携式透析机的 38 名肾病患者感染时复发的真实数据集，我们分析了这些数据，考虑了对内的独立性并使用双变量 Birnbaum-Saunders 加速寿命模型，以便我们可以进行比较并验证在与同一患者相关的感染时间内建模依赖性的重要性。