Precision medicine aims to improve the quality of health care by individualizing the health care process to the uniquely evolving health status of each patient . Dynamic prediction is a method that uses updated follow-up information to predict the individual survival or risk of a disease in real time . Currently, the diagnosis and early treatment of diseases after kidney transplantation are expected to enter an era of individualization. It is important to make dynamic and precise survival predictions for individuals to guide clinical decision-making (such as adjusting immunosuppression, returning to dialysis, or re-enrolling in the transplant waiting list) based on the patients’ longitudinal follow-up information.
Monitoring the survival of renal allografts is a long-term process. During this process, patients want to know the survival probabilities of their allograft at each stage. Patients can learn the condition of their allograft in real time through the use of dynamic prediction models instead of static prediction models. For example, we used the baseline information of kidney transplant patients to build a static prediction model that could only predict the survival of the patients when they entered the study. After a period of time, each patient returned to the hospital for a follow-up, and the values of the covariates were changed. The static prediction model is not suitable for patients who have survived for a period of time after transplantation. In contrast, a dynamic prediction model can use both baseline and follow-up information to predict the survival probabilities of new allografts for patients who have been alive for a period of time after transplantation.
In our study, we selected a landmarking approach to make dynamic predictions that can handle more limitations than joint modeling methods. Many studies have shown that the joint modeling method will have lower predictive performance than the landmarking approach when the model is not specified correctly . Moreover, landmarking the dynamic Cox model can also use the covariates with time-varying effects to make prognoses and predictions  at different selected landmark time points and predict the next few years’ survival for patients, so that patients can know their conditions in real time and early treatment can be applied to patients with predicted high risk of allograft failure.
It is indeed challenging for doctors to integrate baseline and posttransplantation clinical information to dynamically predict the risk of renal allograft failure. However, some studies have shown that clinical decisions based on only clinical data and doctors’ judgments are often not accurate and are highly variable between doctors . Therefore, dynamic risk/survival prediction for individuals is important in clinical decision-making. For instance, it may be possible for a patient to consider an earlier return to dialysis or re-enrollment in the transplant waiting list for retransplantation if the predicted risk is very high within a shorter prediction window of an early landmark time point. Thus, when applying the dynamic prediction model based on the landmarking approach, the selection of landmark time points and prediction windows could also be important.
When we apply the landmarking approach, some detailed settings are necessary. First, the prediction window w depends on the disease duration or the duration of follow-up. For severe cancers, w = 1 or w = 2 is relevant, but for some clinical research with a long duration of follow-up, such as that after kidney transplantation, we choose a window of prediction of 5 years as a relevant time horizon to provide middle-term prognoses . Furthermore, the selection of the landmark time point sl is independent of the actual event time, which implicitly defines the weighting of the prediction time. The simplest method is to use an equidistant grid of points on the prediction interval [s0, sL] from the time to clinical research entry s0 to sL, and the number of time points between 20 and 100 is sufficient . In addition, the length of [s0, sL] may affect the results, usually selecting the time to clinical research entry as s0 and the median follow-up time as the maximum prediction time of interest sL. For example, in this article, the landmark dataset R contained only those patients’ longitudinal information from the time point after kidney transplantation to 10 years after transplantation. Finally, the functional form of time-varying effects β(s) and the baseline hazard changing θ(s), the most commonly used quadratic functions and spline functions should also be chosen in practice.
There are two limitations to our study. First, existing models for predicting the survival of renal allografts also include predictors such as donor information, primary kidney disease, comorbidities, supportive therapies, and immunization therapies, which we did not include in our model [28, 29]. However, these covariates can always be directly manipulated in clinical practice (subgroups could be made for the analysis), whereas we are more concerned with the impact of directly measured covariates that reflect the changes in renal function on patient graft survival. The GFR and proteinuria used in our study are acknowledged indicators that directly reflect the function of the kidneys, and hematocrit can indirectly reflect the improvement in kidney function and systemic inflammatory conditions [30,31,32]. The three variables we analyzed were all obtained by measurement and are representative of the outcomes of any intervention. The landmark dynamic Cox model in our study could later gradually incorporate more variables that might be more satisfactory. Second, although the Monte Carlo cross-validation for internal validation of the proposed models performed well in our study, we still strongly encourage external validation, which can assess generalizability in a larger population of kidney recipients. Moreover, the dynamic Cox model constructed from the data presented in our paper can serve as an example, enabling similar types of data in the transplant field to build models for prediction and prognostic analysis.