Dynamic prediction and analysis based on restricted mean survival time in survival analysis with nonproportional hazards

Developing novel dynamic prediction methods for survival time to analyze short-term and long-term progression of Alzheimer's disease

Tracking and monitoring mild cognitive impairment (MCI) patients to intervene promptly at the imminent onset of Alzheimer's disease (AD) are crucial. However, existing dynamic survival prediction models for the conversion from MCI to AD are mostly based on hazard rates, which are less intuitive to interpret and require adherence to the proportional hazards assumption. To address this, we propose a Bayesian joint model (JM) based on the time scale indicator of the restricted mean survival time (RMST), which can capture the trajectories of multiple longitudinal covariates and dynamically predict the patient time to event. Using Monte Carlo simulation, it can be demonstrated that the JM method has a better prediction performance compared with the static model. To predict the dynamic progression of AD in MCI patients at different stages, based on the landmark (LM) method and the JM method for RMST, we developed an LM-based model for short-term dynamic prediction (LM-ST model) and a JM-based model for long-term dynamic prediction (JM-LT model) utilizing the ADNI database. The internal and external validation results indicate that the predictive performance of the LM-ST and JM-LT models surpasses that of the static RMST model. Additionally, an online web tool for the two dynamic prediction models was created for clinical application. In summary, we propose a novel method and combined it with the existing LM method for AD progression, which improves the predictive power and provides a scientific basis for medical decision-making.

Dynamic risk prediction of survival in liver cirrhosis: A comparison of landmarking approaches

Electronic health records (EHR) data provides the researcher and physician with the opportunity to improve risk prediction by employing newer, more sophisticated modeling techniques. Rather than treating the impact of predictor variables on health trajectories as static, we explore the use of time-dependent variables in dynamically modeling time-to-event data through the use of landmarking (LM) data sets. We compare several different dynamic models presented in the literature that utilize LM data sets as the basis of their approach. These techniques include using pseudo-means, pseudo-survival probabilities, and the traditional Cox model. The models are primarily compared with their static counterparts using appropriate measures of model discrimination and calibration based on what summary measure is employed for the response variable.

Analysis of dynamic restricted mean survival time based on pseudo-observations

In clinical follow-up studies with a time-to-event end point, the difference in the restricted mean survival time (RMST) is a suitable substitute for the hazard ratio (HR). However, the RMST only measures the survival of patients over a period of time from the baseline and cannot reflect changes in life expectancy over time. Based on the RMST, we study the conditional restricted mean survival time (cRMST) by estimating life expectancy in the future according to the time that patients have survived, reflecting the dynamic survival status of patients during follow-up. In this paper, we introduce the estimation method of cRMST based on pseudo-observations, the statistical inference concerning the difference between two cRMSTs (cRMSTd), and the establishment of the robust dynamic prediction model using the landmark method. Simulation studies are conducted to evaluate the statistical properties of these methods. The results indicate that the estimation of the cRMST is accurate, and the dynamic RMST model has high accuracy in coefficient estimation and good predictive performance. In addition, an example of patients with chronic kidney disease who received renal transplantations is employed to illustrate that the dynamic RMST model can predict patients' expected survival times from any prediction time, considering the time-dependent covariates and time-varying effects of covariates.

A Dynamic Prediction Model Supporting Individual Life Expectancy Prediction Based on Longitudinal Time-Dependent Covariates

In the field of clinical chronic diseases, common prediction results (such as survival rate) and effect size hazard ratio (HR) are relative indicators, resulting in more abstract information. However, clinicians and patients are more interested in simple and intuitive concepts of (survival) time, such as how long a patient may live or how much longer a patient in a treatment group will live. In addition, due to the long follow-up time, resulting in generation of longitudinal time-dependent covariate information, patients are interested in how long they will survive at each follow-up visit. In this study, based on a time scale indicator-restricted mean survival time (RMST)-we proposed a dynamic RMST prediction model by considering longitudinal time-dependent covariates and utilizing joint model techniques. The model can describe the change trajectory of longitudinal time-dependent covariates and predict the average survival times of patients at different time points (such as follow-up visits). Simulation studies through Monte Carlo cross-validation showed that the dynamic RMST prediction model was superior to the static RMST model. In addition, the dynamic RMST prediction model was applied to a primary biliary cirrhosis (PBC) population to dynamically predict the average survival times of the patients, and the average C-index of the internal validation of the model reached 0.81, which was better than that of the static RMST regression. Therefore, the proposed dynamic RMST prediction model has better performance in prediction and can provide a scientific basis for clinicians and patients to make clinical decisions.

Dynamic effects of prognostic factors and individual survival prediction for amyotrophic lateral sclerosis disease

OBJECTIVE

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease affecting motor neurons, with broad heterogeneity in disease progression and survival in different patients. Therefore, an accurate prediction model will be crucial to implement timely interventions and prolong patient survival time.

METHODS

A total of 1260 ALS patients from the PRO-ACT database were included in the analysis. Their demographics, clinical variables, and death reports were included. We constructed an ALS dynamic Cox model through the landmarking approach. The predictive performance of the model at different landmark time points was evaluated by calculating the area under the curve (AUC) and Brier score.

RESULTS

Three baseline covariates and seven time-dependent covariates were selected to construct the ALS dynamic Cox model. For better prognostic analysis, this model identified dynamic effects of treatment, albumin, creatinine, calcium, hematocrit, and hemoglobin. Its prediction performance (at all landmark time points, AUC ≥ 0.70 and Brier score ≤ 0.12) was better than that of the traditional Cox model, and it predicted the dynamic 6-month survival probability according to the longitudinal information of individual patients.

INTERPRETATION

We developed an ALS dynamic Cox model with ALS longitudinal clinical trial datasets as the inputs. This model can not only capture the dynamic prognostic effect of both baseline and longitudinal covariates but also make individual survival predictions in real time, which are valuable for improving the prognosis of ALS patients and providing a reference for clinicians to make clinical decisions.

Multi-event survival analysis through dynamic multi-modal learning for ICU mortality prediction

BACKGROUND AND OBJECTIVE

Survival analysis is widely applied for assessing the expected duration of patient status towards event occurrences such as mortality in healthcare domain, which is generally considered as a time-to-event problem. Patients with multiple complications have high mortality risks and oftentimes require specific intensive care and clinical treatments. The progression of complications is time-varying according to disease development and intrinsic interactions between complications with respect to mortality are uncertain. Classical methods for mortality prediction and survival analysis in critical care, such as risk scoring systems and cause-specific survival models, were not designed for this multi-event survival analysis problem and able to measure the competing risks of death for mutually exclusive events. In addition, multivariate temporal information of complications is not taken into consideration while estimating differentiated mortality risks in the early stage.

METHODS

In this paper, we propose a novel multi-event survival analysis solution using a tree-based autoregressive survival model of multi-modal electronic health record data. Specifically, we focus on modeling the temporal trajectory of complications and estimating the mortality risk associated with multiple potential complications simultaneously. In dynamic modeling, no assumptions are made for the relationships between time-dependent variables and risk transition over time.

RESULTS

Validated with the eICU database, our model achieves a better prediction performance with C-index ranging in 74-80%, compared to state-of-the-art machine learning methods in the literature, for the complications of acute respiratory distress syndrome and cardiovascular disease cases.

CONCLUSIONS

Our model provides the distinguishable mortality risk curves over time for specific complications and the track of risk development that could potentially support the ICU resource reallocation.

Restricted Mean Survival Time-Can It Be a New Tool in Assessing the Survival of Non-Small Cell Lung Cancer Patients Treated with Immune Checkpoint Inhibitors?

BACKGROUND

Lung cancer (LC) is the first and most lethal cancer in the world; identifying new methods to treat it, such as immune checkpoint inhibitors (ICIs), is needed. ICIs treatment is very effective, but it comes bundled with a series of immune-related adverse events (irAEs). Restricted mean survival time (RMST) is an alternative tool for assessing the patients' survival when the proportional hazard assumption (PH) fails.

METHODS

We included in this analytical cross-sectional observational survey patients with metastatic non-small-cell lung cancer (NSCLC), treated for at least 6 months with ICIs in the first- and second-line settings. Using RMST, we estimated the overall survival (OS) of patients by dividing them into two groups. A multivariate Cox regression analysis was performed to determine the impact of the prognostic factors on OS.

RESULTS

Seventy-nine patients were included (68.4% men, mean age 63.8), and 34/79 (43%) presented irAEs. The OS RMST of the entire group was 30.91 months, with a survival median of 22 months. Thirty-two out of seventy-nine (40.5%) died before we ended our study. The OS RMST and death percentage favored the patients who presented irAEs (long-rank test, p = 0.036). The OS RMST of patients with irAEs was 35.7 months, with a number of deaths of 12/34 (35.29%), while the OS RMST of the patients without irAEs was 17 months, with a number of deaths of 20/45 (44.44%). The OS RMST by the line of treatment favored the first line of treatment. In this group, the presence of irAEs significantly impacted the survival of these patients (p = 0.0083). Moreover, patients that experienced low-grade irAEs had a better OS RMST. This result has to be cautiously regarded because of the small number of patients stratified according to the grades of irAEs. The prognostic factors for the survival were: the presence of irAEs, Eastern Cooperative Oncology Group (ECOG) performance status and the number of organs affected by metastasis. The risk of dying was 2.13 times higher for patients without irAEs than for the patients who presented irAEs, (CI) 95% of 1.03 to 4.39. Moreover, by increasing the ECOG performance status by one point, the risk of death increased by 2.28 times, with a CI 95% of 1.46 to 3.58, while the involvement of more metastatic organs was associated with a 1.60 times increase in the death risk, with a CI 95% of 1.09 to 2.36. Age and the type of tumor were not predictive for this analysis.

CONCLUSIONS

The RMST is a new tool that helps researchers to better address the survival in studies with ICIs treatment where the PH fails, and the long-rank test is less efficient due to the existence of the long-term responses and delayed treatment effects. Patients with irAEs have a better prognosis than those without irAEs in the first-line settings. The ECOG performance status and the number of organs affected by metastasis must be considered when selecting patients for ICIs treatment.

Individual dynamic prediction and prognostic analysis for long-term allograft survival after kidney transplantation

Background

Predicting allograft survival is vital for efficient transplant success. With dynamic changes in patient conditions, clinical indicators may change longitudinally, and doctors’ judgments may be highly variable. It is necessary to establish a dynamic model to precisely predict the individual risk/survival of new allografts.

Methods

The follow-up data of 407 patients were obtained from a renal allograft failure study. We introduced a landmarking-based dynamic Cox model that incorporated baseline values (age at transplantation, sex, weight) and longitudinal changes (glomerular filtration rate, proteinuria, hematocrit). Model performance was evaluated using Harrell’s C-index and the Brier score.

Results

Six predictors were included in our analysis. The Kaplan–Meier estimates of survival at baseline showed an overall 5-year survival rate of 87.2%. The dynamic Cox model showed the individual survival prediction with more accuracy at different time points (for the 5-year survival prediction, the C-index = 0.789 and Brier score = 0.065 for the average of all time points) than the static Cox model at baseline (C-index = 0.558, Brier score = 0.095). Longitudinal covariate prognostic analysis (with time-varying effects) was performed.

Conclusions

The dynamic Cox model can utilize clinical follow-up data, including longitudinal patient information. Dynamic prediction and prognostic analysis can be used to provide evidence and a reference to better guide clinical decision-making for applying early treatment to patients at high risk.

Restricted mean survival time regression model with time-dependent covariates

In clinical or epidemiological follow‐up studies, methods based on time scale indicators such as the restricted mean survival time (RMST) have been developed to some extent. Compared with traditional hazard rate indicator system methods, the RMST is easier to interpret and does not require the proportional hazard assumption. To date, regression models based on the RMST are indirect or direct models of the RMST and baseline covariates. However, time‐dependent covariates are becoming increasingly common in follow‐up studies. Based on the inverse probability of censoring weighting (IPCW) method, we developed a regression model of the RMST and time‐dependent covariates. Through Monte Carlo simulation, we verified the estimation performance of the regression parameters of the proposed model. Compared with the time‐dependent Cox model and the fixed (baseline) covariate RMST model, the time‐dependent RMST model has a better prediction ability. Finally, an example of heart transplantation was used to verify the above conclusions.