Restricted mean survival time regression model with time-dependent covariates

Time-varying effect in older patients with early-stage breast cancer: a model considering the competing risks based on a time scale

Background

Patients with early-stage breast cancer may have a higher risk of dying from other diseases, making a competing risks model more appropriate. Considering subdistribution hazard ratio, which is used often, limited to model assumptions and clinical interpretation, we aimed to quantify the effects of prognostic factors by an absolute indicator, the difference in restricted mean time lost (RMTL), which is more intuitive. Additionally, prognostic factors of breast cancer may have dynamic effects (time-varying effects) in long-term follow-up. However, existing competing risks regression models only provide a static view of covariate effects, leading to a distorted assessment of the prognostic factor.

Methods

To address this issue, we proposed a dynamic effect RMTL regression that can explore the between-group cumulative difference in mean life lost over a period of time and obtain the real-time effect by the speed of accumulation, as well as personalized predictions on a time scale.

Results

A simulation validated the accuracy of the coefficient estimates in the proposed regression. Applying this model to an older early-stage breast cancer cohort, it was found that 1) the protective effects of positive estrogen receptor and chemotherapy decreased over time; 2) the protective effect of breast-conserving surgery increased over time; and 3) the deleterious effects of stage T2, stage N2, and histologic grade II cancer increased over time. Moreover, from the view of prediction, the mean C-index in external validation reached 0.78.

Conclusion

Dynamic effect RMTL regression can analyze both dynamic cumulative effects and real-time effects of covariates, providing a more comprehensive prognosis and better prediction when competing risks exist.

Comparison of baseline covariate adjustment methods for restricted mean survival time

The restricted mean survival time provides a straightforward clinical measure that dispenses with the need for proportional hazards assumptions. We focus on two strategies to directly model the survival time and adjust covariates. Firstly, pseudo-survival time is calculated for each subject using a leave-one-out approach, followed by a model analysis that adjusts for covariates using all pseudo-values. This method is used to reflect information of censored subjects in the model analysis. The second approach adjusts for covariates for those subjects with observed time-to-event while incorporating censored subjects using inverse probability of censoring weighting (IPCW). This paper evaluates these methods' power to detect group differences through computer simulations. We find the interpretation of pseudo-values challenging with the pseudo-survival time method and confirm that pseudo-survival times deviate from actual data in a primary biliary cholangitis clinical trial, mainly due to extensive censoring. Simulations reveal that the IPCW method is more robust, unaffected by the balance of censors, whereas pseudo-survival time is influenced by this balance. The IPCW method retains a nominal significance level for the type-1 error rate, even amidst group differences concerning censor incidence rates and covariates. Our study concludes that IPCW and pseudo-survival time methods differ significantly in handling censored data, impacting parameter estimations. Our findings suggest that the IPCW method provides more robust results than pseudo-survival time and is recommended, even when censor probabilities vary between treatment groups. However, pseudo-survival time remains a suitable choice when censoring probabilities are balanced.

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.