Sample size calculation for mixture cure model with restricted mean survival time as a primary endpoint.

It is not uncommon for a substantial proportion of patients to be cured (or survive long-term) in clinical trials with time-to-event endpoints, such as the endometrial cancer trial. When designing a clinical trial, a mixture cure model should be used to fully consider the cure fraction. Previously, mixture cure model sample size calculations were based on the proportional hazards assumption of latency distribution between groups, and the log-rank test was used for deriving sample size formulas. In real studies, the latency distributions of the two groups often do not satisfy the proportional hazards assumptions. This article has derived a sample size calculation formula for a mixture cure model with restricted mean survival time as the primary endpoint, and did simulation and example studies. The restricted mean survival time test is not subject to proportional hazards assumptions, and the difference in treatment effect obtained can be quantified as the number of years (or months) increased or decreased in survival time, making it very convenient for clinical patient-physician communication. The simulation results showed that the sample sizes estimated by the restricted mean survival time test for the mixture cure model were accurate regardless of whether the proportional hazards assumptions were satisfied and were smaller than the sample sizes estimated by the log-rank test in most cases for the scenarios in which the proportional hazards assumptions were violated.

Assessing treatment effects with adjusted restricted mean time lost in observational competing risks data.

BACKGROUND: According to long-term follow-up data of malignant tumor patients, assessing treatment effects requires careful consideration of competing risks. The commonly used cause-specific hazard ratio (CHR) and sub-distribution hazard ratio (SHR) are relative indicators and may present challenges in terms of proportional hazards assumption and clinical interpretation. Recently, the restricted mean time lost (RMTL) has been recommended as a supplementary measure for better clinical interpretation. Moreover, for observational study data in epidemiological and clinical settings, due to the influence of confounding factors, covariate adjustment is crucial for determining the causal effect of treatment. METHODS: We construct an RMTL estimator after adjusting for covariates based on the inverse probability weighting method, and derive the variance to construct interval estimates based on the large sample properties. We use simulation studies to study the statistical performance of this estimator in various scenarios. In addition, we further consider the changes in treatment effects over time, constructing a dynamic RMTL difference curve and corresponding confidence bands for the curve. RESULTS: The simulation results demonstrate that the adjusted RMTL estimator exhibits smaller biases compared with unadjusted RMTL and provides robust interval estimates in all scenarios. This method was applied to a real-world cervical cancer patient data, revealing improvements in the prognosis of patients with small cell carcinoma of the cervix. The results showed that the protective effect of surgery was significant only in the first 20 months, but the long-term effect was not obvious. Radiotherapy significantly improved patient outcomes during the follow-up period from 17 to 57 months, while radiotherapy combined with chemotherapy significantly improved patient outcomes throughout the entire period. CONCLUSIONS: We propose the approach that is easy to interpret and implement for assessing treatment effects in observational competing risk data.

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.

Co-immobilization of crosslinked enzyme aggregates on lysozyme functionalized magnetic nanoparticles for enhancing stability and activity.

Surface chemistry of carriers plays a key role in enzyme loading capacity, structure rigidity, and thus catalyze activity of immobilized enzymes. In this work, the two model enzymes of horseradish peroxidase (HRP) and glucose oxidase (GOx) are co-immobilized on the lysozyme functionalized magnetic core-shell nanocomposites (LYZ@MCSNCs) to enhance their stability and activity. Briefly, the HRP and GOx aggregates are firstly formed under the crosslinker of trimesic acid, in which the loading amount and the rigidity of the enzyme can be further increased. Additionally, LYZ easily forms a robust anti-biofouling nanofilm on the surface of SiO2@Fe3O4 magnetic nanoparticles with abundant functional groups, which facilitate chemical crosslinking of HRP and GOx aggregates with minimized inactivation. The immobilized enzyme of HRP-GOx@LYZ@MCSNCs exhibited excellent recovery activity (95.6 %) higher than that of the free enzyme (HRP&GOx). Specifically, 85 % of relative activity was retained after seven cycles, while 73.5 % of initial activity was also remained after storage for 33 days at 4 °C. The thermal stability and pH adaptability of HRP-GOx@LYZ@MCSNCs were better than those of free enzyme of HRP&GOx. This study provides a mild and ecofriendly strategy for multienzyme co-immobilization based on LYZ functionalized magnetic nanoparticles using HRP and GOx as model enzymes.

Facile fabrication of Ti4+-immobilized magnetic nanoparticles by phase-transitioned lysozyme nanofilms for enrichment of phosphopeptides.

In this study, titanium (IV)-immobilized magnetic nanoparticles (Ti4+-PTL-MNPs) were firstly synthesized via a one-step aqueous self-assembly of lysozyme nanofilms for efficient phosphopeptide enrichment. Under physiological conditions, lysozymes readily self-organized into phase-transitioned lysozyme (PTL) nanofilms on Fe3O4@SiO2 and Fe3O4@C MNP surfaces with abundant functional groups, including -NH2, -COOH, -OH, and -SH, which can be used as multiple linkers to efficiently chelate Ti4+. The obtained Ti4+-PTL-MNPs possessed high sensitivity of 0.01 fmol µL-1 and remarkable selectivity even at a mass ratio of ß-casein to BSA as low as 1:400 for phosphopeptide enrichment. Furthermore, the synthesized Ti4+-PTL-MNPs can also selectively identify low-abundance phosphopeptides from extremely complicated human serum samples and their rapid separation, good reproducibility, and excellent recovery were also proven. This one-step self-assembly of PTL nanofilms facilitated the facile and efficient surface functionalization of various nanoparticles for proteomes/peptidomes.

Communicating and understanding statistical measures when quantifying the between-group difference in competing risks.

Competing risks issues are common in clinical trials and epidemiological studies for patients in follow-up who may experience a variety of possible outcomes. Under such competing risks, two hazard-based statistical methods, cause-specific hazard (CSH) and subdistribution hazard (SDH), are frequently used to assess treatment effects among groups. However, the outcomes of the CSH-based and SDH-based methods have a close connection with the proportional hazards (CSH or SDH) assumption and may have an non-intuitive interpretation. Recently, restricted mean time lost (RMTL) has been used as an alternative summary measure for analysing competing risks, due to its clinical interpretability and robustness to the proportional hazards assumption. Considering the above approaches, we summarize the differences between hazard-based and RMTL-based methods from the aspects of practical interpretation, proportional hazards model assumption and the selection of restricted time points, and propose corresponding suggestions for the analysis of between-group differences under competing risks. Moreover, an R package 'cRMTL' and corresponding step-by-step guidance are available to help users for applying these approaches.

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.

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.

Investigations of methods for multiple time-to-event endpoints: A chronic myeloid leukemia data analysis.

BACKGROUND: In randomized controlled trials, multiple time-to-event endpoints are commonly used to determine treatment effects. However, choosing an appropriate method to address multiple endpoints, according to different purposes of clinical practice, is a challenge for researchers. METHODS: We applied single endpoint, composite endpoint and win ratio analysis to chronic myeloid leukemia (CML) data to illustrate the distinctions with different multiple endpoints, including relapse, recovery and death after transplantation. RESULTS: Regarding relapse and death, the hazard ratio in single endpoint analysis (HRs ) were 1.281 (95% CI: 1.061-1.546) and hazard ratio in composite endpoint analysis (HRc ) were 1.286 (95% CI: 1.112-1.486) and 1/WR (win ratio) was 1.292 (95% CI: 1.115-1.497) indicated a similar negative effect for non-prophylaxis patients. However, when considering recovery and death, the corresponding HRs = 1.280 (95% CI: 1.056-1.552) may not be enough to describe the effect on death with nonproportional hazards (p < 0.05), and for the composite endpoint analysis, the HRc = 0.828 (95% CI: 0.740-0.926) cannot quantify and interpret the clinical effect on the composite endpoint with the combination of recovery and death, while the 1/WR = 1.351 (95% CI: 1.207-1.513) showed an unfavourable effect for non-prophylaxis patients CONCLUSIONS: When dealing with multiple endpoints, single endpoints, researchers may choose single endpoints, composite endpoints and WR analysis due to different clinical applications and purposes. However, both single and composite endpoint analyses are hazard-based measures, and thus, the proportional hazards assumption should be considered. Moreover, composite endpoint analysis should be applied for endpoints with similar clinical meanings but not opposing implications. Win ratio analysis can be considered for different clinical importance of multiple endpoints, but the meaning of 'winner' needs to be specified for desired or undesired endpoints.

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.

Implementation of an Alternative Method for Assessing Competing Risks: Restricted Mean Time Lost.

In clinical and epidemiologic studies, hazard ratios are often applied to compare treatment effects between 2 groups for survival data. For competing-risks data, the corresponding quantities of interest are cause-specific hazard ratios and subdistribution hazard ratios. However, they both have some limitations related to model assumptions and clinical interpretation. Therefore, we recommend restricted mean time lost (RMTL) as an alternative measure that is easy to interpret in a competing-risks framework. Based on the difference in RMTL (RMTLd), we propose a new estimator, hypothetical test, and sample-size formula. Simulation results show that estimation of the RMTLd is accurate and that the RMTLd test has robust statistical performance (both type I error and statistical power). The results of 3 example analyses also verify the performance of the RMTLd test. From the perspectives of clinical interpretation, application conditions, and statistical performance, we recommend that the RMTLd be reported along with the hazard ratio in analyses of competing-risks data and that the RMTLd even be regarded as the primary outcome when the proportional hazards assumption fails.

Adapting Virtual Embodiment Through Reinforcement Learning.

In Virtual Reality, having a virtual body opens a wide range of possibilities as the participant's avatar can appear to be quite different from oneself for the sake of the targeted application (e.g., for perspective-taking). In addition, the system can partially manipulate the displayed avatar movement through some distortion to make the overall experience more enjoyable and effective (e.g., training, exercising, rehabilitation). Despite its potential, an excessive distortion may become noticeable and break the feeling of being embodied into the avatar. Past researches have shown that individuals have a relatively high tolerance to movement distortions and a great variability of individual sensitivities to distortions. In this article, we propose a method taking advantage of Reinforcement Learning (RL) to efficiently identify the magnitude of the maximum distortion that does not get noticed by an individual (further noted the detection threshold). We show through a controlled experiment with subjects that the RL method finds a more robust detection threshold compared to the adaptive staircase method, i.e., it is more able to prevent subjects from detecting the distortion when its amplitude is equal or below the threshold. Finally, the associated majority voting system makes the RL method able to handle more noise within the forced choices input than adaptive staircase. This last feature is essential for future use with physiological signals as these latter are even more susceptible to noise. It would then allow to calibrate embodiment individually to increase the effectiveness of the proposed interactions.

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

BACKGROUND AND OBJECTIVE: In the process of clinical diagnosis and treatment, the restricted mean survival time (RMST), which reflects the life expectancy of patients up to a specified time, can be used as an appropriate outcome measure. However, the RMST only calculates the mean survival time of patients within a period of time after the start of follow-up and may not accurately portray the change in a patient's life expectancy over time. METHODS: The life expectancy can be adjusted for the time the patient has already survived and defined as the conditional restricted mean survival time (cRMST). A dynamic RMST model based on the cRMST can be established by incorporating time-dependent covariates and covariates with time-varying effects. We analyzed data from a study of primary biliary cirrhosis (PBC) to illustrate the use of the dynamic RMST model, and a simulation study was designed to test the advantages of the proposed approach. The predictive performance was evaluated using the C-index and the prediction error. RESULTS: Considering both the example results and the simulation results, the proposed dynamic RMST model, which can explore the dynamic effects of prognostic factors on survival time, has better predictive performance than the RMST model. Three PBC patient examples were used to illustrate how the predicted cRMST changed at different prediction times during follow-up. CONCLUSIONS: The use of the dynamic RMST model based on the cRMST allows for the optimization of evidence-based decision-making by updating personalized dynamic life expectancy for patients.

Quality Evaluation, Storage Stability, and Sensory Characteristics of Wheat Noodles Incorporated with Isomaltodextrin.

Wheat noodles incorporated with isomaltodextrin were assessed in relation to physicochemical properties (color), microstructure features, biochemical composition (fiber profile), cooking properties, textural attributes, and sensory evaluations during different storage temperatures (25, 4, -20 °C) and periods (0, 3, 6, 9, 12, 15, 18, 21, 24 months). Meanwhile, an accelerated study was also carried out at 40 °C storage conditions for 12 months to evaluate the fiber profile changes. Under different conditions, the overall quality of both raw and cooked noodle samples depended slightly on both the type and amount of added fiber isomaltodextrin, resistant starch (RS), insoluble high-molecular-weight dietary fiber (IHMWDF), and soluble high-molecular-weight dietary fiber (SHMWDF). However, this significantly changed for the fiber profile under 40 °C of storage for 12 months. Cooking quality, fiber profile, and color parameter did not differ by storage at -20 °C after 24 months than at 0 months, and noodles only slightly differed in texture and sensory characteristics. On sensory analysis, noodle samples were acceptable by panelists, with an acceptability score >5. In short, storage temperature is one of the most important factors in preserving food stability and retail properties. Isomaltodextrin noodles samples should be stored at low temperature to preserve the product functionality.

Functionality of Djulis (Chenopodium formosanum) By-Products and In Vivo Anti-Diabetes Effect in Type 2 Diabetes Mellitus Patients.

Djulis (Chenopodium formosanum Koidz.) is a species of cereal grain native to Taiwan. It is rich in dietary fibre and antioxidants and therefore reputed to relieve constipation, suppress inflammation, and lower blood glucose. The aim of this study was to investigate the composition and physicochemical properties of dietary fibre from djulis hull. Meanwhile, determination of the in vivo antidiabetic effect on patients with type 2 diabetes mellitus (T2DM) after consuming the djulis hull powder. Djulis hull contained dietary fibre 75.21 ± 0.17% dry weight, and insoluble dietary fibre (IDF) reached 71.54 ± 0.27% dry weight. The IDF postponed the adsorption of glucose and reduced the activity of α-amylase. Postprandial blood glucose levels in patients with T2DM showed three different tendencies. First, the area under the glucose curve was significantly lower after ingesting 10 or 5 g djulis hull powder, which then postponed the adsorption of glucose, but the area under the glucose curve was similar with the two doses. After consuming 10 g djulis hull before 75 g glucose 30 and 60 min after the meal, patients with T2DM had blood glucose values that were significantly lower at the same postprandial times than those of patients who did not consume djulis hull. In short, patients who consumed djulis hull prior to glucose administration had decreased blood glucose level compared with those who did not. Djulis hull may have benefits for patients with T2DM.

Moving beyond the Cox proportional hazards model in survival data analysis: a cervical cancer study.

OBJECTIVES: This study explored the prognostic factors and developed a prediction model for Chinese-American (CA) cervical cancer (CC) patients. We compared two alternative models (the restricted mean survival time (RMST) model and the proportional baselines landmark supermodel (PBLS model, producing dynamic prediction)) versus the Cox proportional hazards model in the context of time-varying effects. SETTING AND DATA SOURCES: A total of 713 CA women with CC and available covariates (age at diagnosis, International Federation of Gynecology and Obstetrics (FIGO) stage, lymph node metastasis and radiation) from the Surveillance, Epidemiology and End Results database were included. DESIGN: We applied the Cox proportional hazards model to analyse the all-cause mortality with the proportional hazards assumption. Additionally, we applied two alternative models to analyse covariates with time-varying effects. The performances of the models were compared using the C-index for discrimination and the shrinkage slope for calibration. RESULTS: Older patients had a worse survival rate than younger patients. Advanced FIGO stage patients showed a relatively poor survival rate and low life expectancy. Lymph node metastasis was an unfavourable prognostic factor in our models. Age at diagnosis, FIGO stage and lymph node metastasis represented time-varying effects from the PBLS model. Additionally, radiation showed no impact on survival in any model. Dynamic prediction presented a better performance for 5-year dynamic death rates than did the Cox proportional hazards model. CONCLUSIONS: With the time-varying effects, the RMST model was suggested to explore diagnosis factors, and the PBLS model was recommended to predict a patient's w-year dynamic death rate.

The use of restricted mean time lost under competing risks data.

BACKGROUND: Under competing risks, the commonly used sub-distribution hazard ratio (SHR) is not easy to interpret clinically and is valid only under the proportional sub-distribution hazard (SDH) assumption. This paper introduces an alternative statistical measure: the restricted mean time lost (RMTL). METHODS: First, the definition and estimation methods of the measures are introduced. Second, based on the differences in RMTLs, a basic difference test (Diff) and a supremum difference test (sDiff) are constructed. Then, the corresponding sample size estimation method is proposed. The statistical properties of the methods and the estimated sample size are evaluated using Monte Carlo simulations, and these methods are also applied to two real examples. RESULTS: The simulation results show that sDiff performs well and has relatively high test efficiency in most situations. Regarding sample size calculation, sDiff exhibits good performance in various situations. The methods are illustrated using two examples. CONCLUSIONS: RMTL can meaningfully summarize treatment effects for clinical decision making, which can then be reported with the SDH ratio for competing risks data. The proposed sDiff test and the two calculated sample size formulas have wide applicability and can be considered in real data analysis and trial design.

Comparison of two treatments in the presence of competing risks.

Competing risks data arise frequently in clinical trials, and a common problem encountered is the overall homogeneity between two groups. In competing risks analysis, when the proportional subdistribution hazard assumption is violated or two cumulative incidence function (CIF) curves cross; currently, the most commonly used testing methods, for example, the Gray test and the Pepe and Mori test, may lead to a significant loss of statistical testing power. In this article, we propose a testing method based on the area between the CIF curves (ABC). The ABC test captures the difference over the whole time interval for which survival information is available for both groups and is not based on any special assumptions regarding the underlying distributions. The ABC test was also extended to test short-term and long-term effects. We also consider a combined test and a two-stage procedure based on this new method, and a bootstrap resampling procedure is suggested in practice to approximate the limiting distribution of the combined test and two-stage test. An extensive series of Monte Carlo simulations is conducted to investigate the power and the type I error rate of the methods. In addition, based on our simulations, our proposed TS, Comb, and ABC tests have a relatively high power in most situations. In addition, the methods are illustrated using two different datasets with different CIF situations.

Dynamic prediction and prognostic analysis of patients with cervical cancer: a landmarking analysis approach.

PURPOSE: Providing up-to-date information on patient prognosis is important in determining the optimal treatment strategies. The currently available prediction models, such as the Cox model, are limited to making predictions from baseline and do not consider the time-varying effects of covariates. METHODS: A total of 1501 cervical cancer patients from the Surveillance, Epidemiology, and End Results (SEER) database were included. We introduced three landmark dynamic prediction models (models 1-3) that explore the dynamic effects of prognostic factors to obtain 5-year dynamic survival rate predictions at different prediction times. The performances of these models were evaluated by Harrell's C-index and the Brier score using cross-validation. RESULTS: Some variables did not meet the proportional hazards assumption, indicating that the constant hazard ratios were unreliable. Model 3, which showed the best performance for prediction, was selected as the final model. Significant time-varying effects were observed for age at diagnosis, International Federation of Gynecology and Obstetrics (FIGO) stage, lymph node metastasis, and histological subtypes. Three patients were as examples used to illustrate how the predicted probabilities change at different prediction times during follow-up. CONCLUSIONS: Model 3 can effectively incorporate covariates with time-varying effects and update the probability of surviving an additional 5 years at different prediction times. The use of the landmark approach may provide evidence for clinical decision making by updating personalized information for patients.