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Does my model predict accurately?
Published in Thomas A. Gerds, Michael W. Kattan, Medical Risk Prediction, 2021
Thomas A. Gerds, Michael W. Kattan
Thus, the calculation of the event-specific Brier score in the situation with competing risks and right-censored data needs almost no modification from the censored survival setting. But, there are at least two important differences. First, in the presence of competing risks and censored data, the Kaplan-Meier method is inappropriate for the absolute risk distribution. Hence, to obtain the benchmark null model which predicts the same risk to all subjects, we now use the Aalen-Johansen method [1]. The Aalen-Johansen method calculates the event-specific cumulative incidence in the test set data at the prediction time horizon. The second important difference is that one can, in principle, also predict the competing risks and the corresponding Brier scores. In the prostate cancer dataset, the competing risk is death due to reasons other than cancer, without cancer progression. This is not easy to interpret for the patient. Instead, one could either study prediction of the risk of the combined endpoint (progression or death due to any cause) or study the risk of all-cause mortality. Here, we simply predict the risk of cancer progression based on the cause-specific Cox regression models shown in Table 5.4.1 and calculate the Brier score in the test set of the active surveillance prostate cancer study.
Prognosis: Studies of disease course and outcomes
Published in Milos Jenicek, Foundations of Evidence-Based Medicine, 2019
The Kaplan–Meier method often serves in clinical situations when dates of events are known and when fewer patients are available. The probability of surviving beyond a given time t is estimated and denoted by S(t). The survivorship function S(t) is estimated for all successive time intervals. These intervals are irregular since they are determined by the observed times (moments) of occurrence of events. For example, if death by cancer appears in the fifth month after the entry of one patient into the study, the first interval is five months. If another death occurs eight months after the death of the first patient, the next interval will cover the period from the fifth month of the study to the thirteenth, and so on. Hence, the survivorship function changes (i.e. decreases) only at the moments when deaths occur.
Pre-Clinical Efficacy Studies
Published in Harry Yang, Steven J. Novick, Bayesian Analysis with R for Drug Development, 2019
In survival modeling, two outcome variables (T, δ), are observed for each subject, where T denotes the time to event (animal is sacrificed or dies) and the binary variable δ indicates if the event occurs before the conclusion of the study. When δ = 1, T is set to the time at which the event occurred and when δ = 0, T is set to the final time point and is called right-censored, indicating that the animal has not yet reached the event by the end of the study. Let the survival function for the ith treatment group S(t | θi) = Pr(T > t | θi) denote the probability that a subject with parameter θi survives beyond the time point t. Given treatment groups A and B, one would clearly favor treatment group A at time t if S(t | θA) > S(t | θB). A common model for survival data uses the non-parametric Kaplan-Meier approach. The Kaplan-Meier method, however, is limited in scope and does not, for example, permit the modeling of a covariate, such as the baseline tumor size. Several parametric survival models are available in pre-packaged software; see, for example see the survival library in R, PROC LIFEREG in SAS. In the following section, the Weibull parametric survival model is studied in detail.
Peritoneal transport status and first episode of peritonitis: a large cohort study
Published in Renal Failure, 2021
SPSS 21.0 software was used for statistical analysis. Data were presented as means and standard deviations or medians and interquartile range for continuous variables, and number (percentages) for categorical variables. Differences between the two groups were evaluated by Student’s t-test, Mann–Whitney test, or the Chi-square according to the types of the data. Differences in baseline characteristics of patients due to different transport statuses were evaluated by ANOVA. The Kaplan-Meier method was used to determine the survival time, the technique survival time, and the overall survival time of patients. The Log-Rank test was used to evaluate the difference in the survival rate. Univariate and multivariate Cox proportional hazard regression analyses were performed to evaluate the risk factors for the first episode of peritonitis, technique failure and overall mortality in PD patients. A P-value of <0.05 was considered statistically significant.
Soluble forms of PD-L1 and PD-1 as prognostic and predictive markers of sunitinib efficacy in patients with metastatic clear cell renal cell carcinoma
Published in OncoImmunology, 2020
Christopher Montemagno, Anais Hagege, Delphine Borchiellini, Brice Thamphya, Olivia Rastoin, Damien Ambrosetti, Juan Iovanna, Nathalie Rioux-Leclercq, Camillio Porta, Sylvie Negrier, Jean-Marc Ferrero, Emmanuel Chamorey, Gilles Pagès, Maeva Dufies
Progression-free survival (PFS) was defined as the time between blood sample collection and progression, or death from any cause, censoring those alive and progression free at last follow-up. Overall survival (OS) was defined as the time from blood sample collection to the date of death from any cause, censoring those alive at last follow-up. The sPD-L1 and sPD-1 cutoff point (0.1 ng ml−1 and 1.67 ng ml−1 respectively) for PFS was determined using spline curve analysis. T-test was applied to compare continuous variables, and chi-square test or Fisher’s exact test (when the application condition of χ2-test was not fulfilled) was used for categorical variables. Kaplan–Meier method was used to produce survival curves and analyses of censored data were performed using the log-rank test. To guarantee the independence of sPD-L1 and sPD-1 as a predictive factor from validated predictive factors, a multivariate analysis was performed using Cox regression adjusted on stage score. Adjusted hazard ratio (HR) and 95% confidence interval (95% CI) were calculated. All analyses were performed using R software, version 3.2.2 (Vienna, Austria, https://www.r-project.org/).
Nutritional prognostic factors for survival in amyotrophic lateral sclerosis patients undergone percutaneous endoscopic gastrostomy placement
Published in Amyotrophic Lateral Sclerosis and Frontotemporal Degeneration, 2019
Michele Barone, Maria Teresa Viggiani, Alessandro Introna, Eustachio D’errico, Antonio Scarafino, Andrea Iannone, Alfredo Di Leo, Isabella Laura Simone
Time-to-event outcome (death) was estimated using the Kaplan–Meier method. Patients lost at follow-up were censored. The univariate phase of analysis was performed using the Log-rank test to evaluate the effect of each study factor (BMI category and cholesterol level) and covariate (age, sex, LDL/HDL ratio, duration of disease, age at onset of symptoms, disease presentation, time to generalization, NIV, ALSFRS-r, and progression rate) on the outcome. Since the continuous variables “disease duration” and “time to generalization” had a highly skewed distribution, these two parameters were transformed into logarithms. In addition, continuous variables were analyzed by the Log-rank test for trend prior to their inclusion in the multivariate model. Subsequently, only covariates showing a p-value < 0.25 at univariate analysis were included in the baseline multivariate proportional hazards model together with the two study factors.