scholarly journals Hidden Imputations and the Kaplan-Meier Estimator

2020 ◽  
Vol 189 (11) ◽  
pp. 1408-1411 ◽  
Author(s):  
Stephen R Cole ◽  
Jessie K Edwards ◽  
Ashley I Naimi ◽  
Alvaro Muñoz
Keyword(s):  
Survival Data ◽  
Survival Function ◽  
Data Set ◽  
Kaplan Meier ◽  
Event Times

Abstract The Kaplan-Meier (KM) estimator of the survival function imputes event times for right-censored and left-truncated observations, but these imputations are hidden and therefore sometimes unrecognized by applied health scientists. Using a simple example data set and the redistribution algorithm, we illustrate how imputations are made by the KM estimator. We also discuss the assumptions necessary for valid analyses of survival data. Illustrating imputations hidden by the KM estimator helps to clarify these assumptions and therefore may reduce inappropriate inferences.

scholarly journals Correcting for dependent censoring in routine outcome monitoring data by applying the inverse probability censoring weighted estimator

2016 ◽  
Vol 27 (2) ◽  
pp. 323-335 ◽  
Author(s):  
SJW Willems ◽  
A Schat ◽  
MS van Noorden ◽  
M Fiocco
Keyword(s):  
Dependent Censoring ◽  
Data Set ◽  
Mathematical Skills ◽  
Weighted Estimator ◽  
Inverse Probability ◽  
Kaplan Meier ◽  
Outcome Monitoring ◽  
Censored Observations ◽  
Event Times ◽  
User Friendly

Censored data make survival analysis more complicated because exact event times are not observed. Statistical methodology developed to account for censored observations assumes that patients’ withdrawal from a study is independent of the event of interest. However, in practice, some covariates might be associated to both lifetime and censoring mechanism, inducing dependent censoring. In this case, standard survival techniques, like Kaplan–Meier estimator, give biased results. The inverse probability censoring weighted estimator was developed to correct for bias due to dependent censoring. In this article, we explore the use of inverse probability censoring weighting methodology and describe why it is effective in removing the bias. Since implementing this method is highly time consuming and requires programming and mathematical skills, we propose a user friendly algorithm in R. Applications to a toy example and to a medical data set illustrate how the algorithm works. A simulation study was carried out to investigate the performance of the inverse probability censoring weighted estimators in situations where dependent censoring is present in the data. In the simulation process, different sample sizes, strengths of the censoring model, and percentages of censored individuals were chosen. Results show that in each scenario inverse probability censoring weighting reduces the bias induced in the traditional Kaplan–Meier approach where dependent censoring is ignored.

scholarly journals Tree Based Method for Aggregate Survival Data Modeling

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Asanao Shimokawa ◽  
Yoshitaka Narita ◽  
Soichiro Shibui ◽  
Etsuo Miyaoka
Keyword(s):  
Survival Data ◽  
Survival Function ◽  
Primary Brain Tumor ◽  
Aggregated Data ◽  
Tumor Patient ◽  
Kaplan Meier ◽  
Proposed Model ◽  
Tree Modeling ◽  
Variable Space ◽  
New Interpretation

AbstractIn many scenarios, a patient in medical research is treated as a statistical unit. However, in some scenarios, we are interested in treating aggregate data as a statistical unit. In such situations, each set of aggregated data is considered to be a concept in a symbolic representation, and each concept has a hyperrectangle or multiple points in the variable space. To construct a tree-structured model from these aggregate survival data, we propose a new approach, where a datum can be included in several terminal nodes in a tree. By constructing a model under this condition, we expect to obtain a more flexible model while retaining the interpretive ease of a hierarchical structure. In this approach, the survival function of concepts that are partially included in a node is constructed using the Kaplan-Meier method, where the number of events and risks at each time point is replaced by the expectation value of the number of individual descriptions of concepts. We present an application of this proposed model using primary brain tumor patient data. As a result, we obtained a new interpretation of the data in comparison to the classical survival tree modeling methods.

scholarly journals The Effect of Exclusive Breastfeeding on Child Survival Using Modified Kaplan Meier Model (MKMM)

2019 ◽  
pp. 1-10
Author(s):  
Moses Longji Dashal ◽  
Kazeem Eyitayo Lasisi ◽  
Kaneng Eileen Longji
Keyword(s):  
Exclusive Breastfeeding ◽  
Survival Data ◽  
Survival Probability ◽  
Survival Function ◽  
Child Survival ◽  
Food Supplement ◽  
Information Criteria ◽  
Kaplan Meier ◽  
Number Of Patients ◽  
Milk Substitute

Background: In Survival analysis, Kaplan-Meier estimator serves as a tool for measuring the frequency or the number of patients surviving medical treatment. Kaplan Meier estimates of survival data have become a better way of analyzing data in cohort study. Kaplan- Meier (K-M) is a non-parametric estimates of survival function that is commonly used to describe survivorship of a study population and to compare two study populations. Aims: This research study is aimed at reducing the morbidity and mortality rate of children less than 6 months. Methodology: 58,609 children less than six months were Exclusive Breastfed from the database. The analysis is done using both K-M and the modified K-M model to examine the effects of Exclusive Breastfeeding. The AIC and BIC was also used as the information criteria. Results: Our results revealed that the K-M model 0.998566822 as the estimated survival probability of children under the ages of six months. Also showing, Exclusively Breastfed children stand the chance of 99% survival. The modified K-M model also revealed 6.98276443909739 as the estimated survival probability, due to initiation of milk substitute and food supplement into the breastfeeding pattern. Showing about 70% chances of survival. Implying about 30% of the existence in one disease or the other or the risk of dying before the age of 5 years. From the information criteria, the AIC (2.3119452169420) and BIC (7.8478797677756) in the Modified K-M are both lower compared to Existing Kaplan Meier (4.0012457354876) and (9.5371847322969) respectively. Modified K-M stand as the best model in knowing the types/amount of food to be added to breastfeeding pattern. Conclusion: So far, the Modified Kaplan Meier Model has been verified and the findings agree that the life expectation will be improved by 99% if children are fed exclusively with breast milk while the life span is been reduced that can lead to death by 30% if the children have a mix feeding which agrees with why Exclusive Breastfeeding should be done.

Progression-free survival (PFS) and overall survival (OS) across ethnicities for patients with metastatic renal cell carcinoma (mRCC) receiving targeted therapies (TT) as first-line (1L) treatment.

2020 ◽  
Vol 38 (6_suppl) ◽  
pp. 645-645
Author(s):  
Nicholas Salgia ◽  
Nazli Dizman ◽  
Paulo Gustavo Bergerot ◽  
Cristiane Decat Bergerot ◽  
Joann Hsu ◽  
...  
Keyword(s):  
Ethnic Groups ◽  
Asian American ◽  
Survival Data ◽  
Survival Function ◽  
Progression Free Survival ◽  
Mtor Inhibitors ◽  
Caucasian American ◽  
Kaplan Meier ◽  
Significant Difference ◽  
The Relationship

645 Background: Recent efforts have sought to characterize differences in clinical and pathological characteristics across ethnicities in mRCC (Batai et al CGUC 2018), however, the relationship between ethnicity and treatment outcomes has yet to be explored. We sought to compare survival outcomes across ethnic groups for patients receiving 1L TT for treatment of mRCC. Methods: Patients receiving 1L systemic treatment for mRCC were retrospectively identified from a single institution database from 2009 to present. Patient ethnicity data were collected from electronic health records. Due to the demographics of the patient population, ethnicity was categorized as Non-Hispanic Caucasian American (CA), Hispanic American (HA), or Asian American (AsA). Patients prescribed tyrosine kinase and/or mTOR inhibitors as 1L therapy were included for analysis. PFS and OS were analyzed across ethnic groups and comparisons were performed using the Kaplan Meier Survival Function in SPSS. Results: Of 294 (77:217 F:M) patients with documented survival data, 183 (62%) were CA, 82 (28%) HA, and 29 (10%) AsA. The most frequently used TTs were sunitinib (63%), temsirolimus (10%), pazopanib (7%), sorafenib (5%), and cabozantinib (4%). Median PFS for CA was 5.6 months (95% Confidence Interval [CI]: 4.1-7.1) vs. 4.7 months (95% CI: 3.1-6.2) for HA vs. 4.7 months (95% CI: 2.1-7.3) for AsA. Median OS was 32.0 months (95% CI: 26.2-37.8) for CA vs. 31.7 months (95% CI: 21.1-42.4) for HA vs. 51.7 months (95% CI: 31.6-71.8) for AsA. No significant difference in PFS or OS was calculated across the three ethnic groups (p=0.652 and p=0.435, respectively). Conclusions: The lack of a statistically significant difference in both PFS and OS across ethnic groups is a promising assessment for the current landscape of health disparities in mRCC. As these data are distinct from recent findings identifying disparities in other malignancies (e.g., prostate cancer), multicenter collaborations should be encouraged to validate these findings.

scholarly journals AN APPLICATION OF THE POISSON-WEIBULL MODEL FOR CENSURED DATA

2021 ◽  
Vol 39 (4) ◽  
pp. 505-521
Author(s):  
Valdemiro Piedade VIGAS ◽  
Fábio PRATAVIERA ◽  
Giovana Oliveira SILVA
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Survival Data ◽  
Real Data ◽  
Weibull Model ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Kaplan Meier ◽  
Proposed Model ◽  
The Mean

In this paper, we proposed the Poisson-Weibull distribution for the modeling of survival data. The motivation to study this model since, in addition to generalizing the Weibull distribution, which is widely used in several areas of knowledge among them the Survival and Reliability analysis, it presents great exibility in the forms of the hazard function. The Poisson-Weibull distribution was created in a composition of discrete and continuous distributions where there is no information about which factor was responsible for the component failure, only the minimum lifetime value among all risks is observed. The maximum likelihood approach was used to estimate the parameters of the model. Also was conducted a simulation study to examine the mean, the bias, and the root of the mean square error of the maximum likelihood estimates of the proposed model according to the censoring percentages and sample sizes. The model selection criteria were also applied, in addition to graphic techniques such as TTT-Plot and Kaplan-Meier. Application to the real data set was used to illustrate the usefulnessof the distribution.

scholarly journals Estimation of Heterogeneous Restricted Mean Survival Time Using Random Forest

2021 ◽  
Vol 11 ◽  
Author(s):  
Mingyang Liu ◽  
Hongzhe Li
Keyword(s):  
Random Forest ◽  
Survival Time ◽  
Survival Data ◽  
Survival Function ◽  
Parametric Models ◽  
The Cancer Genome Atlas ◽  
Data Set ◽  
Cancer Data ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time

Estimation and prediction of heterogeneous restricted mean survival time (hRMST) is of great clinical importance, which can provide an easily interpretable and clinically meaningful summary of the survival function in the presence of censoring and individual covariates. The existing methods for the modeling of hRMST rely on proportional hazards or other parametric assumptions on the survival distribution. In this paper, we propose a random forest based estimation of hRMST for right-censored survival data with covariates and prove a central limit theorem for the resulting estimator. In addition, we present a computationally efficient construction for the confidence interval of hRMST. Our simulations show that the resulting confidence intervals have the correct coverage probability of the hRMST, and the random forest based estimate of hRMST has smaller prediction errors than the parametric models when the models are mis-specified. We apply the method to the ovarian cancer data set from The Cancer Genome Atlas (TCGA) project to predict hRMST and show an improved prediction performance over the existing methods. A software implementation, srf using R and C++, is available at https://github.com/lmy1019/SRF.

Impact of digital multi-sided platforms on firm survival in retail

2021 ◽  
pp. 93-122
Author(s):  
E. S. Andronova ◽  
A. I. Rey ◽  
G. R. Akzhigitova
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Positive Impact ◽  
Survival Function ◽  
Firm Survival ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Data Set ◽  
Hazards Model ◽  
Kaplan Meier

This paper explores firm survival in Russian retail industry in cases of digital multi-sided platforms penetration such as aggregator Yandex.Market, marketplace Wildberries, electronic store Ozon and classified-ad service Avito. The panel data set of 130 thousand firms was analyzed using two methods: non-parametric Kaplan—Meier estimator and semi-parametric Cox proportional hazards model with time dependent covariates. Kaplan—Meier estimator calculates the survival function for censored data. Cox proportional hazards model examines the effect of platform penetration on hazard rates of differently sized firms in various industry spheres. Platforms-aggregators Yandex.Market and Wildberries have a strong positive impact on firm survival while platformsdisruptors Ozon and Avito increase likelihood of firm failure. The main results of platform influence in various industry spheres are as follows: the aggregator of price offers has a more positive impact on segments with high information asymmetry; and firms specialized on Wildberries key product categories enjoy lower hazard ratios of bankruptcy or liquidation. These hypotheses are not supported for Ozon and Avito platforms.

How to Assess Prognostic Models for Survival Data: A Case Study in Oncology

2003 ◽  
Vol 42 (05) ◽  
pp. 564-571 ◽  
Author(s):  
M. Schumacher ◽  
E. Graf ◽  
T. Gerds
Keyword(s):  
Test Data ◽  
Survival Data ◽  
Prediction Error ◽  
Classification Scheme ◽  
Neural Nets ◽  
Brier Score ◽  
Data Set ◽  
Independent Test ◽  
Artificial Neural

Summary Objectives: A lack of generally applicable tools for the assessment of predictions for survival data has to be recognized. Prediction error curves based on the Brier score that have been suggested as a sensible approach are illustrated by means of a case study. Methods: The concept of predictions made in terms of conditional survival probabilities given the patient’s covariates is introduced. Such predictions are derived from various statistical models for survival data including artificial neural networks. The idea of how the prediction error of a prognostic classification scheme can be followed over time is illustrated with the data of two studies on the prognosis of node positive breast cancer patients, one of them serving as an independent test data set. Results and Conclusions: The Brier score as a function of time is shown to be a valuable tool for assessing the predictive performance of prognostic classification schemes for survival data incorporating censored observations. Comparison with the prediction based on the pooled Kaplan Meier estimator yields a benchmark value for any classification scheme incorporating patient’s covariate measurements. The problem of an overoptimistic assessment of prediction error caused by data-driven modelling as it is, for example, done with artificial neural nets can be circumvented by an assessment in an independent test data set.

scholarly journals Were VCF patients at higher risk of mortality following the 2009 publication of the vertebroplasty “sham” trials?

2017 ◽  
Vol 29 (2) ◽  
pp. 375-383 ◽  
Author(s):  
K. L. Ong ◽  
D. P. Beall ◽  
M. Frohbergh ◽  
E. Lau ◽  
J. A. Hirsch
Keyword(s):  
Mortality Risk ◽  
Cox Regression ◽  
Compression Fracture ◽  
Balloon Kyphoplasty ◽  
Data Set ◽  
Mortality Risks ◽  
Medicare Data ◽  
Kaplan Meier ◽  
Risk Of Mortality ◽  
Insight Into

Abstract Summary The 5-year period following 2009 saw a steep reduction in vertebral augmentation volume and was associated with elevated mortality risk in vertebral compression fracture (VCF) patients. The risk of mortality following a VCF diagnosis was 85.1% at 10 years and was found to be lower for balloon kyphoplasty (BKP) and vertebroplasty (VP) patients. Introduction BKP and VP are associated with lower mortality risks than non-surgical management (NSM) of VCF. VP versus sham trials published in 2009 sparked controversy over its effectiveness, leading to diminished referral volumes. We hypothesized that lower BKP/VP utilization would lead to a greater mortality risk for VCF patients. Methods BKP/VP utilization was evaluated for VCF patients in the 100% US Medicare data set (2005–2014). Survival and morbidity were analyzed by the Kaplan-Meier method and compared between NSM, BKP, and VP using Cox regression with adjustment by propensity score and various factors. Results The cohort included 261,756 BKP (12.6%) and 117,232 VP (5.6%) patients, comprising 20% of the VCF patient population in 2005, peaking at 24% in 2007–2008, and declining to 14% in 2014. The propensity-adjusted mortality risk for VCF patients was 4% (95% CI, 3–4%; p < 0.001) greater in 2010–2014 versus 2005–2009. The 10-year risk of mortality for the overall cohort was 85.1%. BKP and VP cohorts had a 19% (95% CI, 19–19%; p < 0.001) and 7% (95% CI, 7–8%; p < 0.001) lower propensity-adjusted 10-year mortality risk than the NSM cohort, respectively. The BKP cohort had a 13% (95% CI, 12–13%; p < 0.001) lower propensity-adjusted 10-year mortality risk than the VP cohort. Conclusions Changes in treatment patterns following the 2009 VP publications led to fewer augmentation procedures. In turn, the 5-year period following 2009 was associated with elevated mortality risk in VCF patients. This provides insight into the implications of treatment pattern changes and associated mortality risks.

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