A simple hybrid variance estimator for the Kaplan-Meier survival function

2005 ◽  
Vol 24 (6) ◽  
pp. 827-851 ◽  
Author(s):  
Craig B. Borkowf
2009 ◽  
Vol 6 (3) ◽  
pp. 612-617
Author(s):  
Baghdad Science Journal

Cox regression model have been used to estimate proportion hazard model for patients with hepatitis disease recorded in Gastrointestinal and Hepatic diseases Hospital in Iraq for (2002 -2005). Data consists of (age, gender, survival time terminal stat). A Kaplan-Meier method has been applied to estimate survival function and hazerd function.


2020 ◽  
pp. 181-218
Author(s):  
Bendix Carstensen

This chapter describes survival analysis. Survival analysis concerns data where the outcome is a length of time, namely the time from inclusion in the study (such as diagnosis of some disease) till death or some other event — hence the term 'time to event analysis', which is also used. There are two primary targets normally addressed in survival analysis: survival probabilities and event rates. The chapter then looks at the life table estimator of survival function and the Kaplan–Meier estimator of survival. It also considers the Cox model and its relationship with Poisson models, as well as the Fine–Gray approach to competing risks.


2020 ◽  
Vol 189 (11) ◽  
pp. 1408-1411 ◽  
Author(s):  
Stephen R Cole ◽  
Jessie K Edwards ◽  
Ashley I Naimi ◽  
Alvaro Muñoz

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.


Author(s):  
Jai Jai Shiva Shankar ◽  
Adil Bata ◽  
Krista Ritchie ◽  
Andrea Hebb ◽  
Simon Walling

AbstractBackground: Glioblastoma multiforme (GBM) is known to have poor prognosis, with no available imaging marker that can predict survival at the time of diagnosis. Diffusion weighted images are used in characterisation of cellularity and necrosis of GBM. The purpose of this study was to assess whether pattern or degree of diffusion restriction could help in the prognostication of patients with GBM. Material and Methods: We retrospectively analyzed 84 consecutive patients with confirmed GBM on biopsy or resection. The study was approved by the institutional ethics committee. The total volume of the tumor and total volume of tumor showing restricted diffusion were calculated. The lowest Apparent Diffusion Coefficient (ADC) in the region of the tumor and in the contralateral Normal Appearing White Matter were calculated in order to calculate the nADC. Treatment and follow-up data in these patients were recorded. Multivariate analsysis was completed to determine significant correlations between different variables and the survival of these patients. Results: Patient survival was significantly related to the age of the patient (p<0.0001; 95% CI-1.022-1.043) and the nADC value (p=0.014; 95% CI-0.269-0.860) in the tumor. The correlation coefficients of age and nADC with survival were −0.335 (p=0.002) and 0.390 (p<0.001), respectively. Kaplan Meier survival function, grouped by normalized Apparent Diffusion Coefficient cut off value of 0.75, was significant (p=0.007). Conclusion: The survival of patients with GBM had small, but significant, correlations with the patient’s age and nADC within the tumor.


2011 ◽  
Vol 29 (7_suppl) ◽  
pp. 128-128 ◽  
Author(s):  
S. Oudard ◽  
F. Joulain ◽  
A. De Geer ◽  
A. O. Sartor

128^ Background: TROPIC evaluated the efficacy and safety of the novel taxane cabazitaxel in men with mCRPC previously treated with docetaxel. Median OS was significantly improved, as previously reported (12.7 months in mitoxantrone arm vs 15.1 months in cabazitaxel arm, HR=0.72 [0.61 – 0.84], p<0.0001- updated OS results). Median OS is the most useful descriptive statistic for physicians and patients as it reflects a point estimate in time by which 50% patients may survive regardless of disease status or progression. It avoids assumptions on long-term survival beyond the follow-up period of the clinical trial. Payers however are interested in making a coverage and reimbursement decisions based on the overall therapeutic benefit relative to its risk, and the expected impact on healthcare expenditures. Analyses such as cost-effectiveness analysis therefore require the estimation of mean OS. Methods: Mean OS is only observable when the last patient has died. Its estimation can be derived via an extrapolation of the trial Kaplan-Meier curve using a survival function. Several parametric distributions (exponential, weibull, lognormal, loglogistic and Gompertz) were tested. The parametric distribution that best fitted the trial Kaplan-Meier curves was selected using the Akaike's Information criteria (AIC), the Bayesian Information Criteria (BIC) and graphical method to evaluate the goodness of fit of the distributions. Mean OS from the best fitted model was generated to support payer decision making. Results: Using AIC/BIC and graphical method, the Weibull survival function, S(t)=exp(-l ts) where l is a scale parameter and s a shape parameter, was selected as the distribution that best fitted the TROPIC data. Results of the estimated mean survival assuming a Weibull function are described in the table. Conclusions: Assuming a Weibull distribution, mean OS is estimated at 14.5 months in mitoxantrone arm vs 18.5 months in cabazitaxel arm, leading to 4 months OS difference in favour of cabazitaxel. [Table: see text] [Table: see text]


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ruonan Liu ◽  
Yuhui Yue ◽  
Dongling Miao ◽  
Baodong Cheng

PurposeThis article will select 25 years of subdivided data to perform Kaplan–Meier survival analysis on the export trade relations of Chinese wooden flooring, use discrete-time cloglog models to analyze influencing factors, use logit and probit models to test the robustness, and try to systematically reveal the duration of China's wood flooring export trade and its influencing factors.Design/methodology/approachThis study used Kaplan–Meier survival function estimation method. In the survival analysis, survival function and hazard rate function are often used to characterize the distribution of survival time.FindingsThe continuous average export time of China's wooden flooring is relatively long, about 14 years. China's wooden flooring has a negative time dependency. After the export trade exceeds the threshold value of 15 years, the failure rate of trade greatly decreases, which has a “threshold effect.” Gravity model variables have a significant impact on the duration of China's wooden floor export.Originality/valueStudying the duration of forest products trade is of great significance for clearing deep-level trade relations and promoting sustainable development of forest products trade.


2021 ◽  
pp. 22-33
Author(s):  
Sharma D.K. ◽  
Sonali Saxena

The Shannon interval uncertainty was suggested as a convenient functional uncertainty metric for dual-sided shortened latent variables in the composite reliability. A new measure of disparity has recently been suggested between two doubly truncated distributions of life. The generalised informative discrimination measure for lifetime distribution in the given time interval is described in the present paper. Few features of the new generalised measure are also being investigated. An analysis of lung-cancer data is done using survival function, and Kaplan Meier estimator using Python libraries.


2019 ◽  
Vol 3 (Issue 4) ◽  
pp. 243
Author(s):  
Zhanybek Gaibyldaev ◽  
Zhamalbek Ashimov ◽  
Damirbek Abibillaev ◽  
Fuat Kocyigit

In our study we conducted survival analysis of 204 patients visited Scientific-Research Institute of Heart Surgery and Organs transplantation and who underwent renal transplantation in Kyrgyzstan and other Eurasian countries between 2005 and 2016 years (age range: 9-71 years, mean: 38.21 (12.74) years, median: 34.0 (0.89) years; gender: 142 male (69.6%)). During follow-up period, mortality event was observed in 16 (7.84%) patients. Survival function probabilities of patients and rational risk factors of survival functions were evaluated by Kaplan-Meier and Cox regression analyses, respectively. According to Kaplan-Meier results survival probabilities calculated for 1st year: 0.96 (0.014), for 3rd year: 0.94 (0.018), for 5th year: 0.86 (0.04), for 7th year: 0.75 (0.10). Among age groups 28-39 age ranges prevailed by 11 patients. Nevertheless, that difference did not show statistical significance: p˃0.322. The intensity of transplantation also analyzed according to years, which revealed increasing in numbers of operations by time. For instance, when in 2006 only two cases were registered in our center, but numbers of transplanted patients reached up to 48 in 2015. The association of mortality states and years of transplantation found significantly by Kaplan-Meier test (Breslow p˂0.001). The survival analysis was compared according to countries and revealed significant results (Breslow p˂0.05). From other factors influencing mortality, sex did not show strong impact on survival by Kaplan-Meier analysis, but significant association was found by Cox regression analysis.


2015 ◽  
Vol 16 (2) ◽  
pp. 73-78
Author(s):  
Alexander E Berezin ◽  
Alexander A Kremzer ◽  
Tatayna A Samura

Aim: To evaluate the prognostic value of circulating VE-catherinfor cumulative survivalin patients with ischemic chronic heart failure (CHF).Methods: A total of 154 patients withischemic symptomatic moderate-to-severe CHF were enrolled in the study on discharge from the hospital. Observation period was up to 3 years. Blood samples for biomarkers measurements were collected. ELISA method for measurements of circulating level of VE-catherin was used. Concentrations of VEcatherinfor cumulative survival cases due to advanced CHF were tested. Additionally, all-cause mortality, and CHFrelated death were examined.Results: During a median follow-up of 2.18 years, 21 participants died and 106 subjects were hospitalized repetitively. Medians of circulating levels of VE-catherin in survived and died patient cohort were 0.63 ng/ml (95% confidence interval [CI] = 0.55-0.64 ng/ml) and 1.03 ng/ml (95% CI = 0.97-1.07 ng/ml) (P<0.001). ROC analysis has been shown that cutoff point of VE-catherin concentration for cumulative survival function was 0.755ng/ml. It has beenfound a significantly divergence of Kaplan-Meier survival curves in patients with high (>0.755 ng/ml) and low (<0.755 ng/ml) concentrations of VE-catherin. Circulating VE-catherin independently predicted all-cause mortality (OR = 1.27; 95% CI = 1.08–1.59; P = 0.002), CHF-related death (OR = 1.16; 95% CI 1.02–1.50; P < 0.001), and also CHF-related rehospitalisation (OR = 1.12; 95% CI = 1.07 – 1.25; P<0.001) within 3 years of observation period.Conclusion: Increased circulating VE-catherinassociates with increased 3-year CHF-related death, all-cause mortality, and risk for recurrent hospitalization due to CHF.J MEDICINE July 2015; 16 (2) : 73-78


Blood ◽  
2010 ◽  
Vol 116 (21) ◽  
pp. 3812-3812
Author(s):  
Thomas E. Delea ◽  
Khalid El Ougari ◽  
Jason Rotter ◽  
Alice Wang ◽  
Satyin Kaura ◽  
...  

Abstract Abstract 3812 Background: The Medical Research Council (MRC) Myeloma IX study compared the intravenous (IV) bisphosphonate, zoledronic acid (ZOL) 4 mg q 3–4 wk with the oral bisphosphonate, clodronate (CLO) 1,600 mg/d PO, in 1,970 patients with newly-diagnosed multiple myeloma (MM). After a median follow-up of 3.7 yrs (max. follow-up 6 years), ZOL prolonged OS (median 50.0 vs. 44.5 months; HR=0.842; p=0.0118), increased PFS (median 19.5 vs. 17.5 months; HR=0.883; P=0.0179), and reduced the incidence of skeletal related events (SREs) (27.0% vs. 35.3%; HR=0.74; P=0.0004) compared with CLO. The incidence of acute renal failure (ARF) was similar in the two groups (5.8% vs. 6.1% with ZOL vs. CLO). The incidence of osteonecrosis of the jaw (ONJ) was 3.5% with ZOL and 0.3% with CLO. The objective of this study was to evaluate the cost-effectiveness of ZOL vs. CLO in patients with newly-diagnosed MM based on the reported findings of the MRC Myeloma IX trial. Methods: An economic model was used to project PFS, OS, the incidence of SREs (vertebral and other fractures, radiotherapy, bone surgery, and spinal cord compression) and adverse events (ARF, ONF, thromboembolism, and infection) as well as expected lifetime healthcare costs for patients with newly diagnosed MM who are alternatively assumed to received bishphosphonate therapy with ZOL or CLO. Cost-effectiveness was expressed in terms of the incremental cost per quality-adjusted life-year (QALY) gained with ZOL vs. CLO. Clinical data were based on reported results of the MRC Myeloma IX trial. OS for CLO and ZOL up to 5 years were based on reported Kaplan-Meier survival curves. For CLO, OS after 5 years was projected based on a Weibull survival function fitted to the reported Kaplan-Meier curve. For ZOL, OS after 5 years was obtained by applying the estimated HR for ZOL vs. CLO to the estimated Weibull survival function for CLO. PFS for CLO and ZOL were estimated based on reported medians and the HR for ZOL vs. CLO, assuming proportional hazards Weibull distributions (Kaplan-Meier curves were not reported for PFS). Costs and utility values were obtained from published sources. Costs were in 2009/10 Canadian dollars. Costs and QALY were discounted at 5% annually. Results: Expected lifetime costs of bisphosphonate therapy (including administration and monitoring costs) were $11,967 greater with ZOL vs. CLO ($14,267 vs. $2,301). Expected costs of SREs were reduced by $720 with ZOL ($4,152 vs. $4,872). Expected costs of adverse events were increased by $663 with ZOL ($3,225 vs. $2,562). Expected total lifetime costs were increased by $11,878 ($30,103 vs. $18,225). Life expectancy (undiscounted) was increased by 0.83 years with ZOL (6.43 vs. 5.60). QALYs gained from increased PFS and OS with ZOL vs. CLO were 0.56. QALYs gained from SREs averted with ZOL vs. CLO were <0.01. QALYs lost due to adverse events (predominantly ONJ) were 0.02. Total QALYs gained with ZOL vs. CLO (undiscounted) were 0.56 (4.43 vs. 3.87). On a discounted basis, total QALYs gained were 0.37 (3.51 vs. 3.14). Cost effectiveness with ZOL vs. CLO was $32,210 per QALY gained. In probabilistic sensitivity analyses, the probability that ZOL is preferred to CLO was 85% with a cost-effectiveness threshold of $50,000 per QALY and a 98% with a threshold of $100,000 per QALY. Cost-effectiveness was $43,487 per QALY gained if benefits of ZOL on OS are conservatively assumed to persist for 6 years only (i.e., HR for OS=1.0 after 6 years). Results were sensitive to methods used to estimate PFS and OS (i.e., Kaplan Meier or Weibull models, independent or proportional hazards assumption), and the estimated costs and QALYs lost with ONJ. Conclusions. The cost per QALY gained with ZOL vs. CLO in patients with newly-diagnosed MM is below the commonly-accepted threshold of $50,000 per QALY gained. More precise estimates await release of additional results from the MRC Myeloma IX study. Disclosures: Delea: Novartis: Consultancy, Research Funding. Off Label Use: Zoledronic acid for prevention of skeletal related events in patient with multiple myeloma. Ougari:Novartis: Employment. Rotter:Novartis: Consultancy, Research Funding. Wang:Novartis: Consultancy, Research Funding. Kaura:Novartis: Employment. Morgan:Novartis: Honoraria, Research Funding; Boehringer Ingelheim: Research Funding; Pharmion: Research Funding; Celgene: Research Funding; Chugai: Research Funding; Ortho Biotech: Research Funding.


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