Kaplan-Meier V- and U-statistics

In this paper, we study Kaplan-Meier V- and U-statistics respectively defined as $\theta(\widehat{F}_n)=\sum_{i,j}K(X_{[i:n]},X_{[j:n]})W_iW_j$ and $\theta_U(\widehat{F}_n)=\sum_{i\neq j}K(X_{[i:n]},X_{[j:n]})W_iW_j/\sum_{i\neq j}W_iW_j$, where $\widehat{F}_n$ is the Kaplan-Meier estimator, $\{W_1,\ldots,W_n\}$ are the Kaplan-Meier weights and $K:(0,\infty)^2\to\mathbb R$ is a symmetric kernel. As in the canonical setting of uncensored data, we differentiate between two asymptotic behaviours for $\theta(\widehat{F}_n)$ and $\theta_U(\widehat{F}_n)$. Additionally, we derive an asymptotic canonical V-statistic representation of the Kaplan-Meier V- and U-statistics. By using this representation we study properties of the asymptotic distribution. Applications to hypothesis testing are given

Duration of Regional Unemployment Spells in Slovenia

The paper begins with an overview of the unemployment rate in Slovenia and focuses on duration of unemployment and regional characteristics of the unemployment rates. It is shown that the dispersion of regional unemployment rate is gradually decreasing and is also slightly below European average on NUTS 3 level. The analysis of the duration of regional unemployment spells is based on the data obtained from the Employment Office of the Republic of Slovenia, which consists of the unemployment spells between January 1st, 2002 and November 18th, 2005 with more than 450,000 entries. The Kaplan-Meier estimates of the survival function are presented and the effects of region on the duration of unemployment spells are discussed.unemployment, regions, survival analysis, Kaplan-Meier estimator, Slovenia

Survival Analysis Using Auxiliary Variables Via Nonparametric Multiple Imputation

We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variable to recover information for censored observations. To conduct the imputation, we use two working survival model to define the nearest neighbor imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, two nonparametric multiple imputation methods are considered: risk set imputation, and Kaplan-Meier estimator. For both methods a future event or censoring time is imputed for each censored observation. With a categorical auxiliary variable, we show that with a large number of imputes the estimates from the Kaplan-Meier imputation method correspond to the weighted Kaplan-Meier estimator. We also show that the Kaplan-Meier imputation method is robust to misspecification of either one of the two working models. In a simulation study with the time independent and time dependent auxiliary variables, we compare the multiple imputation approaches with an inverse probability of censoring weighted method. We show that all approaches can reduce bias due to dependent censoring and improve the efficiency. We apply the approaches to AIDS clinical trial data comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable

Inferensi Fungsi Ketahanan Dengan Metode Kaplan-meier

. Let T be a nonnegatif random variable representing the life time of individuals in some population. Life time data of individuals are devided in two kinds, cencored and uncencored data. The probability of an individual surviving till time t is given by the survival function S(t)=P(T≥t). Product Limit estimator (Kaplan-Meier estimator) is a nonparametric method to find the survival function for cencored data

Survival Analysis of Hemodialysis Patients

Survival analysis as a collection of statistical procedures for analyzing the data that its outcome variable was the time to occurrence of an event. Kaplan-Meier method is a type of survival analysis technique, this method is often called the Product Limit Method. Chronic Kidney Disease (CKD) became one of the public health problem throughout the world, including Indonesia. The number of hemodialysis patients has increased every year and have an impact on increasing the number of death in General Hospital Ibnu Sina Gresik. This study was determine the survival of hemodialysis patients using Kaplan-Meier analysis techniques. Non-reactive research with a retrospective cohort using the calculations right censoring. 155 population were taken randomly and sample size of 111. Data were collected using a checklist. The estimated survival time of female, adult age, further education, patients work, patients without insurance, patients with normal nutritional status, patients with a history of disease, patient with hypertention and patient with diabetic had a better survival time. The insurance status, nutritional status, hypertension, and diabetes mellitus were significant difference to the survival time (p-value <0.05). It was necessary special treatment for CKD patients through giving information, education to families and patients to maintain healthy lifestyle