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Incidence Function (incidence + function)

Distribution by Scientific Domains
Mathematics and Statistics100%

Kinds of Incidence Function

  • cumulative incidence function
    		•

    Selected Abstracts

    A Note on Variance Estimation of the Aalen,Johansen Estimator of the Cumulative Incidence Function in Competing Risks, with a View towards Left-Truncated Data

    BIOMETRICAL JOURNAL, Issue 1 2010
    Arthur Allignol
    Abstract The Aalen,Johansen estimator is the standard nonparametric estimator of the cumulative incidence function in competing risks. Estimating its variance in small samples has attracted some interest recently, together with a critique of the usual martingale-based estimators. We show that the preferred estimator equals a Greenwood-type estimator that has been derived as a recursion formula using counting processes and martingales in a more general multistate framework. We also extend previous simulation studies on estimating the variance of the Aalen,Johansen estimator in small samples to left-truncated observation schemes, which may conveniently be handled within the counting processes framework. This investigation is motivated by a real data example on spontaneous abortion in pregnancies exposed to coumarin derivatives, where both competing risks and left-truncation have recently been shown to be crucial methodological issues (Meister and Schaefer (2008), Reproductive Toxicology26, 31,35). Multistate-type software and data are available online to perform the analyses. The Greenwood-type estimator is recommended for use in practice. [source]

    Semiparametric Models for Cumulative Incidence Functions

    BIOMETRICS, Issue 1 2004
    John Bryant
    Summary. In analyses of time-to-failure data with competing risks, cumulative incidence functions may be used to estimate the time-dependent cumulative probability of failure due to specific causes. These functions are commonly estimated using nonparametric methods, but in cases where events due to the cause of primary interest are infrequent relative to other modes of failure, nonparametric methods may result in rather imprecise estimates for the corresponding subdistribution. In such cases, it may be possible to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimators. The cumulative incidence estimators so obtained are simple to compute and are considerably more efficient than the usual nonparametric estimator, particularly with regard to interpolation of cumulative incidence at early or intermediate time points within the range of data used to fit the function. More surprisingly, they are often nearly as efficient as fully parametric estimators. We illustrate the utility of this approach in the analysis of patients treated for early stage breast cancer. [source]

    Direct parametric inference for the cumulative incidence function

    JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 2 2006
    Jong-Hyeon Jeong
    Summary., In survival data that are collected from phase III clinical trials on breast cancer, a patient may experience more than one event, including recurrence of the original cancer, new primary cancer and death. Radiation oncologists are often interested in comparing patterns of local or regional recurrences alone as first events to identify a subgroup of patients who need to be treated by radiation therapy after surgery. The cumulative incidence function provides estimates of the cumulative probability of locoregional recurrences in the presence of other competing events. A simple version of the Gompertz distribution is proposed to parameterize the cumulative incidence function directly. The model interpretation for the cumulative incidence function is more natural than it is with the usual cause-specific hazard parameterization. Maximum likelihood analysis is used to estimate simultaneously parametric models for cumulative incidence functions of all causes. The parametric cumulative incidence approach is applied to a data set from the National Surgical Adjuvant Breast and Bowel Project and compared with analyses that are based on parametric cause-specific hazard models and nonparametric cumulative incidence estimation. [source]

    A Note on Variance Estimation of the Aalen,Johansen Estimator of the Cumulative Incidence Function in Competing Risks, with a View towards Left-Truncated Data

    BIOMETRICAL JOURNAL, Issue 1 2010
    Arthur Allignol
    Abstract The Aalen,Johansen estimator is the standard nonparametric estimator of the cumulative incidence function in competing risks. Estimating its variance in small samples has attracted some interest recently, together with a critique of the usual martingale-based estimators. We show that the preferred estimator equals a Greenwood-type estimator that has been derived as a recursion formula using counting processes and martingales in a more general multistate framework. We also extend previous simulation studies on estimating the variance of the Aalen,Johansen estimator in small samples to left-truncated observation schemes, which may conveniently be handled within the counting processes framework. This investigation is motivated by a real data example on spontaneous abortion in pregnancies exposed to coumarin derivatives, where both competing risks and left-truncation have recently been shown to be crucial methodological issues (Meister and Schaefer (2008), Reproductive Toxicology26, 31,35). Multistate-type software and data are available online to perform the analyses. The Greenwood-type estimator is recommended for use in practice. [source]

    Nonparametric Association Analysis of Exchangeable Clustered Competing Risks Data

    BIOMETRICS, Issue 2 2009
    Yu Cheng
    Summary The work is motivated by the Cache County Study of Aging, a population-based study in Utah, in which sibship associations in dementia onset are of interest. Complications arise because only a fraction of the population ever develops dementia, with the majority dying without dementia. The application of standard dependence analyses for independently right-censored data may not be appropriate with such multivariate competing risks data, where death may violate the independent censoring assumption. Nonparametric estimators of the bivariate cumulative hazard function and the bivariate cumulative incidence function are adapted from the simple nonexchangeable bivariate setup to exchangeable clustered data, as needed with the large sibships in the Cache County Study. Time-dependent association measures are evaluated using these estimators. Large sample inferences are studied rigorously using empirical process techniques. The practical utility of the methodology is demonstrated with realistic samples both via simulations and via an application to the Cache County Study, where dementia onset clustering among siblings varies strongly by age. [source]

    Nonparametric Estimation in a Cure Model with Random Cure Times

    BIOMETRICS, Issue 1 2001
    Rebecca A. Betensky
    Summary. Acute respiratory distress syndrome (ARDS) is a life-threatening acute condition that sometimes follows pneumonia or surgery. Patients who recover and leave the hospital are considered to have been cured at the time they leave the hospital. These data differ from typical data in which cure is a possibility: death times are not observed for patients who are cured and cure times are observed and vary among patients. Here we apply a competing risks model to these data and show it to be equivalent to a mixture model, the more common approach for cure data. Further, we derive an estimator for the variance of the cumulative incidence function from the competing risks model, and thus for the cure rate, based on elementary calculations. We compare our variance estimator to Gray's (1988, Annals of Statistics16, 1140,1154) estimator, which is based on counting process theory. We find our estimator to be slightly more accurate in small samples. We apply these results to data from an ARDS clinical trial. [source]

    Direct parametric inference for the cumulative incidence function

    JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 2 2006
    Jong-Hyeon Jeong
    Summary., In survival data that are collected from phase III clinical trials on breast cancer, a patient may experience more than one event, including recurrence of the original cancer, new primary cancer and death. Radiation oncologists are often interested in comparing patterns of local or regional recurrences alone as first events to identify a subgroup of patients who need to be treated by radiation therapy after surgery. The cumulative incidence function provides estimates of the cumulative probability of locoregional recurrences in the presence of other competing events. A simple version of the Gompertz distribution is proposed to parameterize the cumulative incidence function directly. The model interpretation for the cumulative incidence function is more natural than it is with the usual cause-specific hazard parameterization. Maximum likelihood analysis is used to estimate simultaneously parametric models for cumulative incidence functions of all causes. The parametric cumulative incidence approach is applied to a data set from the National Surgical Adjuvant Breast and Bowel Project and compared with analyses that are based on parametric cause-specific hazard models and nonparametric cumulative incidence estimation. [source]

    Semiparametric Models for Cumulative Incidence Functions

    BIOMETRICS, Issue 1 2004
    John Bryant
    Summary. In analyses of time-to-failure data with competing risks, cumulative incidence functions may be used to estimate the time-dependent cumulative probability of failure due to specific causes. These functions are commonly estimated using nonparametric methods, but in cases where events due to the cause of primary interest are infrequent relative to other modes of failure, nonparametric methods may result in rather imprecise estimates for the corresponding subdistribution. In such cases, it may be possible to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimators. The cumulative incidence estimators so obtained are simple to compute and are considerably more efficient than the usual nonparametric estimator, particularly with regard to interpolation of cumulative incidence at early or intermediate time points within the range of data used to fit the function. More surprisingly, they are often nearly as efficient as fully parametric estimators. We illustrate the utility of this approach in the analysis of patients treated for early stage breast cancer. [source]