Semiparametric analysis of survival data with left truncation and dependent right censoring

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Because mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left-truncated and right-censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. First, we develop a novel estimator for the gamma frailty parameter under left truncation. Using this estimator, we then derive a closed-form estimator for the marginal distribution of the non-terminal event. The large sample properties of the estimators are established via asymptotic theory. The methodology performs well with moderate sample sizes, both in simulations and in an analysis of data from a diabetes registry.     

Sensitivity analysis for informative censoring in parametric survival models

Most statistical methods for censored survival data assume there is no dependence between the lifetime and censoring mechanisms, an assumption which is often doubtful in practice. In this paper we study a parametric model which allows for dependence in terms of a parameter delta and a bias function B(t, theta). We propose a sensitivity analysis on the estimate of the parameter of interest for small values of delta. This parameter measures the dependence between the lifetime and the censoring mechanisms. Its size can be interpreted in terms of a correlation coefficient between the two mechanisms. A medical example suggests that even a small degree of dependence between the failure and censoring processes can have a noticeable effect on the analysis.     

A comparison of several methods of estimating the survival function when there is extreme right censoring

When there is extreme censoring on the right, the Kaplan-Meier product-limit estimator is known to be a biased estimator of the survival function. Several modifications of the Kaplan-Meier estimator are examined and compared with respect to bias and mean squared error.     

Simple parametric survival analysis with anonymized register data: A cohort study with truncated and interval censored event and censoring times

Background

To preserve patient anonymity, health register data may be provided as binned data only. Here we consider as example, how to estimate mean survival time after a diagnosis of metastatic colorectal cancer from Norwegian register data on time to death or censoring binned into 30 day intervals. All events occurring in the first three months (90 days) after diagnosis were removed to achieve comparability with a clinical trial. The aim of the paper is to develop and implement a simple, and yet flexible method for analyzing such interval censored and truncated data.

Methods

Considering interval censoring a missing data problem, we implement a simple multiple imputation strategy that allows flexible sensitivity analyses with respect to the shape of the censoring distribution. To allow identification of appropriate parametric models, a χ²-goodness-of-fit test--also imputation based--is derived and supplemented with diagnostic plots. Uncertainty estimates for mean survival times are obtained via a simulation strategy. The validity and statistical efficiency of the proposed method for varying interval lengths is investigated in a simulation study and compared with simpler alternatives.

Results

Mean survival times estimated from the register data ranged from 1.2 (SE = 0.09) to 3.2 (0.31) years depending on period of diagnosis and choice of parametric model. The shape of the censoring distribution within intervals did generally not influence results, whereas the choice of parametric model did, even when different models fit the data equally well. In simulation studies both simple midpoint imputation and multiple imputation yielded nearly unbiased analyses (relative biases of -0.6% to 9.4%) and confidence intervals with near-nominal coverage probabilities (93.4% to 95.7%) for censoring intervals shorter than six months. For 12 month censoring intervals, multiple imputation provided better protection against bias, and coverage probabilities closer to nominal values than simple midpoint imputation.

Conclusion

Binning of event and censoring times should be considered a viable strategy for anonymizing register data on survival times, as they may be readily analyzed with methods based on multiple imputation.

     

Cancer pain and its impact on diagnosis, survival and quality of life

Cancer pain significantly affects the diagnosis, quality of life and survival of patients with cancer. During the past decade, preclinical and clinical data has begun to provide insight into the mechanisms that drive and mask cancer pain and the mechanisms by which anti-neoplastic agents induce peripheral neuropathy. Developing a mechanism-based understanding and mechanism-based therapies to treat cancer-associated pain and sensory neuropathy, and incorporating these into mainstream cancer research and therapy, will be crucial to improving the quality of life and survival of patients with cancer.     

Distribution-free regression analysis of grouped survival data

Methods based on regression models for logarithmic hazard functions, Cox models, are given for analysis of grouped and censored survival data. By making an approximation it is possible to obtain explicitly a maximum likelihood function involving only the regression parameters. This likelihood function is a convenient analog to Cox's partial likelihood for ungrouped data. The method is applied to data from a toxicological experiment.     

Computer programs for the analysis of cellular survival data

Four programs have been written to enable radiobiologists to build a computer data base of cellular dose-survival data, calculate cell survival with a correction for cell multiplicity at the time of irradiation, fit various survival models to the data by iteratively weighted least squares, and calculate the ratio of survival levels corresponding to specified doses or the ratio of doses that produce specified survival levels (e.g., oxygen enhancement ratio or relative biological effectiveness). The programs make plots of survival curves and data, and they calculate standard errors and confidence intervals of the fitted survival curve parameters and ratios. The programs calculate survival curves for the linear-quadratic, repair-saturation, single-hit multitarget, linear-multitarget, and repair-misrepair models of cell survival and have been designed to accommodate the addition of other survival models in the future. The programs can be used to compare the accuracy with which different models fit the data, determine if a difference in fit is statistically significant, and show how the estimated value of a survival curve parameter, such as the extrapolation number or the final slope, varies with the survival model. The repair of radiation-induced damage is analyzed in a novel way using these programs.