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

Semiparametric linear regression with censored data and stochastic regressors

We propose three new estimation procedures in the linear regression model with randomly-right censored data when the distribution function of the error term is unspecified, regressors are stochastic and the distribution function of the censoring variable is not necessarily the same for all observations ("unequal censoring"). The proposed procedures are derived combining techniques which produce accurate estimates with "equal censoring" with kernel-conditionalı Kaplan-Meier estimates. The performance of six estimation procedures (the three proposed methods and three alternative ones) is compared by means of some Monte Carlo experiments

Estimating the effect of healthcare-associated infections on excess length of hospital stay using inverse probability-weighted survival curves

Background: Studies estimating excess length of stay (LOS) attributable to nosocomial infections have failed to address time-varying confounding, likely leading to overestimation of their impact. We present a methodology based on inverse probability–weighted survival curves to address this limitation. Methods: A case study focusing on intensive care unit–acquired bacteremia using data from 2 general intensive care units (ICUs) from 2 London teaching hospitals were used to illustrate the methodology. The area under the curve of a conventional Kaplan-Meier curve applied to the observed data was compared with that of an inverse probability–weighted Kaplan-Meier curve applied after treating bacteremia as censoring events. Weights were based on the daily probability of acquiring bacteremia. The difference between the observed average LOS and the average LOS that would be observed if all bacteremia cases could be prevented was multiplied by the number of admitted patients to obtain the total excess LOS. Results: The estimated total number of extra ICU days caused by 666 bacteremia cases was estimated at 2453 (95% confidence interval [CI], 1803–3103) days. The excess number of days was overestimated when ignoring time-varying confounding (2845 [95% CI, 2276–3415]) or when completely ignoring confounding (2838 [95% CI, 2101–3575]). Conclusions: ICU-acquired bacteremia was associated with a substantial excess LOS. Wider adoption of inverse probability–weighted survival curves or alternative techniques that address time-varying confounding could lead to better informed decision making around nosocomial infections and other time-dependent exposures

Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates

We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for conditional CDF estimation. Our proof strategy also yields nonasymptotic guarantees for nearest neighbor and kernel variants of the Nelson-Aalen cumulative hazards estimator. We experimentally compare these methods on four datasets. We find that for the kernel survival estimator, a good choice of kernel is one learned using random survival forests.Comment: International Conference on Machine Learning (ICML 2019

Feasibility and Efficacy of Definitive Radiotherapy with 66 Gy and Concurrent Carboplatin-Paclitaxel Chemotherapy for Stage III Non-Small Cell Lung Cancer.

Purpose/Objectives : This study was conducted to assess the feasibility and efficacy of definitive radiotherapy (RT) with a total dose of 66 Gy and concurrent carboplatin-paclitaxel chemotherapy for patients (pts) with stage Ⅲ non-small celllung cancer. Materials/Methods : Between April 2007 and December 2013，99 pts with non-small cell lung cancer were treated using RT with concurrent carboplatin-paclitaxel chemotherapy in our hospital. Sixty-eight of them received RT with a total dose of 66 Gy. We analyzed 46 Stage Ⅲ pts who had been treated with RT using three-dimensional radiotherapy treatment planning. The prophylactic mediastinal lymph nodes were included in the clinical target volume for RT. The survival rate after the start of RT was estimated using the Kaplan-Meier method. We estimated the cumulative local failure and distant metastasis rates with the Fine-Gray method. Adverse events were evaluated according to the CTCAE (v.4.0). Results : The median age of the pts was 70.9 (52.8-78.7) years old (y.o.). The performance status (PS) of each pt was fairly good (ECOG PS 0: 25, PS 1: 20, PS 3:1), and their clinical stages (UICC 7th) were twenty-nine Ⅲ A and seventeen Ⅲ B. Diagnoses were pathologically confirmed in 32 pts. The median follow-up period was 35.7 (2.0-82.2) months among all pts, and 55.9 (40.1-82.2) months among survivors. The 3- and 5-year Kaplan-Meier overall survival rates were 52.2 and 34.0%，respectively, and the median survival time was 36.6 months. The 3- and 5-year Kaplan-Meier progression-free survival rates were 29.1 and 21.9%，respectively, and the median progression-free survival time was 9.9 months. The 5-year local failure rate was 37.6%, and the 5-year distant metastasis rate was 49.7%. Sixteen (34.8%) pts required steroid administration because of radiation pneumonitis (CTCAE Grade 2 or higher) and two of them died (Grade 5). No other severe non-hematologic toxicity (Grade 3 or higher) was observed. Conclusion : These results suggest that definitive RT with a total dose of 66 Gy and concurrent carboplatin-paclitaxel chemotherapy is feasible and may be promising for pts with Stage Ⅲ non-small cell lung cancer

Censored Quantile Regression Redux

Quantile regression for censored survival (duration) data offers a more flexible alternative to the Cox proportional hazard model for some applications. We describe three estimation methods for such applications that have been recently incorporated into the R package quantreg: the Powell (1986) estimator for fixed censoring, and two methods for random censoring, one introduced by Portnoy (2003), and the other by Peng and Huang (2008). The Portnoy and Peng-Huang estimators can be viewed, respectively, as generalizations to regression of the Kaplan-Meier and Nelson-Aalen estimators of univariate quantiles for censored observations. Some asymptotic and simulation comparisons are made to highlight advantages and disadvantages of the three methods.

Modelling competing risks in nephrology research: an example in peritoneal dialysis

BACKGROUND: Modelling competing risks is an essential issue in Nephrology Research. In peritoneal dialysis studies, sometimes inappropriate methods (i.e. Kaplan-Meier method) have been used to estimate probabilities for an event of interest in the presence of competing risks. In this situation a competing risk analysis should be preferable. The objectives of this study are to describe the bias resulting from the application of standard survival analysis to estimate peritonitis-free patient survival and to provide alternative statistical approaches taking competing risks into account. METHODS: The sample comprises patients included in a university hospital peritoneal dialysis program between October 1985 and June 2011 (n = 449). Cumulative incidence function and competing risk regression models based on cause-specific and subdistribution hazards were discussed. RESULTS: The probability of occurrence of the first peritonitis is wrongly overestimated using Kaplan-Meier method. The cause-specific hazard model showed that factors associated with shorter time to first peritonitis were age (>=55 years) and previous treatment (haemodialysis). Taking competing risks into account in the subdistribution hazard model, age remained significant while gender (female) but not previous treatment was identified as a factor associated with a higher probability of first peritonitis event. CONCLUSIONS: In the presence of competing risks outcomes, Kaplan-Meier estimates are biased as they overestimated the probability of the occurrence of an event of interest. Methods which take competing risks into account provide unbiased estimates of cumulative incidence for each specific outcome experienced by patients. Multivariable regression models such as those based on cause-specific hazard and on subdistribution hazard should be used in this competing risk setting