Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

Improving the accuracy of radiation pneumonitis dose response models

The prognosis for lung cancer patients remains poor. Five year survival rates have been reported to be 15%. Studies have shown that dose escalation to the tumor can lead to better local control and subsequently better overall survival. However, dose to lung tumor is limited by normal tissue toxicity. The most prevalent thoracic toxicity is radiation pneumonitis. In order to determine a safe dose that can be delivered to the healthy lung, researchers have turned to mathematical models predicting the rate of radiation pneumonitis. However, these models rely on simple metrics based on the dose-volume histogram and are not yet accurate enough to be used for dose escalation trials. The purpose of this work was to improve the fit of predictive risk models for radiation pneumonitis and to show the dosimetric benefit of using the models to guide patient treatment planning. The study was divided into 3 specific aims. The first two specifics aims were focused on improving the fit of the predictive model. In Specific Aim 1 we incorporated information about the spatial location of the lung dose distribution into a predictive model. In Specific Aim 2 we incorporated ventilation-based functional information into a predictive pneumonitis model. In the third specific aim a proof of principle virtual simulation was performed where a model-determined limit was used to scale the prescription dose. The data showed that for our patient cohort, the fit of the model to the data was not improved by incorporating spatial information. Although we were not able to achieve a significant improvement in model fit using pre-treatment ventilation, we show some promising results indicating that ventilation imaging can provide useful information about lung function in lung cancer patients. The virtual simulation trial demonstrated that using a personalized lung dose limit derived from a predictive model will result in a different prescription than what was achieved with the clinically used plan; thus demonstrating the utility of a normal tissue toxicity model in personalizing the prescription dose.

The utility of rapid participatory appraisal for community assessment, diagnosis, and policy development

The selection of a model to guide the understanding and resolution of community problems is an important issue relating to the foundation of public health practice: assessment, policy development, and assurance. Many assessment models produce a diagnosis of community weaknesses, but fail to promote planning and interventions. Rapid Participatory Appraisal (RPA) is a participatory action research model which regards assessment as the first step in the problem solving process, and claims to achieve assessment and policy development within limited resources of time and money. Literature documenting the fulfillment of these claims, and thereby supporting the utility of the model, is relatively sparse and difficult to obtain. Very few articles discuss the changes resulting from RPA assessments in urban areas, and those that do describe studies conducted outside the U.S.A. ^ This study examines the utility of the RPA model and its underlying theories: systems theory, grounded theory, and principles of participatory change, as illustrated by the case study of a community assessment conducted for the Texas Diabetes Institute (TDI), San Antonio, Texas, and subsequent outcomes. Diabetes has a high prevalence and is a major issue in San Antonio. Faculty and students conducted the assessment by informal collaboration between two nursing and public health assessment courses, providing practical student experiences. The study area was large, and the flexibility of the model tested by its use in contiguous sub-regions, reanalyzing aggregated results for the study area. Official TDI reports, and a mail survey of agency employees, described policy development resulting from community diagnoses revealed by the assessment. ^ The RPA model met the criteria for utility from the perspectives of merit, worth, efficiency, and effectiveness. The RPA model best met the agencies' criteria (merit), met the data needs of TDI in this particular situation (worth), provided valid results within budget, time, and personnel constraints (efficiency), and stimulated policy development by TDI (effectiveness). ^ The RPA model appears to have utility for community assessment, diagnosis, and policy development in circumstances similar to the TDI diabetes study. ^

The utility of N5 for gene therapy of human cancer

Cancer is a result of defects in the coordination of cell proliferation and programmed cell death. The extent of cell death is physiologically controlled by the activation of a programmed suicide pathway that results in a morphologically recognizable form of death termed apoptosis. Inducing apoptosis in tumor cells by gene therapy provides a potentially effective means to treat human cancers. The p84N5 is a novel nuclear death domain containing protein that has been shown to bind an amino terminal domain of retinoblastoma tumor suppressor gene product (pRb). Expression of N5 can induce apoptosis that is dependent upon its intact death domain and is inhibited by pRb. In many human cancer cells the functions of pRb are either lost through gene mutation or inactivated by different mechanisms. N5 based gene therapy may induce cell death preferentially in tumor cells relative to normal cells. We have demonstrated that N5 gene therapy is less toxic to normal cells than to tumor cells. To test the possibility that N5 could be used in gene therapy of cancer, we have generated a recombinant adenovirus engineered to express N5 and test the effects of viral infection on growth and tumorigenicity of human cancer cells. Adenovirus N5 infection significantly reduced the proliferation and tumorigenicity of breast, ovarian, and osteosarcoma tumor cell lines. Reduced proliferation and tumorigenicity were mediated by an induction of apoptosis as indicated by DNA fragmentation in infected cells. We also test the potential utility of N5 for gene therapy of pancreatic carcinoma that typically respond poorly to conventional treatment. Adenoviral mediated N5 gene transfer inhibits the growth of pancreatic cancer cell lines in vitro. N5 gene transfer also reduces the growth and metastasis of human pancreatic adenocarcinoma in subcutaneous and orthotopic mouse model. Interestingly, the pancreatic adenocarcinoma cells are more sensitive to N5 than they are to p53, suggesting that N5 gene therapy may be effective in tumors resistant to p53. We also test the possibilities of the use of N5 and p53 together on the inhibition of pancreatic cancer cell growth in vitro and vivo. Simultaneous use of N5 and RbΔCDK has been found to exert a greater extent on the inhibition of pancreatic cancer cell growth in vitro and in vivo. ^

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^