Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

Is there a subgroup of long-term evolution among patients with advanced lung cancer?: Hints from the analysis of survival curves from cancer registry data

Background: Recently, with the access of low toxicity biological and targeted therapies, evidence of the existence of a long-term survival subpopulation of cancer patients is appearing. We have studied an unselected population with advanced lung cancer to look for evidence of multimodality in survival distribution, and estimate the proportion of long-term survivors. Methods: We used survival data of 4944 patients with non-small-cell lung cancer (NSCLC) stages IIIb-IV at diagnostic, registered in the National Cancer Registry of Cuba (NCRC) between January 1998 and December 2006. We fitted one-component survival model and two-component mixture models to identify short-and long-term survivors. Bayesian information criterion was used for model selection. Results: For all of the selected parametric distributions the two components model presented the best fit. The population with short-term survival (almost 4 months median survival) represented 64% of patients. The population of long-term survival included 35% of patients, and showed a median survival around 12 months. None of the patients of short-term survival was still alive at month 24, while 10% of the patients of long-term survival died afterwards. Conclusions: There is a subgroup showing long-term evolution among patients with advanced lung cancer. As survival rates continue to improve with the new generation of therapies, prognostic models considering short-and long-term survival subpopulations should be considered in clinical research.

Gene selection using iterative feature elimination random forests for survival outcomes.

Although many feature selection methods for classification have been developed, there is a need to identify genes in high-dimensional data with censored survival outcomes. Traditional methods for gene selection in classification problems have several drawbacks. First, the majority of the gene selection approaches for classification are single-gene based. Second, many of the gene selection procedures are not embedded within the algorithm itself. The technique of random forests has been found to perform well in high-dimensional data settings with survival outcomes. It also has an embedded feature to identify variables of importance. Therefore, it is an ideal candidate for gene selection in high-dimensional data with survival outcomes. In this paper, we develop a novel method based on the random forests to identify a set of prognostic genes. We compare our method with several machine learning methods and various node split criteria using several real data sets. Our method performed well in both simulations and real data analysis.Additionally, we have shown the advantages of our approach over single-gene-based approaches. Our method incorporates multivariate correlations in microarray data for survival outcomes. The described method allows us to better utilize the information available from microarray data with survival outcomes.

Component-wise gradient boosting and false discovery control in survival analysis with high-dimensional covariates.

MOTIVATION: Technological advances that allow routine identification of high-dimensional risk factors have led to high demand for statistical techniques that enable full utilization of these rich sources of information for genetics studies. Variable selection for censored outcome data as well as control of false discoveries (i.e. inclusion of irrelevant variables) in the presence of high-dimensional predictors present serious challenges. This article develops a computationally feasible method based on boosting and stability selection. Specifically, we modified the component-wise gradient boosting to improve the computational feasibility and introduced random permutation in stability selection for controlling false discoveries. RESULTS: We have proposed a high-dimensional variable selection method by incorporating stability selection to control false discovery. Comparisons between the proposed method and the commonly used univariate and Lasso approaches for variable selection reveal that the proposed method yields fewer false discoveries. The proposed method is applied to study the associations of 2339 common single-nucleotide polymorphisms (SNPs) with overall survival among cutaneous melanoma (CM) patients. The results have confirmed that BRCA2 pathway SNPs are likely to be associated with overall survival, as reported by previous literature. Moreover, we have identified several new Fanconi anemia (FA) pathway SNPs that are likely to modulate survival of CM patients. AVAILABILITY AND IMPLEMENTATION: The related source code and documents are freely available at https://sites.google.com/site/bestumich/issues. CONTACT: yili@umich.edu.

Reliable survival analysis based on the Dirichlet Process

We present a robust Dirichlet process for estimating survival functions from samples with right-censored data. It adopts a prior near-ignorance approach to avoid almost any assumption about the distribution of the population lifetimes, as well as the need of eliciting an infinite dimensional parameter (in case of lack of prior information), as it happens with the usual Dirichlet process prior. We show how such model can be used to derive robust inferences from right-censored lifetime data. Robustness is due to the identification of the decisions that are prior-dependent, and can be interpreted as an analysis of sensitivity with respect to the hypothetical inclusion of fictitious new samples in the data. In particular, we derive a nonparametric estimator of the survival probability and a hypothesis test about the probability that the lifetime of an individual from one population is shorter than the lifetime of an individual from another. We evaluate these ideas on simulated data and on the Australian AIDS survival dataset. The methods are publicly available through an easy-to-use R package.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Population-based survival estimates for childhood cancer in Australia during the period 1997–2006

Background: This study provides the latest available relative survival data for Australian childhood cancer patients. Methods: Data from the population-based Australian Paediatric Cancer Registry were used to describe relative survival outcomes using the period method for 11 903 children diagnosed with cancer between 1983 and 2006 and prevalent at any time between 1997 and 2006. Results: The overall relative survival was 90.4% after 1 year, 79.5% after 5 years and 74.7% after 20 years. Where information onstage at diagnosis was available (lymphomas, neuroblastoma, renal tumours and rhabdomyosarcomas), survival was significantly poorer for more-advanced stage. Survival was lower among infants compared with other children for those diagnosed with leukaemia, tumours of the central nervous system and renal tumours but higher for neuroblastoma. Recent improvements in overall childhood cancer survival over time are mainly because of improvements among leukaemia patients. Conclusion: The high and improving survival prognosis for children diagnosed with cancer in Australia is consistent with various international estimates. However, a 5-year survival estimate of 79% still means that many children who are diagnosed with cancer will die within 5 years, whereas others have long-term health morbidities and complications associated with their treatments. It is hoped that continued developments in treatment protocols will result in further improvements in survival.

Bayesian survival analysis using gene expression

This thesis developed and applied Bayesian models for the analysis of survival data. The gene expression was considered as explanatory variables within the Bayesian survival model which can be considered the new contribution in the analysis of such data. The censoring factor that is inherent of survival data has also been addressed in terms of its impact on the fitting of a finite mixture of Weibull distribution with and without covariates. To investigate this, simulation study were carried out under several censoring percentages. Censoring percentage as high as 80% is acceptable here as the work involved high dimensional data. Lastly the Bayesian model averaging approach was developed to incorporate model uncertainty in the prediction of survival.

Response to chemotherapy is predictive in relation to longer overall survival in an individual patient combined-analysis with pleural mesothelioma

Background: There is currently no early predictive marker of survival for patients receiving chemotherapy for malignant pleural mesothelioma (MPM). Tumour response may be predictive for overall survival (OS), though this has not been explored. We have thus undertaken a combined-analysis of OS, from a 42 day landmark, of 526 patients receiving systemic therapy for MPM. We also validate published progression-free survival rates (PFSRs) and a progression-free survival (PFS) prognostic-index model. Methods: Analyses included nine MPM clinical trials incorporating six European Organisation for Research and Treatment of Cancer (EORTC) studies. Analysis of OS from landmark (from day 42 post-treatment) was considered regarding tumour response. PFSR analysis data included six non-EORTC MPM clinical trials. Prognostic index validation was performed on one non-EORTC data-set, with available survival data. Results: Median OS, from landmark, of patients with partial response (PR) was 12·8 months, stable disease (SD), 9·4 months and progressive disease (PD), 3·4 months. Both PR and SD were associated with longer OS from landmark compared with disease progression (both p < 0·0001). PFSRs for platinum-based combination therapies were consistent with published significant clinical activity ranges. Effective separation between PFS and OS curves provided a validation of the EORTC prognostic model, based on histology, stage and performance status. Conclusion: Response to chemotherapy is associated with significantly longer OS from landmark in patients with MPM. © 2012 Elsevier Ltd. All rights reserved.

Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study

Background Multilevel and spatial models are being increasingly used to obtain substantive information on area-level inequalities in cancer survival. Multilevel models assume independent geographical areas, whereas spatial models explicitly incorporate geographical correlation, often via a conditional autoregressive prior. However the relative merits of these methods for large population-based studies have not been explored. Using a case-study approach, we report on the implications of using multilevel and spatial survival models to study geographical inequalities in all-cause survival. Methods Multilevel discrete-time and Bayesian spatial survival models were used to study geographical inequalities in all-cause survival for a population-based colorectal cancer cohort of 22,727 cases aged 20–84 years diagnosed during 1997–2007 from Queensland, Australia. Results Both approaches were viable on this large dataset, and produced similar estimates of the fixed effects. After adding area-level covariates, the between-area variability in survival using multilevel discrete-time models was no longer significant. Spatial inequalities in survival were also markedly reduced after adjusting for aggregated area-level covariates. Only the multilevel approach however, provided an estimation of the contribution of geographical variation to the total variation in survival between individual patients. Conclusions With little difference observed between the two approaches in the estimation of fixed effects, multilevel models should be favored if there is a clear hierarchical data structure and measuring the independent impact of individual- and area-level effects on survival differences is of primary interest. Bayesian spatial analyses may be preferred if spatial correlation between areas is important and if the priority is to assess small-area variations in survival and map spatial patterns. Both approaches can be readily fitted to geographically enabled survival data from international settings

An evaluation of the survival of Atlantic salmon (Salmo salar L.)fry stocked in eight streams in the North West of England.

Eight streams from the North West of England were stocked with Atlantic salmon (Salmo salar L.) fed fry at densities ranging from 1 to 4/m2 over a period of up to three years to evaluate survival to the end of the first an d second growing periods and hence assess the value of stocking as a management practice. Survival to the end of the first growin g period (mean duration of 108 days) was found to vary between 7.8 and 41.3% with a mean of 22% and CV of 0.44. Survival from the end of the first growing period to the end of the second growing period (mean duration of 384 days) ranged from 19.9 to 34.1% with a mean of 26.3% and CV of 0.21. Survival was found to be positively related to 0+ trout density (P < 0.05) and negatively related to altitude (P < 0.05). A comparison of the raw survival data (non standardised with respect to duration of experiments) with that from other studies in relation to stocking densities revealed a negative relationship between fry survival and stocking density (P < 0.05). Densities in excess of 5/m2 tended to result in lower levels of survival. Post stocking fry dispersal patterns were examined for the 1991 data. On average 86.7% of the number of fry surviving remained within the stocked zone by the end of the first growing period. With the exception of one stream there was little in the way of dispersal beyond the stocked zone. The dispersal pattern approximated to the normal distribution (P < 0.05). It was estimated that stocking can result in a net gain of fish to a river system compared with natural productivity, however the numerical significance of this gain and its cost effectiveness need to be determined on a river specific basis.

Apoptosis and cell-cycle regulatory proteins in colorectal carcinoma: relationship to tumour stage and patient survival

The quantitative assessment of apoptotic index (AI) and mitotic index (MI) and the immunoreactivity of p53, bcl-2, p21, and mdm2 were examined in tumour and adjacent normal tissue samples from 30 patients with colonic and 22 with rectal adenocarcinoma. Individual features and combined profiles were correlated with clinicopathological parameters and patient survival data to assess their prognostic value. Increased AI was significantly associated with increased bcl-2 expression (p

Temporal characterization and in vitro comparison of cell survival following the delivery of 3D-conformal, intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT)

A phantom was designed and implemented for the delivery of treatment plans to cells in vitro. Single beam, 3D-conformal radiotherapy (3D-CRT) plans, inverse planned five-field intensity-modulated radiation therapy (IMRT), nine-field IMRT, single-arc volumetric modulated arc therapy (VMAT) and dual-arc VMAT plans were created on a CT scan of the phantom to deliver 3 Gy to the cell layer and verified using a Farmer chamber, 2D ionization chamber array and gafchromic film. Each plan was delivered to a 2D ionization chamber array to assess the temporal characteristics of the plan including delivery time and 'cell's eye view' for the central ionization chamber. The effective fraction time, defined as the percentage of the fraction time where any dose is delivered to each point examined, was also assessed across 120 ionization chambers. Each plan was delivered to human prostate cancer DU-145 cells and normal primary AGO-1522b fibroblast cells. Uniform beams were delivered to each cell line with the delivery time varying from 0.5 to 20.54 min. Effective fraction time was found to increase with a decreasing number of beams or arcs. For a uniform beam delivery, AGO-1552b cells exhibited a statistically significant trend towards increased survival with increased delivery time. This trend was not repeated when the different modulated clinical delivery methods were used. Less sensitive DU-145 cells did not exhibit a significant trend towards increased survival with increased delivery time for either the uniform or clinical deliveries. These results confirm that dose rate effects are most prevalent in more radiosensitive cells. Cell survival data generated from uniform beam deliveries over a range of dose rates and delivery times may not always be accurate in predicting response to more complex delivery techniques, such as IMRT and VMAT.

The Conditional Phase-type distribution: Graphical Models for Continuous Non-Normal Data:The Conditional Phase-type (C-Ph) distribution:

Conditional Gaussian (CG) distributions allow the inclusion of both discrete and continuous variables in a model assuming that the continuous variable is normally distributed. However, the CG distributions have proved to be unsuitable for survival data which tends to be highly skewed. A new method of analysis is required to take into account continuous variables which are not normally distributed. The aim of this paper is to introduce the more appropriate conditional phase-type (C-Ph) distribution for representing a continuous non-normal variable while also incorporating the causal information in the form of a Bayesian network.

The role of molecular, clinical and socioeconomic factors in the long-term survival of axillary node negative breast cancer patients

The overall objective of this study was to investigate factors associated with long-term survival in axillary node negative (ANN) breast cancer patients. Clinical and biological factors included stage, histopathologic grade, p53 mutation, Her-2/neu amplification, estrogen receptor status (ER), progesterone receptor status (PR) and vascular invasion. Census derived socioeconomic (SES) indicators included median individual and household income, proportions of university educated individuals, housing type, "incidence" of low income and an indicator of living in an affluent neighbourhood. The effects of these measures on breast cancer-specific survival and competing cause survival were investigated. A cohort study examining survival among axillary node negative (ANN) breast cancer patients in the greater Toronto area commenced in 1 989. Patients were followed up until death, lost-to-follow up or study termination in 2004. Data were collected from several sources measuring patient demographics, clinical factors, treatment, recurrence of disease and survival. Census level SES data were collected using census geo-coding of patient addresses' at the time of diagnosis. Additional survival data were acquired from the Ontario Cancer Registry to enhance and extend the observation period of the study. Survival patterns were examined using KaplanMeier and life table procedures. Associations were examined using log-rank and Wilcoxon tests of univariate significance. Multivariate survival analyses were perfonned using Cox proportional hazards models. Analyses were stratified into less than and greater than 5 year survival periods to observe whether known markers of short-tenn survival were also associated with reductions in long-tenn survival among breast cancer patients. The 15 year survival probabilities in this cohort were: for breast cancerspecific survival 0.88, competing causes survival 0.89 and for overall survival 0.78. Estrogen receptor (ER) and progesterone receptor (PR) status (Hazard Ratio (HR) ERIPR- versus ER+/PR+, 8.15,95% CI, 4.74, 14.00), p53 mutation (HR, 3.88, 95% CI, 2.00, 7.53) and Her-2 amplification (HR, 2.66, 95% CI, 1.36, 5.19) were associated with significant reductions in short-tenn breast cancer-specific survival «5 years following diagnosis), however, not with long-term survival in univariate analyses. Stage, histopathologic grade and ERiPR status were the clinicallbiologieal factors that were associated with short-term breast cancer specific survival in multivariate results. Living in an affluent neighbourhood (top quintile of median household income compared to the rest of the population) was associated with the largest significant increase in long-tenn breast cancer-specific survival after adjustment for stage, histopathologic grade and treatment (HR, 0.36, 95% CI, 0.12, 0.89).