Simulating Coxian Phase-type Distributions for Patient Survival

Coxian phase-type distributions are a special type of Markov model that can be used to represent survival times in terms of phases through which an individual may progress until they eventually leave the system completely. Previous research has considered the Coxian phase-type distribution to be ideal in representing patient survival in hospital. However, problems exist in fitting the distributions. This paper investigates the problems that arise with the fitting process by simulating various Coxian phase-type models for the representation of patient survival and examining the estimated parameter values and eigenvalues obtained. The results indicate that numerical methods previously used for fitting the model parameters do not always converge. An alternative technique is therefore considered. All methods are influenced by the choice of initial parameter values. The investigation uses a data set of 1439 elderly patients and models their survival time, the length of time they spend in a UK hospital.

Intrinsic subtypes of gastric cancer, based on gene expression pattern, predict survival and respond differently to chemotherapy

BACKGROUND & AIMS:
Gastric cancer (GC) is a heterogeneous disease comprising multiple subtypes that have distinct biological properties and effects in patients. We sought to identify new, intrinsic subtypes of GC by gene expression analysis of a large panel of GC cell lines. We tested if these subtypes might be associated with differences in patient survival times and responses to various standard-of-care cytotoxic drugs.
METHODS:
We analyzed gene expression profiles for 37 GC cell lines to identify intrinsic GC subtypes. These subtypes were validated in primary tumors from 521 patients in 4 independent cohorts, where the subtypes were determined by either expression profiling or subtype-specific immunohistochemical markers (LGALS4, CDH17). In vitro sensitivity to 3 chemotherapy drugs (5-fluorouracil, cisplatin, oxaliplatin) was also assessed.
RESULTS:
Unsupervised cell line analysis identified 2 major intrinsic genomic subtypes (G-INT and G-DIF) that had distinct patterns of gene expression. The intrinsic subtypes, but not subtypes based on Lauren's histopathologic classification, were prognostic of survival, based on univariate and multivariate analysis in multiple patient cohorts. The G-INT cell lines were significantly more sensitive to 5-fluorouracil and oxaliplatin, but more resistant to cisplatin, than the G-DIF cell lines. In patients, intrinsic subtypes were associated with survival time following adjuvant, 5-fluorouracil-based therapy.
CONCLUSIONS:
Intrinsic subtypes of GC, based on distinct patterns of expression, are associated with patient survival and response to chemotherapy. Classification of GC based on intrinsic subtypes might be used to determine prognosis and customize therapy.

Low-Dose Aspirin Use After Diagnosis of Colorectal Cancer Does Not Increase Survival: A Case–Control Analysis of a Population-Based Cohort

BACKGROUND & AIMS: Individuals who began taking low-dose aspirin before they were diagnosed with colorectal cancer were reported to have longer survival times than patients who did not take this drug. We investigated survival times of patients who begin taking low-dose aspirin after a diagnosis of colorectal cancer in a large population-based cohort study.

METHODS: We performed a nested case-control analysis using a cohort of 4794 patients diagnosed with colorectal cancer from 1998 through 2007, identified from the UK Clinical Practice Research Datalink and confirmed by cancer registries. There were 1559 colorectal cancer-specific deaths, recorded by the Office of National Statistics; these were each matched with up to 5 risk-set controls. Conditional logistic regression was used to calculate odds ratios (OR) and 95% confidence intervals (CI), based on practitioner-recorded aspirin usage.

RESULTS: Overall, low-dose aspirin use after a diagnosis of colorectal cancer was not associated with colorectal cancer-specific mortality (adjusted OR = 1.06; 95% CI: 0.92-1.24) or all-cause mortality (adjusted OR = 1.06; 95% CI: 0.94-1.19). A dose-response association was not apparent; for example, low-dose aspirin use for more than 1 year after diagnosis was not associated with colorectal cancer-specific mortality (adjusted OR = 0.98; 95% CI: 0.82-1.19). There was also no association between low-dose aspirin usage and colon cancer-specific mortality (adjusted OR = 1.02; 95% CI: 0.83-1.25) or rectal cancer-specific mortality (adjusted OR = 1.10; 95% CI: 0.88-1.38).

CONCLUSIONS: In a large population-based cohort, low-dose aspirin usage after diagnosis of colorectal cancer did not increase survival time.

Experimenting with the Coxian Phase-Type Distribution to Uncover Suitable Fits

In the past few decades, Coxian phase-type distributions have become increasingly more popular as a means of representing survival times. In healthcare, they are considered suitable for modelling the length of stay of patients in hospital and more recently for modelling the patient waiting times in Accident and Emergency Departments. The Coxian phase-type distribution has not only been shown to provide a good representation of real survival data, but its interpretation seems reasonably initiative to the medical experts. The drawback, however, is fitting the distribution to the data. There have been many attempts at accurately estimating the Coxian phase-type parameters. This paper wishes to examine the most promising of the approaches reported in the literature to determine the most accurate. Three performance measures are introduced to assess the fitting process of the algorithms along with the likelihood values and AIC to examine the goodness of fit and complexity of the model. Previous research suggests that the fitting process is strongly influenced by the initial parameter estimates and the data itself being quite variable. To overcome this, one experiment in this research paper will use the same initial parameter values for each estimation and perform the fits on the data simulated from a Coxian phase-type distribution with known parameters.

Investigating the efficiency of fitting Coxian phase-type distributions to health care data

Coxian phase-type distributions are becoming a popular means of representing survival times within a health care environment. They are favoured as they show a distribution as a system of phases and can allow for an easy visual representation of the rate of flow of patients through a system. Difficulties arise, however, in determining the parameter estimates of the Coxian phase-type distribution. This paper examines ways of making the fitting of the Coxian phase-type distribution less cumbersome by outlining different software packages and algorithms available to perform the fit and assessing their capabilities through a number of performance measures. The performance measures rate each of the methods and help in identifying the more efficient. Conclusions drawn from these performance measures suggest SAS to be the most robust package. It has a high rate of convergence in each of the four example model fits considered, short computational times, detailed output, convergence criteria options, along with a succinct ability to switch between different algorithms.

Assessment of the benefits of Discrete Conditional Survival Models in modelling ambulance response times

Many of the challenges faced in health care delivery can be informed through building models. In particular, Discrete Conditional Survival (DCS) models, recently under development, can provide policymakers with a flexible tool to assess time-to-event data. The DCS model is capable of modelling the survival curve based on various underlying distribution types and is capable of clustering or grouping observations (based on other covariate information) external to the distribution fits. The flexibility of the model comes through the choice of data mining techniques that are available in ascertaining the different subsets and also in the choice of distribution types available in modelling these informed subsets. This paper presents an illustrated example of the Discrete Conditional Survival model being deployed to represent ambulance response-times by a fully parameterised model. This model is contrasted against use of a parametric accelerated failure-time model, illustrating the strength and usefulness of Discrete Conditional Survival models.

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.

In-vitro investigation of out-of-field cell survival following the delivery of conformal, intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT) plans

The aim of this work is to determine the out-of-field survival of cells irradiated with either the primary field or scattered radiation in the presence and absence of intercellular communication following delivery of conformal, IMRT and VMAT treatment plans. Single beam, conformal, IMRT and VMAT plans were created to deliver 3 Gy to half the area of a T80 flask containing either DU-145 or AGO-1522 cells allowing intercellular communication between the in-and out-of-field cell populations. The same plans were delivered to a similar custom made phantom used to hold two T25 culture flasks, one flask in-field and one out-of-field to allow comparison of cell survival responses when intercellular communication is physically inhibited. Plans were created for the delivery of 8 Gy to the more radio-resistant DU-145 cells only in the presence and absence of intercellular communication. Cell survival was determined by clonogenic assay. In both cell lines, the out-of-field survival was not statistically different between delivery techniques for either cell line or dose. There was however, a statistically significant difference between survival out-of-field when intercellular communication was intact (single T80 culture flask) or inhibited (multiple T25 culture flasks) to in-field for all plans. No statistically significant difference was observed in-field with or without cellular communication to out-of-field for all plans. These data demonstrate out-of-field effects as important determinants of cell survival following exposure to modulated irradiation fields when cellular communication between differentially irradiated cell populations is present. This data is further evidence that refinement of existing radiobiological models to include indirect cell killing effects is required.

The effect of socioeconomic deprivation on corneal graft survival in the United Kingdom

Objective: To investigate the effect of socioeconomic deprivation on cornea graft survival in the United Kingdom.

Design: Retrospective cohort study.

Participants: All the recipients (n = 13?644) undergoing their first penetrating keratoplasty (PK) registered on the United Kingdom Transplant Registry between April 1999 and March 2011 were included.

Methods: Data of patients' demographic details, indications, graft size, corneal vascularization, surgical complication, rejection episodes, and postoperative medication were collected at the time of surgery and 1, 2, and 5 years postoperatively. Patients with endophthalmitis were excluded from the study. Patients' home postcodes were used to determine the socioeconomic status using a well-validated deprivation index in the United Kingdom: A Classification of Residential Neighborhoods (ACORN). Kaplan–Meier survival and Cox proportional hazards regression were used to evaluate the influence of ACORN categories on 5-year graft survival, and the Bonferroni method was used to adjust for multiple comparisons.

Main Outcome Measures: Patients' socioeconomic deprivation status and corneal graft failure.

Results: A total of 13?644 patients received their first PK during the study periods. A total of 1685 patients (13.36%) were lost to follow-up, leaving 11?821 patients (86.64%) for analysis. A total of 138 of the 11?821 patients (1.17%) developed endophthalmitis. The risk of graft failure within 5 years for the patients classified as hard-pressed was 1.3 times that of the least deprived (hazard ratio, 1.3; 95% confidence interval, 1.1–1.5; P = 0.003) after adjusting for confounding factors and indications. There were no statistically significant differences between the causes of graft failure and the level of deprivation (P = 0.14).

Conclusions: Patients classified as hard-pressed had an increased risk of graft failure within 5 years compared with the least deprived patients.

Financial Disclosure(s): The author(s) have no proprietary or commercial interest in any materials discussed in this article