A New Class of Survival Regression Models with Cure Fraction

Modeling signal transduction in cancer cells has implications for targeting new therapies and inferring the mechanisms that improve or threaten a patient's treatment response. For transcriptome-wide studies, it has been proposed that simple correlation between a ligand and receptor pair implies a relationship to the disease process. Statistically, a differential correlation (DC) analysis across groups stratified by prognosis can link the pair to clinical outcomes. While the prognostic effect and the apparent change in correlation are both biological consequences of activation of the signaling mechanism, a correlation-driven analysis does not clearly capture this assumption and makes inefficient use of continuous survival phenotypes. To augment the correlation hypothesis, we propose that a regression framework assuming a patient-specific, latent level of signaling activation exists and generates both prognosis and correlation. Data from these systems can be inferred via interaction terms in survival regression models allowing signal transduction models beyond one pair at a time and adjusting for other factors. We illustrate the use of this model on ovarian cancer data from the Cancer Genome Atlas (TCGA) and discuss how the finding may be used to develop markers to guide targeted molecular therapies.

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A new class of regression model for a bounded response with application in the study of the incidence rate of colorectal cancer

Statistical Methods in Medical Research ◽

10.1177/0962280219881470 ◽

2019 ◽

Vol 29 (7) ◽

pp. 2015-2033

Author(s):

Vicente G Cancho ◽

Jorge L Bazán ◽

Dipak K Dey

Keyword(s):

Colorectal Cancer ◽

Regression Model ◽

Incidence Rate ◽

Regression Models ◽

Real Data ◽

Unit Interval ◽

Open Unit ◽

Medical Sciences ◽

New Class ◽

New Family

Response variables in medical sciences are often bounded, e.g. proportions, rates or fractions of incidence of some disease. In this work, we are interested to study if some characteristics of the population, e.g. sex and race which can explain the incidence rate of colorectal cancer cases. To accommodate such responses, we propose a new class of regression models for bounded response by considering a new distribution in the open unit interval which includes a new parameter to make a more flexible distribution. The proposal is to obtain compound power normal distribution as a base distribution with a quantile transformation of another family of distributions with the same support and then is to study some properties of the new family. In addition, the new family is extended to regression models as an alternative to the regression model with a unit interval response. We also present inferential procedures based on the Bayesian methodology, specifically a Metropolis–Hastings algorithm is used to obtain the Bayesian estimates of parameters. An application to real data to illustrate the use of the new family is considered.

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