Western michigan university gaussian software

#Western michigan university gaussian software software#

The survival function S( t) is defined as the probability of survival up to time t, S( t) = P( T > t) = 1в€’ F( t), which is a decreasing function ranging from 1 to 0. The cumulative distribution function of T, denoted F( t), is defined as F( t) = P( T в‰¤ t), which is an increasing function of t, ranging from 0 to 1. Let T denote the random variable representing the time to event. We first describe how these functions relate to each other and then we discuss the distributions that may be used. Survival can be described in terms of the survival function, the hazard function or the likelihood. Another example would be the point of origin being the start of cancer treatment and the endpoint being cancer recurrence. For example, for cancer patients, the origin could be time of cancer diagnosis and the endpoint could be death due to the particular cancer studied. Both the time of origin and the event of interest must be precisely specified, so that the length of time from the origin to the endpoint can be calculated. This form of analysis attempts to describe the distribution of the survival time and understand differences in the survival time, perhaps due to demographics, risk factors or spatial location. Survival analysis refers to the analysis of the time taken for a particular event to occur. Section 5 includes a case study for a spatial survival model with random effects using the Louisiana prostate cancer Surveillance, Epidemiology and End Results (SEER) data from the United States ( 7).

#Western michigan university gaussian software software#

In section 4, we discuss various software for spatial survival analysis. In section 3, we introduce current Bayesian models that describe the spatial variation in survival, such as using random effects (subsection 3.1), cure-rates (subsection 3.2) and direct spatial models (subsection 3.3). In section 2, we describe some fundamental survival analysis concepts. In this paper we provide an overview of the fundamental and more advanced Bayesian spatial survival methodologies that can be applied to cancer research. Also, Bayesian methods enable the development of more complex models, inferences and analyses. Advantages of Bayesian models in comparison to other methods include the ease of drawing strength from neighboring regions, usually via spatially correlated or uncorrelated random effects. Bayesian approaches are increasingly commonly used for modelling small area spatial survival data. The geographical location can be used as a surrogate for environmental or lifestyle factors that may influence population cancer survival. Investigating spatial variations in survival patterns is important since it provides evidence to identify areas with poorer cancer outcomes requiring attention, thus assisting public health professionals in their decision making.

The predictors, such as racial composition ( 4) and socio-economic status ( 5) can also have a geographical influence on survival ( 6). Health initiatives, such as Healthy People 2020 in the United States ( 2) and the World Health Organization Health Equity Monitor ( 3) aim to eliminate cancer health disparities, such as those due to geographical location. The use of spatial survival methods in cancer research has become more widespread due to the increased recognition of the association between the spatial location and health outcomes, increased availability of spatial data and improvements in computing power. Survival analysis is an old subfield of statistics, dating back to the development of life tables ( 1). Received: 01 October 2019 Accepted: Published: 30 June 2020. Keywords: Cancer survival spatial Markov chain Monte Carlo Bayesian