Heuristic Perspectives on Parametric Survival Analysis (2020-US-30MP-567)

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Level: Intermediate

Thor Osborn, Principal Systems Research Analyst, Sandia National Laboratories

Parametric survival analysis is often used to characterize the probabilistic transitions of entities — people, plants, products, etc. — between clearly defined categorical states of being. Such analyses model duration-dependent processes as compact, continuous distributions, with corresponding transition probabilities for individual entities as functions of duration and effect variables. The most appropriate survival distribution for a data set is often unclear, however, because the underlying physical processes are poorly understood. In such cases a collection of common parametric survival distributions may be tried (e.g., the Lognormal, Weibull, Frechét and Loglogistic distributions) to identify the one that best fits the data. Applying a diverse set of options improves the likelihood of finding a model of adequate quality for many practical purposes, but this approach offers little insight into the processes governing the transition of interest. Each of the commonly used survival distributions is founded on a differentiating structural theme that may offer valuable perspective in framing appropriate questions and hypotheses for deeper investigation. This paper clarifies the fundamental mechanisms behind each of the more commonly used survival distributions, considering the heuristic value of each mechanism in relation to process inquiry and comprehension.

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Speaker	Transcript
	Hello, and welcome to my
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	over the past 25 years, I
	have performed many studies and
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	share with you a way of thinking
	about the distributions we
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	motivated by precedent, ease of
	use, or empirically demonstrated
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	about its processes. Further,
	when an excellent model fit is
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	genesis of the distributions
	commonly used in parametric
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	seen in the workplace as well as
	in the academic literature.
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	literature, including textbooks
	and web based articles, as well
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	reexamination that may fail to
	glean full value from the work.
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	the exponential.
	Much is often made about the
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	because they model fundamentally
	different system archetypes. In
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	distribution does in fact, fit
	the lognormal data very well.
	The quality of the fit may also
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	fits much better. And secondly,
	there's only a modest coincident
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	the core process mechanisms
	these distributions represent
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	analysis, but it provides a very
	familiar starting point for
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	uncorrelated effects. Let's see
	if that is true.
	In order to create a good
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	25,000. For the individual
	records, we'll use the random
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	see that we did indeed obtain
	the normal distribution.
	Now let's consider the
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	not able to imprint my brain
	with a sufficient knowledge of
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	lognormal distribution are also
	very simple. As you can see, the
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	this demonstration, we reuse the
	fluctuation data that were
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	JSL scripting because I find it
	much more convenient for
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	the number of records in each
	sample. Next, it extracts the
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	products.
	The outer loop tracks the
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	on the previous slide. The
	amplified product compensates
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	distributions may be considered
	as generated secondarily from
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	many similar internal processes
	is represented by its maximum
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	to be Frechet distributed. The
	Weibull distribution represents
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	processes that complete when any
	of multiple elements have
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	using the Pareto distribution
	as the source. In this case, the
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	absolute value of the normal
	distribution as the source.
	Now let's have a quick look at
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	maximum is used.
	For the square root of the
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	is not available, you can also
	see that the other common
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	value of the normal distribution
	quite well.
	Incidentally, Weibull
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	distribution when its core
	behavior is substantially
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	the four heme containing
	subunits mechanically interact
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	up to now have all relied on
	independent samples. Professor
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	extended to produce auto
	correlated data. Generation of
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	sequence autocorrelation is
	about .75, yet the
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	the common survival
	distributions. You can see that
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	good example of the relationship
	between real-world analytical
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	commingle a single family
	residences with heavy industry.
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	have similar features. The
	landowner must apply to the
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	an opportunity to comment. Local
	officials then weigh the
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	parties. This example is not
	approached as a demonstration
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	processing time is 140 days. The
	fit is obviously imperfect, but
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	distributed data results from
	processes yielding the combined
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	ubiquitous, but the loglogistic
	is less frequently used. Without
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	multistep process may be
	insufficient to impart log
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	considered and the complexity
	of the underlying process should
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	whether a process is
	substantially impacted by
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	whether the cooperative element
	is connoted by positive terms such
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	often been said, I would
	sincerely appreciate your
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