[an error occurred while processing this directive]

Life Transitions

During the 1990s, Dr. James Robinson, an actuary, combined a careful examination of data and a continuous-time Markov model to develop a mathematical method for estimating the probability distribution of eight possible "health states" in which an individual of specified gender, initial age, and initial health state might be in after a specified period of time. Thus, the method could specify the probability that a healthy 51-year-old male might be in a health state characterized by severe cognitive impairment one month hence.
This Demonstration implements and explores this method of predicting the future health of individuals. You specify the gender and initial age of the individual. You likewise specify the length of the transition period, choosing to denominate it in terms of days, weeks, months, or years. In "array view", the Demonstration displays the Markov transition matrix showing the distribution of probabilities for each terminal state for each initial state. Each state is labeled with a number; a tooltip associated with each number further describes the state of health. In "Markov view", the Demonstration directly shows the Markov transition matrix. In "flow view", the Demonstration displays a directed graph showing the transitions with edges thickened in accord with their probability. Advanced controls described in the details section permit you to customize these visualizations.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


In order to change the gender of the person, it is necessary to select "Markov" view.
For a copy of Dr. Robinson's work, see A Long-Term-Care Status Transition Model.
Dr. Robinson's methodology and its derivatives are used in the American insurance industry, particularly in long-term care insurance, to develop premiums, reserves, and do other essential computations.
The methodology employed by Dr. Robinson involved empirical work and statistics to determine the best function of initial age and gender that would compute transition rates among the eight states into which the data had divided health. Matrix exponentiation is then used to convert this transition rate matrix into a Markov matrix.
The health states differ according to three variables: (a) the number of "instrumental activities of daily living" that are impaired; (b) the number of "activities of daily living" that are impaired; and (c) whether a "cognitive impairment" exists. An activity of daily living, ubiquitously abbreviated as ADL, means an activity such as bathing, dressing, "transferring" (getting out of bed), toileting, continence, and eating. An instrumental activity of daily living, IADL, refers to something such as an inability to drive, prepare meals, or do housework. A cognitive impairment generally refers to a loss or deterioration in intellectual capacity such as that caused by Alzheimer's disease that requires substantial supervision to protect the person. In State 1, the person has no IADL, no ADLs, and no cognitive impairment. In State 2, the person has an IADL, no ADLS and no cognitive impairment. In State 3, the person has 1 ADL and no cognitive impairment. In State 4, the person has 2 ADLs and no cognitive impairments. In State 5, the person has 3 or more ADLs and no cognitive impairment. In State 6, the person has fewer than 2 ADLs but has cognitive impairment. In State 7, the person has 2 or more ADLS and has cognitive impairment. In State 8, the person is dead. Many long-term care insurance policies use definitions similar to these states to determine whether benefits are owing and whether premiums otherwise due are excused.
The contrast reduction control in the advanced controls permits you to alter the "contrast" of the array displaying the probability matrix. High values of the control greatly reduce contrast and may thus permit better visualization of small numbers.
[an error occurred while processing this directive]

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+