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Developing a daily time step individual level demographic simulation model

Andy Turner

http://bit.ly/TStpJP

Presentation slides prepared for a CSAP research cluster meeting, School of Geography, University of Leeds, UK, 2012-12-11

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Outline

  • Why?
  • What?
  • How?
  • Results
  • Plans and Next Steps
  • Feedback

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Why?

  • Generally...
    • Demographic data is used in a wide range of applications
      • Epidemiology for estimating prevalence and incidence rates
      • Service planning
      • Risk management
      • Commercial
    • Census data tend to be years old by the time outputs are made available
    • Contemporary populations are assumed to be highly and increasingly mobile and fertility in terms of live births is perhaps becoming more variable

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    • Demographic forecasting is important
      • Planning is a key to sustainability
        • Dependency ratios are increasing in many countries with increasing aged populations
        • Pensions
        • Welfare
        • Services and infrastructure
    • Many countries (including the UK) do not have official residential registration data that tracks the location of people (between censuses)
    • Our ability to track where everyone has lived improves continually, but we need the models and the data to forecast and provide the best estimates

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  • Why daily time steps?
    • People tend to be born, die and move residences on specific days
      • It intrinsically makes sense to model at this resolution
      • Modelling for multiple days either misses important events or becomes much more complicated
        • Consider
          • migrations of individuals within a time period
          • births (same mother) at different times within a year
    • Allows for linkage with models of daily activity that work on sub-daily time steps

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    • Allows for variation in mortality, fertility and migration rates over the year to be modelled
      • Mortality, Fertility, Miscarriage and Migration are seasonal
        • Student migration
        • Holidays and fertility
        • Winter mortality
      • Power cuts/flood events and birth spikes
    • Allows for new and exciting aggregate data/statistics to be produced
      • Distribution of the total number of
        • births per month in a region
        • moves per person in a year
          • maximium, minimum, average, variance

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  • Why individual level?
    • Data can be linked with other individual level data
      • e.g. Disease data
    • It has the possibility that other individual data can be augmented or linked
      • Linkage and substitution with "real data"
    • Everybody is different
      • Individuals have their own mortality, fertility and migration probabilities and history
        • There is scope for specifying these in the model
          • In such a way as to keep overall counts of births and deaths at observed levels
        • Return migration

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What?

  • Stages of development
  • The nature of the model
  • Initialisation
  • Daily Simulation
    • Death
    • Birth
    • Migration
  • Results

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Stages of Development

  • Natural change Simulation Model
    • ESRC funded GENESIS Project
    • Leeds Output Area level results produced
  • e-Infrastructure
    • JISC funded NeISS Project
    • Web Portal based User Interface
    • Simulation Models configured, run and results stored on e-Science resources
  • Migration model component
    • Not externally funded
    • Developed since July 2012

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The nature of the model

  • Open Source
    • Development repositories
  • Java

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  • Dependencies
    • Generic Library
    • MoSeS Code
      • For loading 2001 UK Population Census Data
  • Grid enabled
    • Thanks to NeISS collaboration with Tom Doherty based at University of Glasgow
  • Run for multiples of a year
  • Individual representation
    • Males
    • Females

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  • Stochastic yet deterministic
    • Based on pseudo-random sequences
    • Results replicable
  • Study Region
    • Comprised of regions and subregions
  • 2 stages to modelling
    • Initialisation
    • Simulation
  • Simulation proceeds for each subregion in turn, and for each individual in turn
  • Synchronisation needed for each daily step

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  • There are many simplifying assumptions
    • Many things are assumed to be evenly distributed
    • Some things are not explicitly modelled
  • There are interesting model details
    • Pregnancy and miscarriage
    • Multiple births
  • Input data
    • Population count data by age and gender
    • Either birth and death counts or fertility and mortality probabilities
    • Migration data

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  • Output data
    • Produced annually for study region, regions, subregions and aggregates of subregions
    • Includes raw ASCII data (XML,CSV), binary serialised Java object data, and images (PNG)
      • Population count estimates
      • Mortality and fertility estimates
      • Migration estimates
      • Comparisons with an annual time step model
        • Which uses mid year population estimation
      • An individual level population data set

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Initialisation

  • For each region
    • Daily survival probabilities are calculated for each age and gender
      • Death rate assumed to be even throughout the year
    • Daily pregnancy probabilities are calculated for each age of potential mother
      • Annual Live Birth Fertility Rates are factored for multiple births, miscarriage and death of mother
      • Pregnancy rate and miscarriage rate assumed to be even throughout the year

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    • Daily migration
      • Assumes migration evenly distributed throughout the year
      • General migration probability calculated
      • Internal migration rates are calculated for migration within the region
      • In migration rates are calculated for people moving from all regions not in the study region
    • Cumulative sums of migration are calculated to help determine
      • The region destination for each out migration
      • The subregion destination for each in migration

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  • Each person is initialised
    • Assigned a date of birth
    • Assigned to a subregion as usually resident
    • Females are assigned pregnancies and due dates

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Daily Simulation

  • For each person
    • Do they die?
    • Is it their birthday?
      • If so update population statistics
    • Do they migrate?
      • If yes, find out where they move to
  • For each female
    • If pregnant do they have a miscarriage
    • If due give birth
    • If not pregnant, determine if they become pregnant

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  • Having gone through the population for all regions in the study region
    • Migrate those migrating out of the study region
    • Migrate those migrating within the study region
    • For migration into the study region from outside of the study region
      • Create individuals
        • Assigning date of birth
        • Record migration origin location
        • Assign subregion usual resident location

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How?

  • Designed for (scalability) simulating large populations with large numbers of regions and subregions
    • Individual level data stored in collections which are swapped to and from slower access storage as required
    • Numerical indexes are stored in mapped collections
  • Computational demands are considerable
    • Consider simulating a single region, population ~1 million, with ~10 thousand subregions
      • Can all the data be stored in the available fast access memory?

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    • For a simple model, a 10 year simulation might take many days with only one CPU
      • Each individual in the population is updated ~3650 times
    • The amount of persistent data produced and that we want to store is in the order of tens of GigaBytes
    • For a UK Simulation there are in the order of 60 million individuals and 200 thousand subregions
  • Grid enabled
  • Parallelisation
  • Numerical precision
    • Java BigDecimal

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Results

  • Results for simulations without migration
    • Provide confidence in daily probability calculations for natural processes
      • The expected amounts of deaths, pregnancies, miscarriages and births result at a regional level
    • Variation
      • At sub-regional level can be large
      • At regional level are generally small
      • At aggregated sub-regional level are intermediate
      • For less frequently occurring events is greater

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Variation in results

  • 4 runs
    • Everything but the pseudo-random seed start point is the same
    • Usually there are 5 lines on each side of a plot
      • Min and Max are lightest grey
      • Q1 and Q3 are darker grey
      • Median is black
      • Some measures are highly variable
      • There is more variation for smaller regions

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Migration

  • Types of migration modelled
    • Immigration
    • In migration to Study Region
    • Out migration from Study Region
    • Internal migration within Study Region
  • Input data
    • 2001 UK Population Special Migration Statistics
      • LAD to LAD flows by age and gender
      • OA to OA flows by age and gender
  • Region (LAD to LAD) flows are primarily used

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  • Subregion (OA to OA) flows are used to assign individuals to subregions with each region
  • A migration factor and a minimum flow

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Plans and Next Steps

  • Add emigration to the model
  • Detailed results statistics for migration
  • Simulate population change in West Yorkshire from 2001 to 2011
    • Vary migration factor and minimum flow
    • Present results at an appropriate event
    • Publish a paper on the demographic simulation model and the results for West Yorkshire
  • Simulate population change for all of England from 2001 to 2011
    • Compare results with 2011 census data
    • More publication

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  • Further modelling
    • Use Nik Lomax's estimated migration flows for 2001 to 2011
    • Constrain migration using subregion area classifications
    • Allow for variations in mortality, pregnancy, miscarriage and migration rates over the year
      • Student migration
    • Migrating groups (families/households)
    • Fathers

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  • Seek data for more detailed simulations
    • Annual and regional miscarriage data
  • Seek collaboration with statistical offices
  • Seek further funding
    • Secondment to UK ONS funded by ESRC?

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Feedback

  • Much can be done to improve this work
  • What has emerged is something like the simplest demographic model
    • There is much detail to add...
  • Anyone interested in writing this up or collaborating in anyway?
  • Any questions?

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Thank You

http://bit.ly/TStpJP