Modeling Age Patterns of Vital Events

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Modeling Age Patterns of Vital Events
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Model Age Patterns

• Parsimonious representations of empirical
  regularities
• Usually with age or duration as the primary
  dimension
• Serve many purposes
• Standard or normal pattern
• Simplify common tasks and make them more
  reproducible change small number of parameters
  that specify patterns rather than whole patterns
• Allow indirect estimation by providing
  reasonable assumptions about existing patterns
• Robust empirical regularities and differentials
  between them suggest a search for what causes
  these

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Models of Age Patterns

• Mathematical representations
• Summarize an age pattern in an equation
• Possibly some theory involved
• Tabular representations
• Lists age patterns indexed by some quantity i.e.
  life expectancy in the case of mortality
• Relational Models
• Combine the first two and relate a given age
  pattern to a standard age pattern through a
  mathematically defined relation

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Model Age Patterns of Mortality

• Called MODEL LIFE TABLES
• Present all normal life table columns for various
  levels of mortality usually indexed by the
  life expectancy of the corresponding life table
• Predicated on high level of correlation among
  sets of age-specific death rates measured in
  different populations similar age patterns
  often observed

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West - Female
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South - Female
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Latin American Female
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South Asian Female
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General Female
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West Male
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South Male
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Latin American Male
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South Asian Male
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General - Male
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Other Model Age Patterns

• Include models of the age patterns of
• Nuptiality
• Fertility
• Carefully read section 9.3 in the book describing
  the M m model of the age pattern of fertility

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INDEPTH Mortality Patterns for Africa

• To provide a set of model mortality patterns that
  are appropriate for use in Africa Asia
• To create a general model of the age pattern of
  mortality observed at INDEPTH sites
• To identify common age patterns of mortality
  among the many different age patterns observed at
  INDEPTH sites
• To lay the foundation for the creation of an
  INDEPTH system of model life tables

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Principal Components Model of Mortality

• Data Preparation
• Aggregate into site-periods
• Smooth
• Logit transform
• Calculation of Principal Components
• Identify a small number of age patterns whose
  linear combinations are able to reproduce all of
  the observed age patterns
• Use Principal Components variation of Factor
  Analysis to calculate the principal components

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Raw Data
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Site Periods
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Data Transformation

• Within each site-period
• The data are mildly smoothed along the age axis,
  and
• The age-specific probability of dying (nqx) is
  calculated
• The nqx are transformed using the logit
  transformation to linearize the age-pattern and
  increase the sensitivity to changes at midlife
  ages

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Calculation of Principal Components

• 18 x 70 data set for each sex consists of
• 18 rows one for each age group
• 70 columns one for each site-period
• STATAs factor and score routines used to
  calculate fifteen principal components for each
  sex
• For both sexes the first six principal components
  explain more than 99 of the variance across
  site-periods

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Components ?
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Principal Component 1
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Principal Component 2
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Principal Component 3
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Principal Component 4
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Identification of Common Age Patterns of Mortality

• Compare age pattern observed in each site-period
  to the first four principal components
• Regress each site-period on the first four
  principal components using ordinary least squares
  regression
• Save the regression coefficients corresponding to
  each principal component
• Create a 70 x 4 data set consisting of a row for
  each site period and a column for the coefficient
  calculated on each principal component
• Use Agglomerative Hierarchical Cluster Analysis
  to identify similar clusters (groups) of rows
  (coefficient vectors) in the coefficient data set
• Results in reproducible clustering of similar age
  patterns of mortality

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Seven INDEPTH Mortality Patterns

• Cluster analysis of 70 male and female site
  periods yields
• Five easily distinguishable patterns for males
• Seven easily distinguishable patterns for females
• Final patterns are based on female clusters to
  produce seven INDEPTH mortality patterns

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Pattern 1
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Male Pattern 1
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Female Pattern 1
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Pattern 1 Site-Periods

• Bandafassi 80-84
• Bandafassi 85-87
• Bandafassi 88-90
• Bandafassi 91-93
• Bandafassi 94-96
• Bandafassi 97-99
• Bandim 90-91
• CNRFPS 94-95
• CNRFPS 96-98
• Farafenni 96-97
• Farafenni 98-99
• Gwembe Tonga Research Project 50-80
• Gwembe Tonga Research Project 90-92
• Gwembe Tonga Research Project 93-95
• Ifakara 97-99
• Manhiça 98-99
• Niakhar 85-89
• Niakhar 90-94
• Niakhar 95-98

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Pattern 2
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Male Pattern 2
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Female Pattern 2
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Pattern 2 Site-Periods

• Matlab, Comparison Area 88
• Matlab, Comparison Area 98
• Matlab, Treatment Area 88
• Matlab, Treatment Area 98
• Mlomp 85-87
• Mlomp 97-99

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Pattern 3
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Male Pattern 3
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Female Pattern 3
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Pattern 3 Site-Periods

• Agincourt 94-95
• Agincourt 96-97
• Agincourt 98-99
• Dar es Salaam 1994-95
• Dar es Salaam 1995-96
• Dar es Salaam 1996-97
• Dar es Salaam 1997-98
• Dar es Salaam 1998-99
• Bandim 96-97

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Pattern 4
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Male Pattern 4
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Female Pattern 4
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Pattern 4 Site-Periods

• Agincourt 92-93
• Bandim 92-93
• Bandim 94-95
• Farafenni 94-95
• Navrongo 93-95
• Navrongo 96-97
• Navrongo 98-99
• Nouna 93-95

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Pattern 5
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Male Pattern 5
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Female Pattern 5
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Pattern 5 Site-Periods

• Dar es Salaam 1992-93
• Dar es Salaam 1993-94
• Hai 1992-93
• Hai 1993-94
• Hai 1994-95
• Hai 1995-96
• Hai 1996-97
• Hai 1997-98
• Hai 1998-99
• Morogoro 1992-93
• Morogoro 1993-94
• Morogoro 1994-95
• Morogoro 1995-96
• Morogoro 1996-97
• Morogoro 1997-98
• Morogoro 1998-99

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Pattern 6
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Male Pattern 6
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Female Pattern 6
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Pattern 6 Site-Periods

• Butajira 87-89
• Butajira 90-91
• Butajira 92-93
• Butajira 94-96
• Mlomp 88-90
• Nouna 96-98

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Pattern 7
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Male Pattern 7
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Female Pattern 7
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Pattern 7 Site-Periods

• Gwembe Tonga Research Project 81-83
• Gwembe Tonga Research Project 84-86
• Gwembe Tonga Research Project 87-89
• Mlomp 91-93
• Mlomp 94-96

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Are INDEPTH Patterns Unique?

• Comparison to Coale Demeny U.N. Model life
  tables reveals
• Consistent age-dependent deviations
• Substantial differences in age patterns
• In particular patterns 3 5 are consistent with
  mortality caused by HIV/AIDS, and none of the
  existing model life tables have patterns at all
  similar to those

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Model Life Tables

• The data and analysis presented here can form the
  foundation for an INDEPTH system of model life
  tables
• The seven INDEPTH age patterns of mortality can
  be used as the basis for a seven member model
  life table family
• The component model of mortality can be used to
  generate many levels within each pattern

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Where To Go From Here?

• Compile a raw data set consisting of
  individual-level mortality data
• Use that data set to analyze INDEPTH mortality at
  a finer level of resolution with respect to age
  and time and to control for various confounders
  such as period
• Redo the analysis presented here
• Construct model life tables based on the INDEPTH
  mortality patterns