The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.
Data structure for a discrete-time event history analysis
Jane E. Miller, PhD
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Overview• Structure of most survey data: One record per
respondent• Discrete-time event history analysis requires separate
records for each person-time unit at risk of the event• Review: How to create one record per spell• How to create one record per person-time unit
– Components of the dependent variable– Fixed characteristics– Time varying characteristics
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Data preparation for an event history
• Survey data often contains one record per respondent
• Continuous-time event history data contain one record per spell
• Discrete-time event history analysis requires one record per person-time unit within each spell– E.g., one record for each person-month at risk of divorce,
within each spell at risk of divorce
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Source data from survey: 1 record per respondent
IDDate of
birthDate of 1st marriage
Date of 1st
divorce
Date of 2nd
marriage
Date of 2nd
divorceDate of death
Date 1st observed
Date last observed Gender
Date of 1st child's
birth
Date of 2nd child's
birth
1 2/1/52. . . . . 7/15/85 10/1/10 F . .
2 7/15/69 6/22/10. . . . 9/21/85 11/5/10 M . .
3 3/1/65 8/1/90 1/1/97 10/1/04. . 10/8/85 5/1/05 M 12/5/95.
4 3/1/42 6/1/63. . . 10/1/02 12/2/85 10/2/02 F 9/21/64 5/11/67
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Example timelines for study of divorce
End of observation period
L
M = MarriedD = DivorcedL = Lost to follow-upO = Censored by end of study.X = Died
D
M
M
M O
X
M
Case 1: Never married -> no spells
Case 2: Married once, censored by end of survey
Case 3: Married twice, lost to follow-up before end of survey
Case 4: Married once, died before end of survey
Not married -> not at risk of divorce -> not part of a spell
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Continuous-time event history data• One record for each period at risk (spell)
– Duration of overall spell– Event indicator at end of spell
IDSpell #
(marriage #)
Date spell
started
Duration of spell (mos.)
Status at end of spell
Divorce event
indicator
Age first observed
(yrs)
Age at start of
spell (yrs)
Age last observed
(yrs) Gender
# kids at start of
spell
2 1 6/22/10 3.5 0 0 16 40 41 male 0
3 1 8/1/90 76.5 1 1 20 25 45 male 0
3 2 10/1/04 6.5 2 0 20 39 45 male 1
4 1 6/1/63 474.5 3 0 43 21 60 female 0
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Event history timeline: Discrete time specification
Case 2, Continuous time version: One four-month spell
Married 6/22/2010 Last surveyed 11/5/2010
1st person-month
Four person-month units
Case 2, Discrete-time version: Each person-month unit becomes one record -> unit of analysis. All records for each spell include respondent ID and other characteristics.
Married O2nd person-month O O3rd person-month O O
4th person-month O End of survey
O = Censored
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
One record per person-month
IDSpell #
(marriage #)Record #
w/in spell2 1 12 1 22 1 32 1 43 1 13 1 23 1 33 1 …3 1 773 2 13 2 23 2 …3 2 7
One record per spell
IDSpell #
(marriage #)
Duration of spell (mos.)
Status at end of spell
Divorce indicator
2 1 4 0 03 1 77 1 13 2 7 2 0
Discrete-time data set: ID codes on person-time records
• Each person-month record carries the respondent ID
• Each record within a given spell also includes the spell # for that respondent
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Record number within spell
• Each month in a spell will generate one person-month record, e.g.,
– respondent #2 is observed for 4 months -> 4 person-month records
– respondent #3 contributes a total of 84 records
• 77 in his first spell • 7 in his second spell
One record per person-month
IDSpell #
(marriage #)Record #
w/in spell2 1 12 1 22 1 32 1 43 1 13 1 23 1 33 1 …3 1 773 2 13 2 23 2 …3 2 7
One record per spell
IDSpell #
(marriage #)
Duration of spell (mos.)
Status at end of spell
Divorce indicator
2 1 4 0 03 1 77 1 13 2 7 2 0
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Month counter within spell
One record per person-month
IDSpell #
(marriage #)Record #
w/in spell
month # within spell
2 1 1 02 1 2 12 1 3 22 1 4 33 1 1 03 1 2 13 1 3 33 1 … …3 1 77 763 2 1 13 2 2 23 2 … …3 2 7 6
One record per spell
IDSpell #
(marriage #)
Duration of spell (mos.)
Status at end of spell
Divorce indicator
2 1 4 0 0
3 1 77 1 1
3 2 7 2 0
The “month # within spell” counter indicates the start time of the person-month at risk for that record. E.g., the first record for a given spell starts at baseline (time point 0).
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Duration measure for each record within spell
The duration measure will = 1 time units for all person-time records within a given spell EXCEPT = 0.5 for the last month in a spell
One record per person-month
ID
Spell # (marriage
#)
Record # w/in spell
month # within spell
Person-months
w/in record
2 1 1 0 12 1 2 1 12 1 3 2 12 1 4 3 .53 1 1 0 13 1 2 1 13 1 3 3 13 1 … … 13 1 77 76 .53 2 1 1 13 2 2 2 13 2 … … 13 2 7 6 .5
One record per spell
IDSpell #
(marriage #)
Duration of spell (mos.)
Status at end of spell
Divorce indicator
2 1 4 0 0
3 1 77 1 1
3 2 7 2 0
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Status indicator for each record within spell
The indicator for status at end of record will = 0 for all person-time records within a given spell EXCEPT the last one because by definition they end in censoring (the spell is not yet complete)
One record per person-month
ID
Spell # (marriage
#)
Record # w/in spell
month # within spell
Person-months
w/in record
Status at end
of record
2 1 1 0 1 02 1 2 1 1 02 1 3 2 1 02 1 4 3 .5 03 1 1 0 1 03 1 2 1 1 03 1 3 3 1 03 1 … … 1 03 1 77 76 .5 13 2 1 1 1 03 2 2 2 1 03 2 … … 1 03 2 7 6 .5 2
One record per spell
IDSpell #
(marriage #)
Duration of spell (mos.)
Status at end of spell
Divorce indicator
2 1 4 0 0
3 1 77 1 1
3 2 7 2 0
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Status indicator for last record within spell
The indicator for status at end of record for the last person-time record within each spell will take on the value of the status indicator for the overall spell
One record per person-month
ID
Spell # (marriage
#)
Record # w/in spell
month # within spell
Person-months
w/in record
Status at end
of record
2 1 1 0 1 02 1 2 1 1 02 1 3 2 1 02 1 4 3 .5 03 1 1 0 1 03 1 2 1 1 03 1 3 3 1 03 1 … … 1 03 1 77 76 .5 13 2 1 1 1 03 2 2 2 1 03 2 … … 1 03 2 7 6 .5 2
One record per spell
IDSpell #
(marriage #)
Duration of spell (mos.)
Status at end of spell
Divorce indicator
2 1 4 0 0
3 1 77 1 1
3 2 7 2 0
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Event indicator for each record within spell
One record per person-month
IDSpell #
(marriage #)Record #
w/in spell
month # within spell
Divorce indicator for record
2 1 1 0 02 1 2 1 02 1 3 2 02 1 4 3 03 1 1 0 03 1 2 1 03 1 3 3 03 1 … … 03 1 77 76 13 2 1 1 03 2 2 2 03 2 … … 03 2 7 6 0
One record per spell
IDSpell #
(marriage #)
Duration of spell (mos.)
Status at end of spell
Divorce indicator
2 1 4 0 0
3 1 77 1 1
3 2 7 2 0
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Fixed covariates for each person-time record
IDSpell #
(marriage #)Record #
w/in spell
month # within spell
Divorce indicator for record
Age at start of
spell (yrs) Gender
# children at start of
spell2 1 1 0 0 40 male 02 1 2 1 0 40 male 02 1 3 2 0 40 male 02 1 4 3 0 40 male 03 1 1 0 0 25 male 03 1 2 1 0 25 male 03 1 3 3 0 25 male 03 1 … … 0 25 male 03 1 77 76 1 25 male 03 2 1 1 0 39 male 13 2 2 2 0 39 male 13 2 … … 0 39 male 13 2 7 6 0 39 male 1
Age, number of children at start of spell, and gender do not change during the course of a spell, so they have the same value for each person-time record within a given spell
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Example timelines for number of children as time-varying covariate in study of divorce
L
M = Married D = Divorced C = Child bornL = Lost to follow-up O = Censored by end of study. X = Died
D
M
M
X
MCase 3:
Case 4:
C
C C
No kids
No kids
One kid
Two kidsOne kid
IDDate of
birthDate 1st observed
Date of 1st
marriage
Date of 1st
child's birth
Date of 2nd
child's birth
Date of 1st
divorce
Date of 2nd
marriage
Date of 2nd
divorceDate of death
Date last observed
3 3/1/65 10/8/85 8/1/90 12/5/95. 1/1/97 10/1/04. . 5/1/05
4 3/1/42 12/2/85 6/1/63 9/21/64 5/11/67. . . 10/1/02 10/2/02
Columns reordered into chronological order
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Discrete time with time-varying covariates
• Case 3 has his first child 64 months into his first marriage, and no additional children while observed. # kids at start of record is 0 for his first 63 records of
spell 1 1 for records 64 through 77
of spell 1 1 for all records in spell 2
ID Spell #month #
w/in spell
Divorce indicator for
record
# kids at start of
spell
# kids at start of record
3 1 0 0 0 03 1 1 0 0 03 1 … 0 0 03 1 64 0 0 13 1 77 1 0 13 2 0 0 1 13 2 … 0 1 13 2 6 0 1 1
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Discrete time with time-varying covariates
• Case 4 has her first child 15 months into her marriage, a second child in month 47 after marriage. For her the # kids at start of record is 0 for her first 15 records 1 for records 15 through
46 2 for records 47 or higher,
all in spell 1
ID Spell #month #
w/in spell
Divorce indicator for
record
# kids at start of
spell
# kids at start of record
4 1 0 0 0 04 1 … 0 0 04 1 15 0 0 14 1 … 0 0 14 1 47 0 0 24 1 … 0 0 24 1 474 0 0 2
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Presenting information on event history construction: Background work• Most of the gory details of creating an event history are part
of behind-the-scenes work– Important to do consistency checks to make sure event histories
were created correctly given • Original data source of information for timeline construction• Type of event under study• Fixed covariates• Time-varying covariates
– E.g., correct • Number of spells per respondent• Number of person-time records for each spell• Duration and event indicators for each person-time record• Values of fixed- and time-varying covariates for each person-time record
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Presenting information on event history construction
• In the data and methods section, describe:– Original data source of information for timeline construction
• Dates, status, duration of events
– Type of event under study– Unit of person-time (e.g., person-years, person-months)– What constitutes censoring– Fixed covariates– Time-varying covariates
• Source(s) of information for determining timing of changes in those variables
• See checklist in chapter 17 of Writing about Multivariate Analysis, 2nd Edition for more detail on what to report
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Summary• A discrete-time event history analysis requires a separate
record for each person-time unit at risk of the event• For each respondent, create correct number of spells• For each spell, calculate
– Correct number of person-time units– Components of the dependent variable
• Duration measure• Event indicator
– Fixed characteristics– Time-varying characteristics
• In data and methods section, describe data sources and variables for the event history
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Suggested resources
• Allison, P. D. 2010. Survival Analysis Using the SAS System: A Practical Guide, 2nd Edition. Cary, NC: SAS Institute.
• Miller, J. E. 2013. The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition. University of Chicago Press, chapter 17.
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Suggested online resources
• Podcast on data structure for a continuous-time event history analysis
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Suggested exercises
• Study guide to The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.– Question #3a in the problem set for chapter 17– Suggested course extensions for chapter 17
• “Reviewing” exercises #2a through 2h• “Applying statistics and writing” exercises #1 and 2a
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.Event history analysis: discrete time data
Contact information
Jane E. Miller, [email protected]
Online materials available athttp://press.uchicago.edu/books/miller/multivariate/index.html
The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.