ciqle workshop: longitudinal data analysis, silke aisenbrey ciqle workshop: introduction to...

CIQLE Workshop: Longitudinal data analysis, Silke Aisenbrey

CIQLE Workshop:

Introduction to longitudinal data analysis with stata panel models and event history analysis

Silke Aisenbrey, Yale University

CIQLE Workshop: Longitudinal data analysis

Goals for the workshop:

-Intro to stata

-Modeling Change over time:Panel Regression Models (fixed, between and random)

-Modeling whether and/or when events occur:Event History Analysis (Data management for event history data, kaplan-meier, cox, piecewise constant)


open stata:

COMMAND

RESULTSresults and syntax

REVIEWof syntax: commands or menu

VARIABLESof open file


open data, with menu (stata data--> eventex.dta)


to see real data

to make changes directly in data

erase variables, cases, make single changes in cases

-->


relational and logical operators in stata:

== is equal to~= is not equal (also !=)

> greater than< less than>= greater than or equal<= less than or equal

& and| or~ not (also!)

basic descriptive commands


sum vartab var1 var2tab var1 var2, col

combine with: …… if var1==2 & var3>0

by var1: ……………sort …………

exercise:

e.g.:

tab abitur sex, coltab abitur sex if cohort==1930, col

sort cohortby cohort: tab abitur sex

basic descriptive commands


help “command”

gen var1 = var2recode var1 (0=.) (1/8=2) (9=3)rename var1 var100

**use the following variables:cohort (indicator of cohort membership)sex (1=male, 2=female)agemaryc (age @ first marriage)

exercise:

e.g.: sum agemaryc

recode age @ married in groups-generate a new variable-recode new variable into groups

-recode if marcens==0

basic commands for data management


possible break


Intro to panel regression with stata:

-panel data

-fixed effects

-between effects

-random effects

-fixed or random?


panel data (panelex1.dta)


Panel data, also called cross-sectional time series data, are data where multiple cases (people, firms, countries etc) were observed at two or more time periods.

Cross-sectional data: only information about variance between subjects

Panel data: two kinds of information between and within subjects

--> two sources of variance

Panel data:


Janet: Basics of panel regression models


cross sectional vs. panel analyses

open panelex1.dtaignore the fact that we have repeated measures:

conclusion: more children --> higher income

regress childrn income


Fixed effects model

Answers the question: What is the effect of x when x changes within persons over time e.g.

Person A has two children at first point of time and three children at second, what effect has this change on income?

Information used: fixed effects estimates using the time-series information in the data

Variance analyzed: within

Problems: only time variant variables


Fixed effects

exercise: separate regression for each unit and then average it:

regress income childrn if id==1regress income childrn if id==2


+( )_____________________________ 2

= - 2.5

exercise: generate dummy variable for person and regress with dummy variable

tab id, g(iddum)

reg income childrn iddum1 iddum2

conclusion: more children --> lower income


Fixed effects

-define data set as panel datatsset id t

-regression with fixed effects commandxtreg income chldrn, fe


Between effects modelAnswers the question: What is the effect of x when x is different (changes) between persons:

Person A has “on the average” three children and Person B has “on the average” five children, what effect has this difference on their income?

In the between effects model we model the mean response, where the means are calculated for each of the units.

Information used: cross-sectional information (between subjects)

Variance analyzed: between variance

Time variant and time invariant variables


Between effects

regress income childrn

conclusion: more children --> more income

define data as panel data xtreg dependent independent, be

average--->


Random effects model: Assumption: no difference between the two answers to the questions:

1) what is the effect of x when x changes within the person: Person A has two children at first point of time and three children at second, what effect does this change have on their income?

2) what is the effect of x when x is different (changes) between persons: Person A has two children and Person B has three children children, what effect does this difference have on their income?

Information used: panel and cross-sectional (between and within subjects)

Variance analyzed: between variance and within variance

Time variant and time invariant variables


Random effects model:

-matrix-weighted average of the fixed and the between estimates.

-assumes b1 has the same effect in the cross section as in the time-series

-requires that individual error terms treated as random variables and follow the normal distribution.

use:

xtreg dependent independent if var==x, re


possible break


open data: panelex2.dta

varlist:


tell stata the structure of the data:

tsset X Y

X= caseidY=time/wave

summary statistics:

xtdesxtsum


use the effects

xtreg dependent independent if sex==1, fe xtreg dependent independent if sex==1, be xtreg dependent independent if sex==1, re

exercise: compare/discuss models

e.g.: xtreg indvar1 indvar2 … if sex==1, fe

try to include time invariant variablestry to make theoretical/empirical argument why you use which model


Problems/Tests/Solutions:

What’s the right model: fixed or random effects?

Test: Hausman Test

Null hypothesis:Coefficients estimated by the efficient random effects estimator are same as those estimated by the consistent fixed effects estimator.

If same (insignificant P-value, Prob>chi2 larger than .05) --> safe to use random effects.

If significant P-value --> use fixed effects.

xtreg y x1 x2 x3 ... , fe estimates store fixed xtreg y x1 x2 x3 ... , re estimates store random hausman fixed random


Problems/Tests/Solutions:

Autocorrelation?

What is autocorrelation:

Last time period’s values affect current values

test: xtserial

Install user-written program, type

findit xtserial or net search xtserial

xtserial depvar indepvars


Significant test statistic indicates presence of serial correlation.

Solution: use model correcting for autocorrelation

xtregar instead of xtreg


possible break


panel

-waves-number of children @ wave1 / 2/ 3/ 4-employed @ wave1 / 2/ 3/ 4-income @ wave1 / 2/ 3/ 4

regression models: dependent variable continuous

event

-dates of events-birth of first child @ 1963-birth of second child @ 1966…-start of first employment @…-start of unemployment @…-start of second employment @…

time information in event data more precise: dependent variable event happens 0/1

different data structure


Different Faces of Event History Data

Time

continuous discrete


Types of censoring

• Subject does not experience event of interest

• Incomplete follow-up Lost to follow-up Withdraws from study

• Left or right censored


open data eventex.dta


tell stata that our data is “survival data”

stset

stset X, failure(Y) id(Z)

X= time at which event happens or right censored, this is always needed

Y= 0 or missing means censored, all other values are interpreted as representing an event taking place/ failure

Z= id

three examples:

• stset ageendschevent: end of schooltime: age @ end of school

• stset agemaryc, failure (marcens) id (caseid) event: marriage

• stset agestjob, failure (stjob) id (caseid) event: first job


DATA MANGAGEMENT HANNAH


Different Models of Event History

Time

continous discrete

non-parametric semi-parametric parametric

-kaplan-meier

-nelson-aalen

-log-rank test for comparison b/w groups

-cox

-piecewise constant

-exponential

-weibull

-log-logistic

-lognormal

-gompertz

-generalized gamma

-logistic

-log-log

only qualitative covariates

inclusion of covariates in models

-compare survival experiences between groups (sex, cohorts)

-univariate -multivariate

Extended from Jenkins 2005


survivor function and hazard function

• Survivor function, S(t) defines the probability of surviving longer than time t

• Survivor and hazard functions can be converted into each other

• Hazard (instantaneous hazard, force of mortality), is the risk that an event will occur during a time interval (Δ(t)) at time t, given that the subject did not experience the event before that time


List the Kaplan-Meier survivor function . sts list . sts list, by(sex) compare

Graph the Kaplan-Meier survivor function . sts graph . sts graph, by(sex)

non-parametric: kaplan-meier



exercise:

stset your data for marriage, endschool or first job

e.g.:

1) sts list

2) sts graph

3) sts list, by (…) compare

4) sts graph, by (..)


List the Nelson-Aalen cumulative hazard function . sts list, na . sts list, na by(sex) compare

Graph the Nelson-Aalen cumulative hazard function . sts graph, na . sts graph, na by(sex)

non-parametric: Nelson-Aalen


non-parametric: Nelson-Aalen

exercise:

stset your data for marriage, endschool or first job

1) sts list, na

2) sts graph, na

3) sts list, na by (…) compare

4) sts graph, na by (..)


Comparing Kaplan-Meier curves

Log-rank test can be used to compare survival curves

Hypothesis test (test of significance)

H0: the curves are statistically the same

H1: the curves are statistically different

Compares observed to expected cell counts


for age@marr:


Comparing Kaplan-Meier curvesnon-parametric: kaplan-meier

exercise:

Test equality of survivor functions

e.g.: sts test abitur


Limit of Kaplan-Meier curves

• What happens when you have several covariates that you believe contribute to survival?

• Example Education, marital status, children, gender contribute to job change

• Can use K-M curves – for 2 or maybe 3 covariates

• Need another approach – multivariate Cox proportional hazards model is most common -- for many covariates



Cox proportional hazards model

• Can handle both continuous and categorical predictor variables

• Without knowing baseline hazard ho(t), can still calculate coefficients for each covariate, and therefore hazard ratio

• Assumes multiplicative risk -

-->proportional hazard assumption

semi-parametric models: cox



example age of first marriage stcox sex

Interpretation:

because the cox model does not estimate a baseline, there is no intercept in the output.

sex (male=1) (female=2)whatever the hazard rate at a particular time is for men, it is 1.5 times higher for women

what does this mean in our case?

women get married younger than men do.


Interpretation of the regression coefficients

• An estimated hazard rate ratio greater than 1 indicates the covariate is associated with an increased hazard of experiencing the event of interest

• An estimated hazard rate ratio less than 1 indicates the covariate is associated with a decreased hazard of experiencing the event of interest

• Estimated hazard rate ratio of 1 indicates no association between covariate and hazard.



Graphically: estimates for functions:

stcox sex, basehc (H0)stcurve, hazard at1(sex=0) at2(sex=1)

stcox sex, basesurv (S0)stcurve, surviv at1(sex=0) at2(sex=1)


exercise:

make your own cox model

and estimate the hazard and survival


Assessing model adequacy

• Proportional assumption: covariates are independent with respect to time and their hazards are constant over time

• Three general ways to examine model adequacy Graphically: Do survival curves intersect? Mathematically: Schoenfeld test Computationally: Time-dependent variables (extended

model)


compare with kaplan maier:

stcoxkm, by (sex)

exercise: do this with one of your estimates


"log-log" plots

stphplot, by (sex)

exercise: do this with one of your estimates, stphplot can be adjusted--> look in stphplot help


Mathematically: Schoenfeld Test

tests if the log hazard function is constant over time, thus a rejection of the null hypothesis indicates a deviation from the proportional hazard assumption

stcox sex, schoenfeld(sch*) scaledsch(sca*)

estat phtest (if more var estat phtest, detail)

exercise: do this with your model, try to find a model which fits


Summary

• Survival analyses quantifies time to a single, dichotomous event

• Handles censored data well

• Survival and hazard can be mathematically converted to each other

• Kaplan-Meier survival curves can be compared graphically

• Cox proportional hazards models help distinguish individual contributions of covariates to survival, provided certain assumptions are met.


It can get a lot more complicated than this

• The proportional hazards model as shown only works when the time to event data is relatively simple

• Complications non proportional hazard rates time dependent covariates competing risks multiple failures non-absorbing events etc.

Extensive literature for these situations and software is available to handle them.


Semi-parametric models: Piecewise constant

-transition rate assumed to be not constant over observed time

-splits data in user defined time pieces,

-transition rates constant in each “time piece”

-but: transition rates change between time pieces


Semi-parametric models: piecewise constant

in STATA a user written command, an “ado file” by J. Sorensen: stpiece

net search stpiece

install file

stpiece abitur, tp(20 30 40) tv(sex)

tp: time pieces, intervals

tv: covariates whose influence might vary over time pieces


the end

ciqle workshop: longitudinal data analysis, silke aisenbrey ciqle workshop: introduction to...

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