Event History Analysis: Introductions

Sociology 229 Event History Analysis

Class 1

Copyright © 2008 by Evan Schofer

Do not copy or distribute without permission

Announcements

• Agenda• Introductions• Review Syllabus• Short Intro lecture• Break• Optional statistics review session (~2 hours)

Regression and EHA: Examples

• Medical Research on Drug Efficacy

• Question #1: Do patients with larger doses of a drug have lower cholesterol?

• Approach: OLS Regression• If assumptions are met, OLS is appropriate• Independent Variable = dosage (“level” of drug)• Dependent Variable = cholesterol (“level”)

Regression Example: CholesterolRelationship between level of

X and Y is modeled as a linear function:

Y = a + bX + e

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Example 2: Drug & Mortality

• Suppose a different question:

• Does increased drug dosage reduce the incidence of mortality among patients?

• The dependent variable has a different character

• 1. Whereas cholesterol is measured as a “level” (continuously), mortality is “discrete”

• Either the patient lives or they don’t (not a “level”)

• 2. Also, TIMING is an issue• Not just if a patient survives, but how long• A drug that extends life is good, even if patients die

Logit/Probit Strategies• Research strategies to address this problem:

• 1. Use a non-linear regression model for discrete outcomes: Logit, Probit, etc.

• Dependent variable is a dummy for patient mortality• Look for relationship between dosage and mortality

• Benefit: Easy. An analog of regression

• Limitation: Doesn’t take timing into account• All patients that die have the same influence on the

model (whether they live 5 days or 20 years due to the drug dosage).

Logit/Probit Strategy: Visual

Relationship between level of X and the discrete

variable Y is modeled as a non-linear function

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Drug & Mortality: OLS Regression

• Option #2: Use OLS regression to model the time elapsed (duration) until mortality– Rather than ask “did they live or die”

(logit/probit), you ask “how long did they live”?• Compute a variable that reflects the time until mortality

(in relevant time units – e.g., months since drug therapy is started)

• Model time as the dependent variable• Observe: Do patients with high drug doses die later

than ones with low doses?

OLS Duration Strategy: Visual

Q: Where do you put individuals

who were alive at the end of the

study?

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Drug & Mortality: OLS Regression

• Problem #1: What about patients who don’t experience mortality during study?

• This is called “censored data”• If study is 80 months, you know that Y>80…

– But, you don’t have an exact value

• What do you do?– Treat them as experiencing mortality at the very end of the

study? Or approximate time of mortality?– Exclude them? NO! That selects on the dependent variable!

• Possible solution: Use models for censored data– Ex: tobit model; “censored normal regression

» Stata: tobit, cnreg.

Drug & Mortality: OLS Regression

• Problem #2: Temporal data often violates normality assumption of OLS regression

• Often violations are quite bad• “Censored” data is a surmountable problem, but

normality violation is usually not• So – we shouldn’t typically use OLS

Drug and Mortality: EHA Strategy• Event History Analysis (EHA) provides purchase on

this exact type of problem• And others, as well

• In essence, EHA models a dependent variable that reflects both:– 1. Whether or not a patient experiences mortality (like

logit),

and… – 2. When it occurs (like a OLS regression of duration)

• Note: This information is typically encoded in 2 or more variables

EHA: Overview and Terminology

• EHA is referred to as “dynamic” modeling• i.e., addresses the timing of outcomes: rates

• Dependent variable is best conceptualized as a rate of some occurrence

• Not a “level” or “amount” as in OLS regression• Think: “How fast?” “How often?”

• The “occurrence” may be something that can occur only once for each case: e.g., mortality

• Or, it may be repeatable: e.g., marriages, strategic alliances.

EHA: Overview

• EHA involves both descriptive and parametric analysis of data

• Just like regression• Scatterplots, partialplots = descriptive• OLS model/hypothesis tests = parametric

• Descriptive analyses/plots• Allow description of the overall rate of some outcome• For all cases, or for various subgroups

• Parametric Models • Allow hypothesis testing about variables that affect

rate (and can include control variables).

EHA: Types of Questions

• Some types of questions EHA can address:

• 1. Mortality: Does drug dosage reduce rates?• Does “rate” decrease with larger doses?• Also: control for race, gender, treatment options, etc

• 2. Life stage transitions: timing of marriage• Is rate affected by gender, class, religion?

• 3. Organizational mortality• Is rate affected by size, historical era, competition?

• 4. Inter-state war• Is rate affected by economic, political factors?