Event History Analysis: Introduction Sociology 229 Class 3 Copyright © 2010 by Evan Schofer Do not copy or distribute without permission

Agenda Introduce EHA Motivation Limitations of alternative approaches

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: Cholesterol Relationship between level of X and Y is modeled as a linear function: Y = a + bX + e Drug Dosage (mg) Cholesterol Level

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 Yes No Drug Dosage (mg) Mortality

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? Drug Dosage (mg) Months Until Mortality

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… or models for censored data that assume normality…

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?