Event History Analysis

Introduction to Event History Analysis

• Event History Analysis is also known as Survival Analysis, Analysis of Duration Data, Hazard Analysis, or Gebeurtenissenanalyse in Dutch and Ereignisanalyse in German.

• It is used to assess the influence of independent variables on the duration from time zero until the occurrence of an event or the hazard (probability/rate) of occurrence of an event at a certain time point.

• The crucial variable in Event History Analysis is the hazard rate, which is the propensity or intensity to have an event at a specific time.

• The analysis cannot handle censored data or include time-varying covariates, which makes it different from ordinary linear regression of duration until an event.

• An event is a change in status or something that happens at a certain time point without a change in status.

• The probability of an event occurring between time t and t' is conditional on the population at risk of having the event at time t.

• The hazard is the dependent variable in Event History Analysis, and its application leads to a survival function, which is the probability of surviving until time t or the event's duration being at least t long.

• The survival function can be used to calculate the probability of migration, the probability of a child living for at least t years, or the probability of no first child being born at least t years after partnership formation.

• The analysis can deal with censoring, which occurs when an observation ends before the event of interest occurs.

• Left censoring happens when the observation begins after the event's occurrence, while right censoring happens when the observation ends before the event's occurrence.

• Observation window and survey attrition can also lead to censoring.

• Event History Analysis allows for the estimation of the effect of educational level on the hazard of marrying at a specific age in a population.Event History Analysis and Cox Regression

• Left censoring is problematic in Cox regression, but can be handled in discrete-time logit models.

• Right censoring is not a problem as long as it can be assumed to be random.

• Descriptive methods for duration data include the Kaplan Meier estimator for survival function.

• Kaplan Meier graphs can be used to compare survival rates between different groups, but do not provide information on the size of the effect of variables.

• Event history models are used to model the hazard rate of quitting a job.

• The Cox model is a type of event history model that assumes proportional hazards, where the hazard is a constant ratio of the baseline hazard and the exponentiated values of explanatory variables.

• The Cox model is also known as the proportional hazards model.

• The Cox model assumes that the hazard is proportional over time, which may not always be the case.

• If the proportionality assumption fails, separate baseline hazard rates can be specified for different categories.

• The stset command is used in Stata to prepare data for survival analysis.

• The Cox regression model can be used to analyze job duration, with the sex variable as an example.

• The Cox regression model provides coefficients for the effects of variables on the log hazard and the hazard ratio.Cox Regression Model for Job Duration in Stata

• The Cox regression model is used to analyze the relationship between covariates and time-to-event data.

• The first step in running the Cox model in Stata is to set the data using the stset command.

• The stset command specifies the time variable and the failure variable, which indicates the occurrence of the event of interest.

• The stcox command is used to estimate the Cox regression model.

• The covariates of interest are included after the stcox command, with the option nohr for the hazard ratio output.

• If multiple records per individual are present in the data, the vce(cluster id) option can be added to obtain robust standard errors.

• The output of the Cox model includes the estimated coefficients, standard errors, z-scores, and p-values for each covariate.

• The log-likelihood value is also reported, which indicates the goodness of fit of the model.

• The probability value for the chi-squared test and the chi-squared value are reported, which test the null hypothesis that all coefficients are zero.

• The time at risk, number of failures, and number of subjects are also reported in the output.

• If more than one episode per person is present in the data, the vce or robust cluster(id) option should be used to obtain robust standard errors.

• The Cox regression model is a useful tool for analyzing time-to-event data and can be easily implemented in Stata.

Advanced Statistical Analysis: Event History Analysis 2

• The lecture covers event history analysis 2, including parametric models, cumulative hazard, and Cox regression.
• Parametric event history models require specifying a mathematical function for the hazard rate and estimating parameters of the function and independent variables, but Cox regression is semiparametric and does not assume a mathematical function for the hazard rate.
• The cumulative hazard function measures the total amount of risk accumulated up to a certain time and can be used to compute the survival function and test model performance.
• Survival can only go down, while the hazard may fluctuate, and the steeper the survival curve goes down, the lower the hazard.
• The Cox model in Stata can be used to plot predicted hazard, cumulative hazard, and survival functions, and to test the proportionality assumption.
• If there is more than one episode per person, the "vce" or "robust cluster" option can be used to obtain robust standard errors, and the "id" option can be used to specify the person identifier.
• The coefficient and hazard ratio for men can be calculated if women are used as the reference category, and confidence intervals and hazard ratios can be derived from coefficients and standard errors.
• The lecture provides examples and exercises for students to practice these concepts.
• The lecture recommends reading Handbook Chapter 9 on survival analysis for further information.
• The lecture was given by Clara Mulder and colleagues in the Faculty of Spatial Sciences.
• The lecture materials are intended for advanced statistical analysis students.
• The lecture materials are presented in English.

Advanced Statistical Analysis: Event History Analysis 2

• The lecture covers event history analysis 2, including parametric models, cumulative hazard, and Cox regression.
• Parametric event history models require specifying a mathematical function for the hazard rate and estimating parameters of the function and independent variables, but Cox regression is semiparametric and does not assume a mathematical function for the hazard rate.
• The cumulative hazard function measures the total amount of risk accumulated up to a certain time and can be used to compute the survival function and test model performance.
• Survival can only go down, while the hazard may fluctuate, and the steeper the survival curve goes down, the lower the hazard.
• The Cox model in Stata can be used to plot predicted hazard, cumulative hazard, and survival functions, and to test the proportionality assumption.
• If there is more than one episode per person, the "vce" or "robust cluster" option can be used to obtain robust standard errors, and the "id" option can be used to specify the person identifier.
• The coefficient and hazard ratio for men can be calculated if women are used as the reference category, and confidence intervals and hazard ratios can be derived from coefficients and standard errors.
• The lecture provides examples and exercises for students to practice these concepts.
• The lecture recommends reading Handbook Chapter 9 on survival analysis for further information.
• The lecture was given by Clara Mulder and colleagues in the Faculty of Spatial Sciences.
• The lecture materials are intended for advanced statistical analysis students.
• The lecture materials are presented in English.

Advanced Statistical Analysis: Event History Analysis

• The lecture covers event history analysis, including Cox regression and discrete-time event history analysis using logistic regression of person-period data.

• Extensions to the models are discussed, such as time-varying covariates, non-proportional hazards, and multiple risks.

• Complications such as left censoring, non-random right censoring, and periods of missing information are also addressed.

• The assignment on Cox regression involves analyzing a dataset with events occurring before age 30, with hazards crossing at age 30 and odd findings above age 40.

• Respondents clustered in households, requiring robust cluster(nohhold).

• Predicted cohort survival is forced into proportionality, and interpretation findings for the level of education are discussed.

• Reminder assignments include passing a minimum number of practicals and assignments, and uploading resit assignments in the correct folder by a certain date.

• Preparation for event history analysis involves defining the event and determining the population at risk and time 0.

• The time unit and end of observation are also important considerations in preparation.

• The choice of method can depend on the assumptions being made and the data available.

• The discrete-time logistic regression model is discussed, including the units of analysis, dependent variable, covariates, duration, and hazard assumptions.

• Violations of the assumption of independence of observations and multilevel problems may require robust standard errors. Data preparation involves constructing a person-period file.Event History Analysis: Four Extensions and Complications

• Event history analysis involves studying the timing of events or transitions in individuals' lives.

• Four extensions in event history analysis include time-varying covariates, non-proportional hazards, multiple spells, and multiple risks.

• Time-varying covariates can be handled by using methods such as Cox model or discrete-time logistic regression model to update the value of covariate each time unit.

• Non-proportional hazards, where the effects of covariates change through time, can be handled by splitting episodes or including interaction of covariate with duration variable.

• Multiple spells, where there is re-appearance in the population at risk and more than one spell/event per person, can be corrected by using multi-level modeling or Stata subcommand: robust cluster.

• Multiple risks, such as transition from rent to other rent or own, can be handled by using discrete-time multinomial logistic regression.

• Complication 1: left censoring can be handled by including a duration variable with a category 'unknown' or by imputing.

• Complication 2: non-random right censoring, such as panel attrition, can be modeled as extra risk.

• Complication 3: periods of missing information can be handled by copying values from the previous time unit or by imputing.

• The assignment involves using logistic regression of person-years to explain the transition to first-time home-ownership using information available in the data.

• Data in this format is not suitable for preparatory survival analysis; use person/episode data instead.

• Mulder & Wagner 1998 in Urban Studies can be used as inspiration for the assignment.

Advanced Statistical Analysis: Event History Analysis

• The lecture covers event history analysis, including Cox regression and discrete-time event history analysis using logistic regression of person-period data.

• Extensions to the models are discussed, such as time-varying covariates, non-proportional hazards, and multiple risks.

• Complications such as left censoring, non-random right censoring, and periods of missing information are also addressed.

• The assignment on Cox regression involves analyzing a dataset with events occurring before age 30, with hazards crossing at age 30 and odd findings above age 40.

• Respondents clustered in households, requiring robust cluster(nohhold).

• Predicted cohort survival is forced into proportionality, and interpretation findings for the level of education are discussed.

• Reminder assignments include passing a minimum number of practicals and assignments, and uploading resit assignments in the correct folder by a certain date.

• Preparation for event history analysis involves defining the event and determining the population at risk and time 0.

• The time unit and end of observation are also important considerations in preparation.

• The choice of method can depend on the assumptions being made and the data available.

• The discrete-time logistic regression model is discussed, including the units of analysis, dependent variable, covariates, duration, and hazard assumptions.

• Violations of the assumption of independence of observations and multilevel problems may require robust standard errors. Data preparation involves constructing a person-period file.Event History Analysis: Four Extensions and Complications

• Event history analysis involves studying the timing of events or transitions in individuals' lives.

• Four extensions in event history analysis include time-varying covariates, non-proportional hazards, multiple spells, and multiple risks.

• Time-varying covariates can be handled by using methods such as Cox model or discrete-time logistic regression model to update the value of covariate each time unit.

• Non-proportional hazards, where the effects of covariates change through time, can be handled by splitting episodes or including interaction of covariate with duration variable.

• Multiple spells, where there is re-appearance in the population at risk and more than one spell/event per person, can be corrected by using multi-level modeling or Stata subcommand: robust cluster.

• Multiple risks, such as transition from rent to other rent or own, can be handled by using discrete-time multinomial logistic regression.

• Complication 1: left censoring can be handled by including a duration variable with a category 'unknown' or by imputing.

• Complication 2: non-random right censoring, such as panel attrition, can be modeled as extra risk.

• Complication 3: periods of missing information can be handled by copying values from the previous time unit or by imputing.

• The assignment involves using logistic regression of person-years to explain the transition to first-time home-ownership using information available in the data.

• Data in this format is not suitable for preparatory survival analysis; use person/episode data instead.

• Mulder & Wagner 1998 in Urban Studies can be used as inspiration for the assignment.