How do you handle censoring and truncation in event history analysis?

1 What is censoring?

Censoring occurs when the event of interest is not observed for some individuals or units in the study, either because it has not happened yet, or because it is hidden or missing. For example, if you are studying the survival time of patients with a certain disease, some patients may still be alive at the end of the study period, or may drop out or switch treatments. These are censored observations, because you do not know their exact event times.

2 What is truncation?

Truncation occurs when some individuals or units are excluded from the study based on their event times. For example, if you are studying the duration of unemployment, you may only have data on people who applied for a job after a certain date. This means that you are missing the information on people who found a job before that date, or who never applied. These are truncated observations, because they do not reflect the whole population of interest.

3 How to identify censoring and truncation?

The first step to handle censoring and truncation is to identify them in your data. You can use descriptive statistics, plots, or tests to check for the presence and type of censoring and truncation. For example, you can use a Kaplan-Meier plot to visualize the survival function and the censoring pattern, or a log-rank test to compare the survival distributions of different groups. You can also use a Cox-Snell residual plot to detect truncation, or a likelihood ratio test to compare models with and without truncation.

4 How to model censoring and truncation?

The second step is to choose an appropriate model that accounts for censoring and truncation. You cannot use ordinary regression models, such as linear or logistic regression, because they assume that the dependent variable is fully observed and normally distributed. Instead, you need to use models that are specifically designed for event history analysis, such as Cox proportional hazards model, parametric survival models, or discrete-time models. These models use the partial likelihood or the hazard function to estimate the effects of covariates on the event rate, while adjusting for censoring and truncation.

5 How to evaluate and compare models?

The third step is to evaluate and compare the performance and fit of your models. You can use various criteria, such as the Akaike information criterion (AIC), the Bayesian information criterion (BIC), or the deviance, to select the best model among competing alternatives. You can also use diagnostic tools, such as the Schoenfeld residuals, the Cox-Snell residuals, or the martingale residuals, to check the assumptions and validity of your models. For example, you can use the Schoenfeld residuals to test the proportionality assumption of the Cox model, or the Cox-Snell residuals to assess the goodness-of-fit of your model.

6 How to interpret and communicate results?

The final step is to interpret and communicate your results in a clear and meaningful way. You can use various measures, such as the hazard ratio, the survival probability, or the median survival time, to summarize the effects of covariates on the event outcome. You can also use graphical methods, such as the survival curves, the hazard curves, or the cumulative incidence curves, to illustrate the patterns and differences of event occurrence among groups. You should also report the confidence intervals, the p-values, and the model fit statistics to indicate the uncertainty and significance of your estimates.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?