Fitting interval-censored Cox model with time-varying covariates in Stata

In survival analysis, interval-censored event-time data occur when the event of interest is not always observed exactly but is known to lie within some time interval. These types of data arise in many areas, including medical, epidemiological, economic, financial, and sociological studies. Ignoring interval-censoring will often lead to biased estimates. A semiparametric Cox proportional hazards regression model is used routinely to analyze uncensored and right-censored event-time data. It is also appealing for interval-censored data because it does not require any parametric assumptions about the baseline hazard function. Also, under the proportional-hazards assumption, the hazard ratios are constant over time. Semiparametric estimation of interval-censored event-time data is challenging because none of the event times are observed exactly. Thus, “semiparametric” modeling of these data often resorted to using spline methods or piecewise-exponential models for the baseline hazard function. Genuine semiparametric modeling of interval-censored event-time data was not available until recent methodological advances, which are implemented in the stintcox command. In this presentation, I will describe two basic formats for interval-censored data and will demonstrate how to fit the Cox model to these data using Stata's stintcox command. I will then demonstrate how to create time-varying covariates (TVCs) automatically using the stintcox command and how to use TVCs to test the proportional-hazards assumption. Last but not least, I will show how to incorporate TVCs in your predictions and plots of survivor and other functions.