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I have event time data for subjects with different categories (A, B, C etc.) yearly observed. To my understanding my data is both right and interval censored (?).

Subjects' category can change from year to year, e.g. A for years 0 to 2, than B from year 3 onwards for subject 1 etc. Each subject can be exposed to the "event" independent of its category. For time being I am not interested in transition effects.

Which estimators can be suggested for the 1 year failure probability per category?

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  • $\begingroup$ Explain more about your data! Are you sure it is interval censored beyond the general level of resolution (eg if all your variables have a yearly resolution, than event times do not really have to be more precise)? Does you usage of "1 year failure probability" implies that you think it is constant over time, i.e. the probability of failing in year 1 is the same as in year 5 (assuming the same category)? $\endgroup$
    – Aniko
    Commented Jan 16, 2012 at 14:26
  • $\begingroup$ @Aniko The event can happen during the year but is only recorded at the end of the year (I am not considering other variables for time being). The probability is surely time dependent, but I am interested in a "average" probability over the observation window. Actually one of the question I have is which observation window should I choose? I will use the probabilities for prediction, I need to balance accuracy versus stability... $\endgroup$
    – teucer
    Commented Jan 16, 2012 at 15:10

3 Answers 3

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You can split each of your patients up into multiple records. For example, if Patient Joe is followed for 5 years, switching from A to B two years in, and B to C two years after that, he'd be three records. Joe # 1 who entered at Year 0, and left at year 2. Joe #2 who enters at year 2 and leaves at year 4, and Joe #3, who enters at year 4 and leaves at year 5.

You then use a robust variance estimator that takes care of the fact that you have some non-independence in your data, and you can run any survival analysis you want. I suspect if you're looking for a 1 year probability of failure, you'd use some parametric estimator of the survival curve, or a Kaplan-Meyer type analysis.

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The simplest approach is to break up each subject into multiple person-years with each year associated with only one category and an event yes/no indicator. You can get yearly probabilities from this without difficulties. Note that this would assume that the probabilities are constant over time. Poisson regression can be used for inference.

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If I understand you description correctly, you case falls within discrete time survival/hazard analysis (discrete time in the sense of discretized intervals of a continuous process, not in the sense that events only happen after fixed intervals).

In that case I would follow Aniko's suggestion and use a logistic regression model with person-years as observations, with event occurrence as a dependent variable and category as a time-variant explanatory variable (together with time of course).

An applied handbook recommended for this case is Applied Longitudinal Data Analysis by Singer & Willett, ch. 10-12. See here for worked examples/syntax for different programs.

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