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I am new to survival analysis, although in the past weeks I have done my share of reading, hence this might be a non-problem. I have marriage and divorce data, spanning many years. I'm trying to model the causal change in hazard of divorce of a reform. A marriage is considered treated if it starts after the year of the reform, otherwise it is in the control group.

The year in which exposure to risk starts (i.e. the marriage year) is of course heterogeneous across individuals. Do I need to take this into account somehow? I am already controlling for year of birth and I am wondering if there's more I need doing, both from an identification perspective and from a technical one.

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The date of marriage could be considered analogous to the date of diagnosis of a condition in a clinical study, taken as the date of entry into the study. Time t=0 for each case would be the date of marriage (or diagnosis) and the time to event or censoring would be expressed relative to that date. There is no general need to take that date into account unless the actual date of entry into the study is also associated with the risk of the event of interest (divorce, in your case).

You, however, are already postulating that the actual date of entry into the study matters: you are taking the "year of reform" as being a divider that separates your cases into what could be considered 2 treatment group. So readers will certainly want to see evidence that something special happened in that year that couldn't be explained as some secular trend in divorce rates independent of the "reform." For example, if divorce rates were always increasing with time regardless of the "reform," then comparing marriages before and after the date of "reform" would still show higher divorce rates thereafter.

So in your case careful modeling of the relationship of divorce rate to actual year of marriage would seem very important.

One more thought: if your time values are measured in long intervals like years instead of days, then you might want to consider a discrete-time survival model instead.

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  • $\begingroup$ This is helpful. I am also aware of the problems that you are pointing out, which is what makes me worry. I renspond to them with more questions: (1) shouldn't the inclusion of year of birth dummies (or birth cohort, to save degrees of freedom) already control for the cultural propensity to divorce embedded in a particular generation? (2) If treatment is defined by year of marriage (and state of residence at that time), wouldn't the inclusion of year of marriage dummies kill the results by construction? $\endgroup$ – Fabio I. Jan 25 '19 at 23:48
  • $\begingroup$ PS: The reform I use affects only a part of the country of interest, while the rest of the country (i.e. of the individuals living in the rest of the country) is used as control group. So if there is a common time trend it should be accounted for. More precisely, given a 2001 reform of interest, an individual $i$ living in region $r$ and getting married in year $t$ is treated if r="treated region" & t>2001. He is not treated otherwise. $\endgroup$ – Fabio I. Jan 26 '19 at 0:46
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    $\begingroup$ @FabioI. You will have to use your knowledge of the subject matter to decide whether year of birth, versus year of marriage, adequately controls for divorce propensity over time. Whichever way you choose, consider an interaction of "treatment" with year of marriage/birth as a way to address your question. The relation of year of marriage/birth to divorce should be the same across all states in years before "treatment" started (an important control), then diverge in the "treated" states thereafter. Modeling year of birth/marriage as a continuous variable will save more df than using cohorts. $\endgroup$ – EdM Jan 26 '19 at 17:43

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