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Why I’m skeptical of interrupted time series

Today I have a mystery chart for you. Take a look at it:

What do you see here? Obviously the trend changes around 2022, but when exactly would you say it changes? The beginning of 2022? The middle? Towards the end?

My take is pretty simple: the trendline quite obviously starts to jump right at the start of 2022. Then, maybe around August or September, it levels out and once again continues rising at its old rate.

Now let's take down the curtain and show you the exact same chart, but this time as presented in a recent study, "Changes in Permanent Contraception Procedures Among Young Adults Following the Dobbs Decision":

The authors use an interrupted time series to demonstrate that women got their tubes tied more often in the wake of the Dobbs decision. But this is why I hate interrupted time series: they're abused way too often. The authors certainly show that the number of tubal ligations is higher in 2023 than in 2021, but they don't show that the increase started after the Dobbs decision. In fact, it quite clearly started many months before.

So what really happened? That's still a mystery. There's no obvious reason I can think of for more tubal ligations starting in January 2022. It's especially mysterious because the authors also look at vasectomies, and it really does look like those increased right after Dobbs:

Even here I'm skeptical. The rate of vasectomies jumped in a single month, literally within weeks of the Dobbs decision. That's not impossible, but it sure seems like a remarkably quick response. Can you even schedule a vasectomy in less than a month?

At the moment, your guess about this is as good as mine. But if Dobbs really did cause more women to opt for permanent birth control, I'd expect to see a change a few months after the decision was handed down. Maybe around September 2022 at the earliest. In any case, I certainly wouldn't expect to see a sharp increase six months before it was handed down and four months before it was leaked.

22 thoughts on “Why I’m skeptical of interrupted time series

  1. rick_jones

    Can you even schedule a vasectomy in less than a month?

    Probably. It isn’t even outpatient surgery, but something performed in something just a couple steps up from a regular exam office. Under local anesthesia.

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  2. Austin

    Wasn't the decision leaked months prior to the Dobbs dotted line on the chart, which appears to be when the decision was officially issued? Could that be playing a part here, along with months prior to that of more and more media figures stating out loud that Roe's days were numbered and Roe would likely end in 2022?

    Unlike most other creatures, humans are capable of making pretty accurate predictions about the near future and acting to avoid those predictions if they deem them to be really bad in some personal way. The fact that millions of humans don't do this isn't evidence that it's impossible for some women to have realized "holy shit SCOTUS might be serious this time" and that motivated them to finally schedule the tubal ligation they had been thinking about for months/years prior. If you told me today that I was likely to not have the ability to, say, take a tax break next year for buying an EV, I might step up my plans to buy one right now instead... and if others join me, you'd see a jump in the EV sales ahead of the actual repeal of EV credits.

    1. golack

      Not just the leak....the Court let the Texas law take effect instead of just keeping things as they were well before the leak.

    2. Joseph Harbin

      Oral arguments: Dec 1, 2021
      Leaked opinion: May 2, 2022
      Decision: June 24, 2022

      Do some people change behavior now in anticipation of something happening later? I've heard it happens.*

      Does that mean the expectation of Dobbs accounts for the increase in 2022? Maybe, maybe not. If so, then what accounted for the doubling between 2019 and the beginning of 2022?

      * They're saying some people are buying stocks in early 2024 anticipating the election of Donald Trump in late 2024. Saw a man on television claiming that was true.

      1. rick_jones

        The regular, steady increase which, probably, started before 2019. And which continued after the however-triggered step circa Dobbs.

  3. cmayo

    As mentioned, it was leaked before the official was released, but even before it was leaked the writing was on the wall to the extent that I would expect an "early" response from people.

    There is no surprise here in this data and no reason to be skeptical. It all tracks.

    1. Excitable Boy

      Yes, this is a man in his 60s with no children wants to be contrarian and has to come up with another post. He can only make this plausible by disappearing the reporting the weeks and months before the leak that Dobbs was gone, and the actual leak 7 weeks before the decision was handed down. If he can’t disappear that pertinent information from the real timeline, then he has no post.

      1. cmayo

        The impulsive contrarian explanation also tracks with the stream of "young people are fine" and "there is no housing crisis" posts.

  4. Austin

    Some states also are stockpiling mifepristone now, even though it's fully legal to buy it today, tomorrow and for at least the next 2 months or so until the ruling is issued. So I wouldn't be surprised if you charted "sales of mifepristone" if they would also have already had a jump earlier this year or even late last year, despite it being before SCOTUS actually decides to uphold banning it. There's not much point in waiting... if SCOTUS bans something and makes that ruling effective immediately, your waiting will mean you missed your chance to get whatever it is.

    Really, Kevin, it's pretty easy to think of examples of "people buying something to stockpile it or get it before it's no longer available" either because they fear it's going to be banned by government or discontinued by the manufacturer or whatever. Not sure what your point was in this post, but it's just plain wrong.

  5. FrankM

    There is a time-tested (no pun intended) method of analyzing data such as this: calculate the differences between pairs of data points. If data is excessively noisy you can smooth using moving averages before calculating the differences.

    1. bluegreysun

      A sudden massive increase in time spent with their children - as schools, day care and child care largely stopped, with everyone working from home?

      I know a few parents who became quite desperate, honestly.

      I do think your point about psychological fallout is a real one though, and is constituted of much more than just an overdose of children. Genuine society level psychic harm. (Dunno if it caused an increase in permanent contraception procedures though).

  6. KJK

    Something definitely occurred with respect to the jump in the number vasectomies and tubal ligations, and the cause of Roe V Wade seems perfectly plausible. Note that people will only do these procedures if they do not want any more children (or any children).

    It would be interesting to see the data with the States that currently have liberal abortion laws washed out. Though these days, who knows how long that will last if Orange Jesus and more Christian Nationalists are elected to Federal office. Passing a national abortion ban would be wet dream for Mike Johnson.

  7. brainscoop

    As someone who occasionally tries to figure out when a noisy time series changed in a professional capacity, I'd say that precisely when the rate of tubal ligations changed around 2022 is harder to suss out than you seem to think. While I don't think it's obvious that it happened right at the beginning of 2022, skepticism over it being Dobbs based on the time series alone is reasonable.

  8. rrouda

    You can put me down with the list of "Not Disproven by the Timeline". This was one of the most telegraphed punches in history. McConnell made the result almost certain when he refused to hold hearings on Garland. Then Trump was elected. Then Barrett was appointed. In December, the Supreme Court upheld the Texas Bounty law (SB8). Legal nuance aside, pretty much everyone understood that there was very little chance that the Court would allow some religious fanatic in Uganda to effectively ban abortions in Texas by filing frivolous lawsuits while insisting that the elected Texas State Legislature couldn't do the same.

    That prediction was borne out when the draft Dobbs decision leaked on May 2. While it wasn't the final word, it was pretty clear that the decision to cite a centuries past witch burner as a controlling authority on the proper treatment of women before the law indicated an intractable hostility toward any social development since Oliver Cromwell was on the sky side of the grass.

    Finally, two months later, at the end of June, the final punch landed.

    Interestingly, that history works pretty well with the graphs showing a soft start to the increase in tubal ligations early in the year, and then a sharper increase in vasectomies after the formal ruling. Its not hard to see how those conversations might have played out. Women becoming increasingly concerned over the entire period from Trump's election through Barrett's appointment and knowing that they would need fairly significant surgery to protect themselves would have started calling their doctors in increasing numbers starting in January. Men, needing less lead and recovery time for their procedure, and possibly more inclined to wait until the last sliver of hope for rationality was gone, might have been more likely to put off their call until that first conversation with their partners following the final ruling.

    I'd still like to see something else beyond coincidence in timing in the US to support the SCOTUS/Permanent Contraception Theory. (For instance, is there any evidence of a similar effect in other countries? Is there any state by state variation? Even knowing the weaknesses of such survey data, did anyone just plain ask the patients or their doctors if Dobbs was a factor?

  9. fentex

    Might I suggest, Kevin, you're missing something from your interpretation of this data...

    "...it quite clearly started many months before."

    Behaviour revealed before a momentous decision should be influenced by worries, or expectations, for the decision.

    A court expected to decide one way in several months should effect behaviour several months before it's decision as people are not Pavlovian dogs simply reacting solely to stimuli after the fact - they are agents making decisions with expectations.

  10. cmayo

    Upon another look at the chart, what's truly shocking to me is there was something around a 10x increase in vasectomies since 2019. The increase in tubal ligations was "only" about 3x. That's nuts.

  11. Devyn

    Two comments:

    1. As many others have already noted, the decision was leaked 1.5 months before and the hearing itself was in December 2021. That right there is Kevin's early-2022 change. Though also, it was clear for months and even years this was coming, so there's that to factor in.

    However:

    2. If you ignore the threndline and focus on the top graph, it actually looks like there was a) a small steady increase 2019 to March 2020, b) a jump in April 2020, c) followed by a leveling off through January 2022, then d) a rise through February 2022 - September 2022, then e) mostly a leveling off.

    The obvious dates there are start of Covid and the pandemic, coming into Dobbs.

    Perhaps these numbers are a little more pandemic-related than Dobbs-related, or at least these should factored together.

  12. steve22

    As significant number of tubal ligations are done post delivery, especially at C section. If you were considering a tubal after what you thought might be your last child and knew the Dobbs case was underway and realized 6 members of the court had already decided to overturn Roe that could certainly help you finalize your decision. Note this was in the 18-30 age group where maintaining fertility in case of remarriage or whatever is pretty common.

    Steve

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