Category Archives: health care

Whales, Tails and How Far to Trust AI

How can you train an AI?

By AI, we're referring to "artificial intelligence" systems, which are a special class of machine learning computer programs that are increasing showing up in some pretty amazing applications. Whether its generating an image based on text you enter or nearly instantaneously writing the equivalent of a school report on a particular subject, AI systems are leaving the world of science fiction and becoming today's reality.

But how do their developers train these systems to do these things?

Last year, Matt Parker visited Antartica, where he learned how to apply maths to identify specific humpback whales. The following 22-minute video describes how the mathematical methods developed for advanced image recognition made it possible for him to use an Excel spreadsheet to identify a specific whale he photographed swimming off the north coast of Antartica*.

Clearly, AI can deliver impressive results, but how far can you trust those results?

One area where photo-recognition AI systems could make a real impact is in radiology, where such systems could potentially diagnosis serious health conditions much more quickly at much lower cost than can be done by professional radiologists.

A recent study published in the British Medical Journal (BMJ) asked if AI could pass the Royal College of Radiologists' board examination. Spoiler alert: It couldn't, where why it couldn't tells us something about the limitations of these AI deep maching learning systems. Chuck Dinerstein of the American Council on Science and Health summarizes the study's main findings, in which the performance of AI-trained systems and human radiologists were compared (emphasis ours):

First, the obvious, with two exceptions, humans did better than the AI on diagnosis where both had been trained; when unfamiliar pathology was introduced, AI failed across the board. Second, while the humans fared better, theirs was not a stellar performance. On average, newly minted radiologists passed 4 of the ten examinations.

“The artificial intelligence candidate... outperformed three radiologists who passed only one mock examination (the artificial intelligence candidate passed two). Nevertheless, the artificial intelligence candidate would still need further training to achieve the same level of performance and skill of an average recently FRCR qualified radiologist, particularly in the identification of subtle musculoskeletal abnormalities.”

The abilities of an AI radiology program remain brittle, unable to extend outside their training set, and as evidenced by this testing, not ready for independent work. All of this speaks to a point Dr. Hinton made in a less hyperbolic moment.

“[AI in the future is] going to know a lot about what you’re probably going to want to do and how to do it, and it’s going to be very helpful. But it’s not going to replace you.”

Here's the kicker according to Dinerstein:

We would serve our purposes better by seeing AI diagnostics as a part of our workflow, a second set of eyes on the problem, or in this case, an image. Interestingly, in this study, the researchers asked the radiologists how they thought the AI program would do; they overestimated AI, expecting it to do better than humans in 3 examinations. That suggests a bit of bias, unconscious or not, to trust the AI over themselves. Hopefully, experience and identifying the weakness of AI radiology will hone that expectation.

Like any human expert, AI has limitations. Identifying and knowing what those limitations are will be key to determining how trustworthy they are. In the case of health care, as the example from radiology makes clear, it could be your health that's on the line if you blindly put more trust into a system than it deserves.

Reference

Shelmerdine, S.C.; Martin, H.; Shirodkar, K.; Shamshuddin, S.; Weir-McCall, J.R. "Can artificial intelligence pass the Fellowship of the Royal College of Radiologists examination? Multi-reader diagnostic accuracy study." BMJ 2022; 379. DOI: 10.1136/bmj-2022-072826. (Published 21 December 2022).

* If you know your geography, you already knew every coast of Antartica is the north coast!...

The Ebb and Flow of COVID-19 in Arizona’s ICUs

Unlike other states coping with the winter surge in serious COVID-19 cases in their hospitals, Arizona never ran out of available Intensive Care Unit (ICU) bed space.

Here's a chart from the Arizona Department of Health Services COVID-19 data dashboard, which shows the daily percentage usage of ICU beds in the state, including for COVID-19 patients from 10 April 2020 through 20 February 2021:

Arizona Number of Intensive Care Unit (ICU) Beds Available and In Use at Arizona Hospitals, with Data for COVID-19 Patients from 10 April 2020 through 20 February 2021

ICU bed usage peaked at 93% on 30 December 2020, as the number of open ICU beds in the state dropped to 121, the lowest figure recorded during the state's experience with the coronavirus pandemic.

But while this chart ably communicates the percentage share of ICU beds that were either open, used by COVID-19 patients, or by non-COVID-19 patients, it doesn't communicate the story of how Arizona was able to avoid the situation that states like California faced in running out of ICU beds during the same period of time.

The following chart reveals that part of Arizona's secret to avoiding running out of ICU bed capacity was to increase its supply of ICU beds. In the chart, we've shown the daily numbers of open ICU beds, the ICU beds used by both COVID-19 and non-COVID patients, and also the total number of ICU beds in the period from 10 April 2020 through 20 February 2021, against the backdrop of the major turning points driving the number of COVID-19 cases in Arizona.

Arizona ICU Bed Usage, 10 April 2020 through 20 February 2021

Here, we find that Arizona went from an average total of roughly 1,650 ICU beds early in the coronavirus pandemic to over 1,800 at its peak.

We also see that the number of COVID-19 and non-COVID-19 patients are inversely related, with one rising while the other falls, which points to another secret to Arizona's relative success in managing its limited ICU capacity. Hospital officials proactively managed non-COVID-19 patient ICU bed usage, which helped ensure ICU beds would be available for COVID patients.

At the same time, treatments available for COVID-19 patients have improved from lessons learned during the state's first wave of SARS-CoV-2 coronavirus infections. These improved treatments helped keep a considerable COVID-19 patients from needing to be placed in ICU beds.

That can be seen by the relative number of COVID-19 patients in Arizona hospital ICU beds. That number peaked at 970 during the state's first wave, and peaked at 1,183 during the state's second wave, a 22% increase.

By contrast, the rolling seven day moving average for the number of patients admitted to Arizona hospitals for COVID-19 peaked at 315 per day on 16 July 2020 during Arizona's first wave, and at 535 per day on 8 January 2021 during the state's second wave, a 70% increase. The much smaller percentage increase in ICU bed usage during Arizona's second wave may therefore be attributed to improved care and treatments available for COVID-19 patients at Arizona's hospitals.

The story of how Arizona's hospitals have managed its periodically worst-in-the-nation surge of COVID-19 has been absent in media reports. We thought it was time that somebody addressed even a small part of what looks to be an all-too-rare good news story.

Previously on Political Calculations

Here is our previous coverage of Arizona's experience with the coronavirus pandemic, presented in reverse chronological order.

References

We've continued following Arizona's experience during the coronavirus pandemic because the state's Department of Health Services makes detailed, high quality time series data available, which makes it easy to apply the back calculation method to identify the timing and events that caused changes in the state's COVID-19 trends. This section links that that resource and many of the others we've found useful throughout the coronavirus pandemic.

Arizona Department of Health Services. COVID-19 Data Dashboard. [Online Application/Database].

Stephen A. Lauer, Kyra H. Grantz, Qifang Bi, Forrest K. Jones, Qulu Zheng, Hannah R. Meredith, Andrew S. Azman, Nicholas G. Reich, Justin Lessler. The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application. Annals of Internal Medicine, 5 May 2020. https://doi.org/10.7326/M20-0504.

U.S. Centers for Disease Control and Prevention. COVID-19 Pandemic Planning Scenarios. [PDF Document]. Updated 10 September 2020.

More or Less: Behind the Stats. Ethnic minority deaths, climate change and lockdown. Interview with Kit Yates discussing back calculation. BBC Radio 4. [Podcast: 8:18 to 14:07]. 29 April 2020.

Arizona Arrives at Critical Junction for Coronavirus Cases

One week ago, we projected the state of Arizona would soon arrive at a critical juncture in its experience with the coronavirus pandemic. With the rate of ICU bed usage in the state for COVID-19 patients now surpassing a key threshold, that time has now arrived.

That state of affairs may be seen in a chart tracking Daily COVID-19 ICU Bed Usage in Arizona, where the number of beds occupied by COVID-19 patients now exceeds the level would be considered easily sustainable.

Daily COVID-19 ICU Bed Usage in Arizona, 3 March 2020 - 18 November 2020

Arizona's hospitals still have available ICU bed capacity, so the situation in the state isn't as critical as other areas that are currently experiencing a significant surge in cases. What exceeding this threshold means is that Arizona hospitals need to begin more actively managing their ICU beds usage to accommodate the rising numbers of COVID-19 patients. Ideally, those measures will involve increasing their ICU bed capacity. Unlike many states, Arizona saw two new hospitals open this month in its major metropolitan areas, which will provide some additional breathing room.

Sharp eyed readers will note we've added a new event to this chart. Event I marks an increase in the trend for COVID-19 ICU bed usage that coincides with political events that took place in the state during the period from 23 October 2020 through 25 October 2020. Using the back calculation method to identify the period in which the incidence of coronavirus exposures points to this period as a significant event. The latest update to our chart tracking daily new COVID-19 hospital admissions in Arizona identifies each of the major events associated with a changes in the risk of coronavirus exposure among Arizona's population.

Daily COVID-19 New Hospital Admissions in Arizona, 3 March 2020 - 18 November 2020

The data for this latter chart is still incomplete, where the ICU bed usage chart has proven to be a good real time indicator of the progression of SARS-CoV-2 coronavirus infections within the state. We anticipate the rolling 7-day moving average will soon confirm the surge in COVID-19 hospitalizations.

Data for positive COVID-19 test results in Arizona already confirms a surge in new cases, pointing once again to the period of 23 October 2020 through 25 October 2020 as the period in which the incidence of new infections increased. The following chart of daily newly confirmed COVID-19 cases in Arizona shows the latest surge:

Daily COVID-19 Confirmed Cases by Sample Collection Date in Arizona, 3 March 2020 - 18 November 2020

Meanwhile, since it has the greatest lag between the incidence of exposure and observed change in trend, a chart of deaths attributed to COVID-19 in Arizona does not yet confirm a change in trend. We project the rolling 7-day moving average of coronavirus deaths will show a change in trend taking place in the period from 9 November through 13 November 2020 as these deaths are reported in the weeks ahead.

Daily COVID-19 Deaths in Arizona, 3 March 2020 - 18 November 2020

We track Arizona's COVID-19 data because the state provides high quality, relatively detailed data that makes it possible to use the back calculation method to identify when the rate of incidence of coronavirus infections has changed for the state's residents. To better show how that method works, we put together the following chart to track the incidence of COVID-19 infections among the various demographic age groups reported by Arizona's Department of Health Services. The chart focuses on the time from 9 August 2020 through 18 November 2020, which covers Arizona's 'back-to-school' period for its state universities.

In this chart, we're identifying trend-changing events by number instead of letter, so here's the basic summary:

20-22 August 2020: In-person classes begin at state universities.
4-6 September 2020: Social mixing during Labor Day weekend.
13-15 September 2020: University of Arizona imposes lockdown measures on its students (the outbreak of cases in the state during this time was concentrated at the UA campus). After this third significant event affecting the incidence of new coronavirus cases in Arizona, it's important to note the divergence that takes place among demographic age groups in the state. The Age 0-19 group sees a falling number of cases, as Arizona schools have measures that are largely effective in limiting the spread of new cases. But the Age 20-44 group sees an increasing number of cases as compared to all other age groups, where this group is the most likely to frequent high exposure risk venues, such as bars, gyms, and other businesses for which public health officials have established specific operating requirements.
23-25 October 2020: Political rallies centered around the occasion of the 24 October 2020 National Vote Early Day, less than two weeks ahead of the U.S. elections.

The current upward trend in cases and what we can identify as contributing factors to it using the back calculation method suggests the most effective approach state and local government officials can take to reverse its adverse trend would be to restrict the operation of high exposure risk businesses in local communities as the ICU beds usage within them nears 95% of capacity. Arizona has already demonstrated a decentralized approach can be highly effective in coping with a surge in cases, without unnecessarily imposing economic hardships on the state's residents in areas where the number of cases and burden on loal hospital resources is relatively low.

Local officials could also mandate wearing masks at public venues within their jurisdictions, though we think this option would provide little benefit. That is because most areas in the state already have relatively high rates of compliance with wearing masks inside local businesses, where there is little evidence to suggest a statewide mandate would significantly alter the trend. The current situation differs from the situation that applied during the summer when Arizona became a national hotspot for COVID-19 infections, when the rate of mask wearing was very low prior to the state governor's order allowing local officials to impose mask wearing requirements for their residents. Starting from an already higher level of mask wearing, any additional benefit that might be realized is much smaller.

With the elections now in the past, removing that contributor to the risk of virus exposure, Arizona's next challenge in its coronavirus pandemic experience will be to address the social mixing that will take place during the Thanksgiving holiday. We'll present our next follow up after the holidays to see how the state fared.

Previously on Political Calculations

Here's our previous Arizona coronavirus coverage, with a sampling of some of our other COVID analysis!

References

Arizona Department of Health Services. COVID-19 Data Dashboard. [Online Application/Database].

Maricopa County Coronavirus Disease (COVID-19). COVID-19 Data Archive. Maricopa County Daily Data Reports. [PDF Document Directory, Daily Dashboard].

U.S. Centers for Disease Control and Prevention. COVID-19 Pandemic Planning Scenarios. [PDF Document]. Updated 10 September 2020.

COVID Tracking Project. Most Recent Data. [Online Database]. Accessed 10 November 2020.

More or Less: Behind the Stats. Ethnic minority deaths, climate change and lockdown. Interview with Kit Yates discussing back calculation. BBC Radio 4. [Podcast: 8:18 to 14:07]. 29 April 2020.

What Happened In New Jersey’s Nursing Homes?

New York has been, far and away, the worst state to be in for the coronavirus epidemic in the United States. Especially for elderly Americans with illnesses that require they live in nursing homes or long term care facilities, where one single poorly-considered policy implemented after the state's governor and public health officials began to panic when the going got tough has needlessly cost thousands of lives.

New Jersey has been the second most-impacted state or territory in the U.S. thanks to its proximity to New York City, which has been the nation's epicenter for the coronavirus epidemic. In fact, you can tell which counties of New Jersey can be considered to be part of New York City's greater metropolitan area just from a map indicating the number of confirmed COVID-19 cases have been recorded in each.

That close proximity to New York means that New Jersey has shared a very similar experience in dealing with the SARS-CoV-2 coronavirus. The following charts show the daily progression of the epidemic in New Jersey, the amount and results of medical testing in the state, and also the rolling 7-day totals for newly confirmed cases and deaths, all of which have generally tracked along with New York, although in the third, rightmost chart, you can see New Jersey was more successful in flattening its curve compared with how the spread of the coronavirus played out in New York.

New Jersey: Daily Progression of COVID-19, Daily Test Positivity Rate, and Rolling 7-Day Totals for Newly Confirmed Cases and Deaths, 10 March 2020 through 20 May 2020

While New Jersey's situation has improved significantly from what it was just three weeks ago, it too has seen an outsized number of deaths occurring in the state's nursing homes and long term care facilities, with numbers similar to New York. Unfortunately, the reason that is the case is the same: New Jersey Governor Phil Murphy and the state's public health officials copied what Governor Cuomo did in New York in mandating the state's nursing homes and long term care facilities admit patients known to be infected with the SARS-CoV-2 coronavirus, which ran rampant through the nursing homes, needlessly contributing to the premature deaths of thousands of New Jersey's most vulnerable residents. The following chart shows the results of that policy has been since it was adopted on 31 March 2020:

The question is why did New Jersey Governor Phil Murphy copy such a misguided policy? When the state of New York's Department of Health issued its infamous directive on 25 March 2020, the policy was slammed in the pages of the Wall Street Journal the next day. Less noticed however was a press release issued by the Committee to Reduce Infection Deaths on the same day, in which the anti-hospital infection public interest advocacy group also slammed New York's policy, but which cited an example from New Jersey for how the state should work to prevent the spread of coronavirus infections within the state's nursing homes.

Dear RID Friends and Healthcare Providers:
The State of New York is adopting a dangerous new policy requiring nursing homes to blindly admit patients infected with Covid-19, according to a new report in The Wall Street Journal.
Cuomo's edict, if reported correctly, dooms thousands of elderly to illness and likely death. Basic infection control says to identify and contain. Cuomo's edict does the opposite: conceal and spread. It spreads the infections to nursing homes and forcing homes to operate in the blind, not even knowing which incoming patients are coronavirus carriers.
A model of what should be done is how CareOne, an exemplary facility in New Jersey, knowingly emptied one of its locations to protect other uninfected residents and then welcomed coronavirus patients from St. Josephs to that facility.

You can find out more about the model New Jersey was setting here. Clearly, something dramatic changed, because just six days later, the Murphy administration issued a directive with the following instruction mandating that nursing homes and long term care facilities in New Jersey to admit patients with contagious coronavirus infections (the underlining is contained in the original document):

No patient/resident shall be denied re-admission or admission to the post-acute care setting solely based on a confirmed diagnosis of COVID-19 … Post-acute care facilities are prohibited from requiring a hospitalized patient/resident who is determined medically stable to be tested for COVID-19 prior to admission or readmission.

What changed? We've pieced together the story as best we can from contemporary reports, where the first indication that Governor Murphy would soon follow Governor Cuomo's bad example came on 28 March 2020, as a number of hospitals in northern New Jersey began to divert, or to not accept, new patients for 4-hour blocks of time because they were either at or near their full capacity.

The timing of these events coincides with the worst case projections the influential Institute for Health Metrics and Evaluation (IHME) has issued for New Jersey, which as in New York, was used by state policymakers to make decisions. In this case, we think those early diversions prompted New Jersey's leaders into thinking they were facing a worst-case scenario. The following chart shows what the IHME's projection for the number of hospital beds above New Jersey's available capacity looked like on 30 March 2020, just before Governor Murphy's administration implemented its policy that would allow hospitals to move as many asymptomatic or partially recovered coronavirus patients as they could to other medical facilities, which in the case of elderly patients, would mean moving them to nursing homes and long term care facilities throughout the state.

So the motive for Governor Murphy's administration to adopt the same policy that Governor Cuomo had less than a week earlier is the same. For Governor Murphy however, the lack of condemnation or criticism for Governor Cuomo's disastrous move other than in the Wall Street Journal cleared a path to act with impunity, where he could safely assume his own deadly action would not be challenged by the nation's media.

To understand what happened, let's take a moment to review the chart showing the 7-day rolling total for new coronavirus cases in New Jersey. On 31 March 2020, the number of confirmed cases was rocketing upward, which would go on to peak at 25,437 new cases per week on 7 April 2020. After that point, the state's curve flattened out under that level for the next three weeks, before the incidence of newly confirmed cases began to fall rapidly after that point.

Within that period, the number of COVID-19 hospitalizations peaked on 14 April 2020, just within the state's available capacity to accommodate these patients at its hospitals, thanks in large part to efforts they had made to expand their capacity in the preceding weeks. In the following chart, we've pieced together the number of New Jersey's long term care facilities that reported housing coronavirus patients at various points throughout the state's coronavirus epidemic from various reports, along with the figures the state's Department of Health began reporting for these facilities on 20 April 2020.

Before Governor Murphy's directive forcing nursing homes to admit infected coronavirus patients on 31 May 2020, 73 long term care facilities in the state reported having infected patients. On 8 April 2020, that figure had risen to 123. Twelve days later, with the number of new coronavirus infections throughout the state reaching and holding near its peak, the state's Department of Health began reporting the number of cases within the state's nursing homes, where that number had skyrocketed to 425 facilities.

That figure has continued to grow, where though 20 May 2020, the New Jersey Department of Health reports a cumulative 529 of the state's nursing homes long term care facilities have housed coronavirus-infected patients.

That outcome did not happen by accident. Nursing homes and long term care facilities are geographically dispersed, where they can be thought of as relatively isolated islands, where an outbreak of infections at one would not travel to others on its own. It took a deliberate policy by the governor and the state's public health officials to make that happen. And once it did, with recently transferred contagious patients exposing nursing home staff members to the infection, who in turn spread it to previously uninfected, but especially vulnerable nursing home residents with fatal effect.

The spread of coronavirus infections within New Jersey nursing homes and long term care facilities resulting from the Murphy administration's policy can be seen in the following chart, where we find from the available data that the number of infections at these facilities begins to take off after 31 March 2020, where by 20 May 2020, New Jersey's nursing homes account for 19% of all confirmed coronavirus cases in the state:

Cumulative COVID-19 Confirmed Cases in New Jersey, Total Cases in State and in Long Term Care Facilities, 1 March 2020 - 20 May 2020

The deadly impact of the Murphy administration's policy can be seen in the next chart, where we find that New Jersey's nursing home residents account for over 51% of the deaths attributed to the COVID-19 coronavirus in New Jersey.

Cumulative COVID-19 Deaths in New Jersey, Total Deaths in State and in Long Term Care Facilities, 1 March 2020 through 20 May 2020

Were any of these nursing home deaths inevitable? It would be fair to assume that whatever portion of coronavirus infections that had made it into the 73 nursing homes that had them before Governor Murphy's policy went into effect on 31 March 2020 would be deadly, but only within those facilities. The Murphy administration's policy expanded the viral risk to hundreds of more facilities, where these COVID-19 attributed deaths could wholly have been avoided. If only Governor Murphy hadn't been a copycat of Governor Cuomo.

References

2019 Novel Coronavirus COVID-19 (2019-nCoV) Data Repository by Johns Hopkins CSSE. CSSE COVID-19 Time Series Data: Confirmed U.S. [CSV File]. Last updated 20 May 2020. Accessed 20 May 2020.

2019 Novel Coronavirus COVID-19 (2019-nCoV) Data Repository by Johns Hopkins CSSE. CSSE COVID-19 Time Series Data: Deaths U.S. [CSV File]. Last updated 20 May 2020. Accessed 20 May 2020.

New Jersey Department of Health. NJ Long Term Care Facilities with COVID-19 Outbreaks. [PDF Document]. Posted: 20-Apr-2020, 22-Apr-2020, 24-Apr-2020, 27-Apr-2020, 29-Apr-2020, 1-May-2020, 4-May-2020, 6-May-2020, 8-May-2020, 11-May-2020, 13-May-2020, 15-May-2020, 18-May-2020, 20-May-2020.

Arco, Matt. Number of coronavirus patients at N.J. hospitals drops to 3-week low with 5th straight day of declines. NJ.com. [Online Article]. 26 April 2020.

Associated Press. New Jersey reports 9 coronavirus deaths; elections postponed. Dayton 24/7 Now. [Online Article]. 19 March 2020.

Associated Press. NJ COVID-19 deaths climb by 17 to 44 in biggest jump yet. APNews.com. [Online Article]. 24 March 2020.

Associated Press. Coronavirus in 43 NJ nursing homes — death toll now at 81. New Jersey 101.5. [Online Article]. 27 March 2020.

Associated Press. 8 nursing home residents die of COVID-19, N.J. mayor says. Philadelphia Tribune. [Online Article]. 30 March 2020.

Broadt, Lisa. 3 deaths, 10 coronavirus cases ID’d at Mount Laurel nursing home. Burlington County Times. [Online Article]. 25 March 2020.

Institute for Health Metrics and Evaluation (IHME). COVID-19 Estimate Downloads. IHME. [Zip File]. 30 March 2020.

Washburn, Lindy. An unseen crisis: Coronavirus deaths mount at NJ nursing homes as virus spreads, staff dwindles. NorthJersey.com. [Online Article]. 8 April 2020.

Bending the Health Care Cost Curve Ever Upward

Did the Affordable Care Act (a.k.a. "Obamacare") succeed in making health care more affordable for the average American household?

Data from the Consumer Expenditure Survey says... no!

Change in Average Annual Health Care Expenditure per Consumer Unit (Household) Since 2008, 2008-2016

Update 1 June 2018: The vertical dashed line in the chart indicates a break in the U.S. Census Bureau's methodology for collecting information about health insurance coverage that was implemented after 2013, where data in the periods before and after this change are not strictly comparable to each other. That said, the Consumer Expenditure Survey's data since 2013 confirms that the Affordable Care Act has failed to restrain the growth of average health insurance costs by American households during the period that it has been in effect.

Although the chart above focuses on what happened after it took effect, in reality, the health care cost curve began bending upward almost immediately after the Affordable Care Act was passed in 2010, leaving millions of Americans who had been promised by the ACA's supporters that it would reduce the cost of their health insurance sorely disappointed.

But that disappointment didn't extend to the people who owned stock in the U.S.' major health insurers, such as Centene (NYSE: CNC), United Healthcare (NYSE: UNH), WellCare (NYSE: WCG), Cigna (NYSE: CI), Humana (NYSE: HUM), Aetna (NYSE: AET), Molina (NYSE: MOH) and Anthem (NYSE: ANTM), where the Affordable Care Act has been a government-granted license to print money since it went into effect after 2013....

Percentage Change in Health Insurer Stock Prices from 2 January 2008 through 25 May 2018

References

U.S. Bureau of Labor Statistics. Consumer Expenditure Survey. Multiyear Tables. [PDF Documents: 2008-2012, 2013-2016]. Accessed 28 May 2018. [Note: Data for 2017 will become available in September 2018.]

Afterword

Added 4 June 2018: Here's a neat chart that accompanied a September 2017 Motley Fool article by Keith Speights:

Average Annual Health Insurance Costs for Family Coverage, Premiums and Deductibles, 2008-2017 - Source: https://www.commercialappeal.com/story/opinion/contributors/2017/09/08/access-health-insurance-but-can-we-afford-it/636570001/

The cost of health insurance, both in premiums and in deductibles, jumped considerably after 2013 when the Affordable Care Act went into effect.