How Many Statistically Significant Estimates Make a Guess?

The moment you’ve produced a single numeric “estimate,” you’ve created a guess dressed in statistical clothing. As you add more estimates, your guess may become more or less respectable, but it remains a guess. The value of that guess depends on what you’re after. 

A single estimate with a 90% certainty has only a 10% chance of betraying you. But a calculation that includes three of those 90% certainties, a 27% chance of betrayal, good for pub trivia, “shaky” for designing a bridge. By the time the calculation has five variables, you are in flip-a-coin territory. Population studies involving large numbers are helpful because of the law of large numbers – many estimates of the same population result in greater confidence, like the wisdom of the crowd. However, when using estimates in calculations, another feature of population studies is that diminishing returns play a greater role, and certainty shrinks fast.

Today’s example comes from a global estimate of the impact of phthalate exposures on cardiovascular disease published in a Lancet spinoff, eBiomedicine. Despite a roughly 60% reduction in cardiovascular deaths since 1950 and a 5% reduction in the last decade, recent trends are moving upward, and the researchers wanted to investigate “a new and previously unrecognized risk for CVD: exposure to plastic polymers and their chemical additives.”

More specifically, the researchers consider phthalates, chemical compounds used to increase plastic flexibility, transparency, durability, and longevity, citing linkages to cardiovascular mortality. The researchers considered a ubiquitous phthalate, di-2-ethylhexylphthalate (DEHP) because

“it is one of the most widely used and studied phthalates, with extensive human exposure leading to robust data from regional biomonitoring surveys and epidemiological studies.”

However, when we turn to their cited meta-analysis of phthalates and cardiovascular disease, we find this

“When cardiovascular mortality was the outcome, continuous models were nearly significant for DEHP …  Exclusion of NHANES 2001–2002 participants attenuated DEHP associations with all-cause mortality to null.” [emphasis added]

The assumption that DEHP exposure is linked to cardiovascular mortality is the critical assumption underlying all the subsequent calculations we will briefly discuss. But nearly significant is not significant, and when you pull two years of data out of a study and the association disappears, how strong might that association be? But I digress. 

The methodology section of the current study details descriptions of the data utilized in the calculations. 

• Estimate 1 – DEHP Exposure was, when possible, based on DEHP metabolites, a reasonable set of biomarkers for exposure available for Canada, the US, and Europe. For other global regions without robust public data (Africa, Australia, Eastern Asia and the Pacific, The Middle East and South Asia, and Latin America), DEHP metabolite concentrations were estimated.
• Estimate 2 - Country-specific baseline Cardiovascular Mortality Rates (CVMR) for the target population aged 55-64 in 2018 were based on estimated deaths and estimated country-specific cardiovascular mortality.
• Estimate 3 - Country population and target population aged 55-64 were estimates
• Estimate 4 - Hazard Ratios (HR) for cardiovascular mortality due to DEHP were extrapolated values based on a single US study of biomarkers to mortality data and then used to estimate country-specific hazard ratios from estimated phthalate concentrations
• Estimate 5 – Excess Cardiovascular Mortality, Baseline Deaths, and Excess or Attributable Deaths were calculations using hazard ratios, estimated cardiovascular mortality risk, and populations, all of which were estimates
• Estimate 6 – The key outputs reported by the study, excess years of life lost and mortality attributable to plastics, were further calculations based on all these other estimates. 

Given all these estimates, this statement by the researchers is even less credulous.

“Exposure to MEHP, MEHHP, MEOHP, and MECPP contributed 13.497% of all CV deaths in 2018 worldwide, with plastics contributing 98% of these deaths, comprising 13.227% of all CV deaths globally.”

It is quite a feat to use all these estimates and still report a value with five significant digits. [1]

In addition to passing estimates as more certain than they possibly can be, there are other additional facts mentioned in passing by the researchers. 

“Overall, regions containing a higher proportion of populations from low- and middle-income countries bear the brunt of this burden while regions containing more high-income countries face less exposure to DEHP, and thus less attributable mortality.”

But the high-income countries had actual data, those low and middle-income countries had exposures and attributable mortality based on a chain of estimates with no actual data point in sight.

And then there is this,

“Between 2008 and 2018, Canada enforced limits on DEHP in children’s toys and products related to childcare domestically in 1999 and banned items containing over 0.1% concentration by weight of DEHP in childcare sectors, the USA exacted a prohibition of DEHP childcare articles and toys containing more than 0.1% DEHP… it is notable that many of these regulations were not in place at the time of data acquisition for the present study and their effect is not reflected in our results.”

Yes, not only are we given estimates, but in many cases where the data may be more certain, the data is out of date. According to the EPA,

“From 2007-2008 to 2017-2018, the 95th percentile concentration of DEHP metabolites decreased from 567 µg/L to 40 µg/L.”

A ten-fold reduction. DEHP has been mostly phased out of food packaging. The FDA still permits indirect use in food-contact materials like adhesives, coatings, paperboard, acrylic polymers, cellophane, and foil.

When research relies on a half-dozen layers of estimates, extrapolations, and unverified assumptions to produce conclusions with five-digit precision, it moves from the realm of epidemiology to that of educated fiction. While plastics and chemical exposures absolutely warrant scrutiny, that scrutiny should be grounded in current, robust data—not a game of telephone across models, countries, and decades. Before we reshape global health policies or ignite panic over plastic, let’s ensure we’re not just dressing guesses in lab coats and calling them truths.

[1] Significant digits express the precision of a number; the more you have, the more finely the quantity has been pinned down. Here is noted statistician John Oliver on specific numbers. 

Source: Phthalate Exposure From Plastics And Cardiovascular Disease: Global Estimates Of Attributable Mortality And Years Life Lost eBiomedicine DOI: 10.1016/j.ebiom.2025.105730