A Grayscale Opioid Mortality Map Bound for a Legislative Packet
A state health department is publishing a legislative packet on opioid overdose mortality. The dataset has 1,412 census tracts, three-year death rates per 100,000 residents, and raw counts. Two hundred forty tracts recorded fewer than 10 deaths in the period, and 88 tracts were suppressed because counts were between 1 and 4. The packet will be printed in grayscale on 60 lb paper; the web version will be in color. The director wants 'red for the worst tracts' and asks that the ten highest-rate tracts be labeled by name. A preliminary quantile map paints a large rural tract with six deaths and 3,100 residents in the same darkest class as an urban tract with 61 deaths, and puts several tracts with zero deaths in a mid-tone because the classification is relative. The legislature's redistricting office will use the map to allocate a $4 million mobile treatment unit.
1. Evaluate the preliminary quantile map and recommend a classification and data treatment for the 240 low-count tracts and the 88 suppressed tracts.
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Quantile classification forces equal counts into each class. That is useful for ranking and misleading for magnitude: a rural tract with six deaths among 3,100 residents lands in the same class as an urban tract with 61 deaths, and a zero-death tract gets shaded because the breaks are relative to each other rather than to risk. With 240 low-count and 88 suppressed tracts, the bottom of the distribution is mostly noise.
Address stability first. Compute a smoothed rate, using empirical Bayes or a spatial model that shrinks small-population rates toward the local or state mean, and classify the smoothed values. Keep crude rate and count available in a companion table. Never code suppressed as zero; give suppressed tracts their own fill and legend entry.
If the policy question is really 'where do rates differ from the state,' map statistical significance rather than raw magnitude. Whatever you choose, state the method, the class breaks, and the smoothing model in the map's own text so the map cannot travel without its caveats.
2. Design grayscale-safe symbology and a legend, and respond to the director's request for red.
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In grayscale, value must be carried by luminance order, not hue. Use one sequential ramp from light to dark with no more than five classes, and keep identical breaks in print and web or the two products will tell different stories.
For the color version, a sequential yellow-orange-red ramp satisfies the director's instinct and still reads correctly, provided it is monotonic in lightness: the darkest class must also be the visually darkest, not merely the reddest. That keeps it legible for red-green color vision deficiency and after photocopying.
Practical print checks: make sure the lightest class is visibly darker than the paper, because a very pale tint disappears on an office laser printer; add a thin outline or hatching for suppressed areas so they are not read as low rates; and include a small histogram or inset showing how many tracts fall in each class.
On labeling the ten highest-rate tracts by name: allow it only if counts and confidence accompany the names, or replace map labels with proportional symbols sized by deaths and move names to an inset table.
3. The map will drive allocation of a $4 million mobile treatment unit. What are the risks of that reuse and what would you add to the deliverable?
Read the worked answer
The largest risk is that a rate map is read as a ranking of need. A tract with three deaths in 900 residents can top the list on rate while representing far less absolute burden than a tract with 40 deaths in 60,000 residents. Labeling names onto that list invites both misallocation and stigma.
Add a second panel or companion map showing counts and population, and a note that rate and burden answer different questions. Consider proportional symbols for deaths, and overlay existing treatment facilities and drive times, because a mobile unit's value depends on access as much as incidence.
Document the limits explicitly: three-year aggregation, the suppression rule, smoothing method, and the fact that 2020 tract boundaries changed, so cross-vintage comparisons are constrained. State plainly that the map is a screening tool and not a substitute for a needs assessment.
Finally, offer a short briefing note to the redistricting office explaining how to read the classes. A map that arrives without interpretation will be interpreted by someone else.