Air Exchange, Dome Age and Density as Predictors of Respiratory Complaints: A Panel of 36 Domed Districts of the Sprawl, 2039–2044

1. Introduction

Many residents of the Sprawl live under geodesic domes, and in most districts the dome is as old as the district it covers. The dome shell encloses a district's air, and the ventilation plant that exchanges that air with the outside is among the first systems to age. Residents, clinics and municipal committees have long associated domed districts with respiratory complaints: cough, wheeze, breathlessness and the chest infections that follow them. There is less agreement about why. Older shells leak, lose coatings and carry deposits in their ducts. Dense districts share air among more people. Poorly ventilated districts accumulate whatever their residents produce.

The three explanations overlap. Older domes tend to have older ventilation plant, and dense districts have often been built under the domes that the municipalities could afford to maintain. A district's complaint rate may therefore reflect any one, or any combination, of age, density and air exchange. Earlier studies of the Axis examined one factor at a time (Sandoval-Reyes, 2040; Tamsett, 2040), and the registry analysis that first established the burden of respiratory presentation in domed districts drew on clinic registers alone and could not adjust for ventilation, because routine district ventilation logging had not yet begun (Nwosu-Harlan, 2039). Instrumented ventilation logging has since spread (Pryor-Banks, 2041).

Responsibility for the ventilation plant itself falls across municipal boundaries. Where a dome covers parts of several legacy municipalities, upkeep depends on arrangements among operators and not on a single authority (Ashby, 2042), and replacement of shell components is deferred when no one budgets for it (Cuthbert, 2043). A mapping and interview study of one partly domed segment at the Atlanta end of the Axis found that infrastructure crossing legacy boundaries there is kept running by informal agreements among operators. If ventilation depends on arrangements of that kind, then ventilation performance may differ between districts for reasons unrelated to dome age.

We use a panel of districts to separate the three factors as far as observational data allow. We ask whether air-exchange rate is associated with complaint rates after allowing for dome age and density, and how much of the association of age with complaints disappears when air exchange is included. We write in 2045 and report district-years from 2039 to 2044.

2. Methods

Districts and period. The panel covers 36 domed districts of the Boston–Atlanta Metropolitan Axis for the six calendar years 2039 to 2044, giving 216 district-years. Districts were included if they lay wholly under a single dome, had a district clinic reporting continuously for the period and had instrumented ventilation logs for at least 90% of hours in each year. Mid-year resident population ranged from 25 to 338 thousand (BAMA Municipal Records, 2044). Complaint counts come from the clinic registers of the BAMA Public Health Authority and count new presentations in which a respiratory symptom was the primary complaint, in each calendar year (BAMA Public Health Authority, 2044).

Exposures. Air exchange is the annual mean of the dome's hourly recorded air changes per hour (ACH), taken from ventilation logs. Dome age is the number of years since commissioning, measured at mid-year, and ranges from 1 to 14 years; no dome in the panel was commissioned before 2030. Density is the district's resident population per square kilometre of domed floor area, in thousands, taken once from the 2039 register and held fixed over the period. These three exposures are not independent: across district-years, air exchange and dome age were negatively correlated (r = -0.37), and air exchange and density slightly so (r = -0.01).

Analysis. The outcome is a count of events with a known population at risk. We fitted a negative binomial model with the logarithm of the population as an offset, so that coefficients describe rate ratios per resident. A Poisson model fitted to the same data had a Pearson dispersion statistic of 121, far above 1, which supports allowing for overdispersion. Sandwich variance estimates with few clusters can be too narrow (Lindqvist-Ruiz, 2041), so we use the small-sample t reference and report a bootstrap check below. The predictors were air exchange per additional air change per hour, dome age per five years, density per ten thousand residents per square kilometre, and calendar year as a linear term. Observations from the same district are correlated, so standard errors are clustered on district, and intervals use the t distribution with 35 degrees of freedom. To see how much of the age association lies alongside air exchange, we refitted the model without the air-exchange term and compared the age rate ratios. We resampled the 36 districts with replacement 400 times, refitted both models in each resample, and took the percentile interval of the difference between the two log age coefficients. A further model tested whether the air-exchange association differs by dome age. Intervals are 95% and all tests are two-sided.

3. Results

The 216 district-years contained 789,947 respiratory complaints among 20.8 million resident-years, a rate of 37.9 complaints per 1,000 residents per year. District mean air exchange ranged from 1.2 to 4.7 ACH, with an overall mean of 3.0. Districts with lower mean air exchange had higher crude complaint rates (Table 1). Table 1 gives mean dome age, density and crude complaint rates by third of district air exchange.

In the full model, each additional air change per hour was associated with a complaint rate 0.84 times as high (95% CI 0.77–0.91; p < .001). Each additional five years of dome age was associated with a rate 1.08 times as high (95% CI 0.95–1.22; p = .211), and each additional ten thousand residents per square kilometre with a rate 1.14 times as high (95% CI 1.09–1.19; p < .001). The calendar-year term indicated a small upward drift of 1.7% per year (95% CI 0.994–1.041; p = .135). The estimated dispersion parameter was 0.034.

When air exchange was omitted, the age association was stronger: 1.26 per five years (95% CI 1.10–1.44; p = .001). Measured on the log scale, the age coefficient fell by about 66% when air exchange was added. In the district bootstrap the difference in log age coefficients between the two models had a 95% percentile interval of 0.07 to 0.28, which excludes zero. The two models use the same data and the intervals of the separate estimates overlap, so this is the appropriate comparison. It shows that the age coefficient is smaller with air exchange in the model, not why. With air exchange included, the age association is no longer distinguishable from no association at the 5% level. The interaction between air exchange and dome age was not detected (ratio 1.00 per ACH per five years, 95% CI 0.91–1.10; p = .998).

To give the air-exchange estimate a practical scale, we computed the complaint count that the model implies for district-years in the lowest third of districts with air exchange below the overall district-year median of 2.9 ACH, if their air exchange were set to the median and everything else were unchanged. The model implies 15% fewer complaints in those 72 district-years. This is a model-based illustration of the size of the association, not an estimate of the effect of any intervention.

4. Discussion

Air exchange was associated with complaint rates independently of dome age and density. The direction is the one expected from the ventilation explanation, and the size is substantial: each additional air change per hour, on a range of about 4 ACH across the panel, was associated with a rate about 16% lower. Density behaved as expected too, with higher rates in denser districts. Density was measured once and does not vary over the panel, so its estimate rests on differences between districts.

Dome age is the more interesting case. Older domes had more complaints, and the association was weaker once air exchange was included, which fits the idea that part of what age stands for is lower air exchange. The residual association is small and imprecise: a rate ratio of 1.08 per five years remains after adjustment for the measured air exchange and density, with an interval that includes 1. That remainder may reflect features of ageing shells that the air-exchange log does not capture, such as deposits in ducts or leakage that lets outside air in without ventilating the district, or it may reflect characteristics of the people who live in older districts. The bootstrap supports a smaller age coefficient with ventilation in the model. It does not show that ventilation lies on a causal path from age to complaints, because age and air exchange may share causes, and we draw no conclusion about how much of the age association passes through ventilation.

The unexplained variation between districts is large enough to be worth attention. The earlier mapping of operator coordination suggests one hypothesis: where several operators share a dome, ventilation upkeep depends on informal agreements, and the quality of such agreements may vary by district without relation to age. We did not measure this, and the panel cannot test it.

For public health practice, the finding suggests that ventilation logs belong with clinic registers in routine district monitoring. A district with low air exchange and rising complaints has a plausible target for inspection, whatever the age of its dome. The association alone does not justify claims about the benefit of any particular repair, and the model-based illustration above should be read as an indication of scale and not as a forecast.

5. Limitations

This is an ecological analysis of districts, not of individuals. A district with low air exchange may also differ in income, housing quality or occupational mix, none of which we could adjust for, and the associations may partly reflect these. With 36 districts the cluster-robust intervals are approximate and may be too narrow.

Air exchange was measured at the dome's plant and not in dwellings. Air does not circulate evenly under a dome, and some residents live in poorly served corners of districts with a good average. The resulting misclassification may weaken the observed association, although its direction is not certain when the errors are related to dome age. Complaint counts depend on residents seeking care and on clinics recording the complaint, and clinics differ in access and in practice. A district with better clinic access would record more complaints without having more illness.

Population denominators are taken from municipal registers, which undercount informal housing, and the undercount is probably larger in older, denser districts. Counts, when divided by an undercounted population, overstate rates in exactly those districts. The panel covers six years and includes only districts with complete logs, which excludes districts where logging was neglected, quite possibly the worst maintained. We cannot say how the findings would change if they were included.