NR AAWI
AU Bacchetti,P.
TI Unexamined assumptions in explorations of upper limit for cases of variant Creutzfeldt-Jakob disease
QU Lancet 2001 Jan 6; 357(9249): 3-4
PT journal article
VT
Deaths due to variant Creutzfeldt-Jakob disease (vCJD) were not detected before 1995 and have increased from three in that year to 25 in the first 10 months of 2000.[1] Projecting from these data is very difficult because of uncertainty about the number of people infected and the incubation period (ie, the probability of death from vCJD as a function of time since infection). Projections thus have to rely on assumptions about these missing inputs. Investigators have sought to assess uncertainty by exploring dozens [2,3] to millions [4,5] of sets of assumptions, termed scenarios, that are consistent with observed data and thought to be plausible. Not surprisingly, the larger the number of explorations, the greater the upper limit to the epidemic (as high as 140.000 cumulative deaths by the year 2040 on one recent estimate [5]), but whether the ranges are too wide or too narrow is unclear.
The incubation distribution and pattern of infections over time determine expected numbers of deaths. For example, expected deaths in the year 2000 equal the number infected in 1982 times the probability of an 18- year incubation (to the point of death rather than clinical diagnosis), plus infections in 1983 times the probability of a 17-year incubation, and so on (with deaths from competing causes subtracted). Because infection counts and incubation probabilities are always multiplied together, changes in one can often be compensated by changes in the other to produce similar expected deaths. This means that death counts alone cannot reliably throw light on infection or incubation patterns. For HIV epidemics, by contrast, additional knowledge about incubation did permit back-calculation of the infection pattern. [6,7] This was also possible for bovine spongiform encephalopathy (BSE). [4] There are, however, no incubation data for vCJD. Instead, the main additional information is that the shape of the infection hazard over time is linked to the BSE epidemic, because the BSE agent is the likely cause of vCJD. (The hazard is an event's chance of occurring at a given time conditional on its not having occurred previously.) Lack of knowledge about the efficiency of transmission to human beings, via consumption of infected beef products, leaves the scale of the infection hazard unknown.
The above limitations mean that for vCJD very large numbers of infections cannot be ruled out. A scenario that produces a good fit to the observed data with a moderate number of infections, say 2000, can be rescaled to produce a scenario with 2 million simply by multiplying infections by 1000 and dividing the probabilities of death over the first 20 years by 1000. The new scenario produces the same fit to observed deaths and is still consistent with the assumed infection hazard shape, because 2 million is still a small fraction of the total number of susceptibles (assumed currently to be methionine homozygotes, about 40% of the population). Rescaling the number of infections up to a large fraction of the susceptibles while maintaining an assumed infection hazard shape would change the shape of the infection pattern over time, so the rescaled incubation might no longer produce a good fit to observed deaths. A good fit could probably still be achieved, however, by also changing the incubation shape. The clear influence of age on risk of vCJD (patients older than 45 have been rare) does not prevent rescaling, because the influence of age can be explained by different incubations for different ages, which does not restrict scaling up the number of infections. (Proposed separate age effects [5] on infection and incubation can be combined and applied entirely to incubation.)
An additional limitation is that the presumed absence of infections before 1980 implies a complete lack of information about probabilities of death beyond the first 20 years since infection, because no-one has been infected that long. Indeed, the small number of infections before 1985 (ref 4, figure 10.2b) implies a near-absence of information about incubation beyond 15 years. For backcalculation of HIV, much more information on the incubation was available and only short-term projections were attempted, so future probabilities had little influence. Future probabilities may have much more impact on vCJD projections, even short-term, because it is possible that very little of the incubation has so far contributed to observed deaths. In summary, the data available so far tell little or nothing, not even indirectly, about two crucial inputs for projections: the number infected and future incubation probabilities.
Uncertainty in forecasts might thus appear to be even greater than that implied by seemingly conservative published ranges. [2,5] But just as rescaling can have no impact on fitted numbers of deaths, it may also have no impact on future deaths. Large numbers of infections require very low probabilities of death in the first 15-20 years after infection to match observed data, so large epidemics can occur only if probabilities subsequently increase very rapidly. Otherwise, most infected people will never develop vCJD. While such rapid increases are possible, they may not really be plausible, particularly if the incubation is flat or only modestly increasing near the end of the period that contributes to observed death counts. This might be the case if recent increases in recorded cases [1] are due mainly to increasing numbers of infection during the 1980s rather than increasing incubation hazard. Unfortunately, studies have assumed a particular mathematical form for the entire incubation [2-5] that makes extrapolation assumptions only implicitly and may ignore or assume away the possibility of scaling up infections. Only a very strong biological rationale for a particular form would justify ignoring these two key aspects.
Because no studies of animals with natural or experimental prion disease or of similar human diseases are large enough to address the very small incubation probabilities potentially involved in vCJD to date, strong reliance on mathematical assumptions is probably not justifiable. A more explicit approach would first consider the initial part of the incubation that is constrained to produce expected cases than match observed data and then separately examine the most pessimistic and optimistic plausible extrapolations and rescalings. Without directly relevant data, only judgment can guide the assumptions, so modellers must clearly show what has been assumed. Thorough examination of a vast number of scenarios is impossible, but such scrutiny is feasible for the few that project the largest epidemics. In addition, methods similar to back-calculation can be used to find early incubation estimates that are most consistent with observed death data and an assumed infection pattern, [8,9] so that thorough exploration can be accomplished by examination of many fewer scenarios.
This commentary has argued that key assumptions require explicit scrutiny because data limitations make those assumptions so influential. This situation could improve. For example, screening for abnormal prion protein has produced encouraging results, [10] but interpretation is currently hampered by uncertainty about what a negative test implies for the probability of future disease. Greater biological understanding might help by guiding incubation assumptions. Also helpful would be continued absence of vCJD among genotypes other than methionine homozygotes and among people born after measures taken in the late 1980s to keep the BSE agent out of the human food chain. [11]
Without a scientific breakthrough, greater certainty may come only with additional years of surveillance. A downturn in deaths would, of course, be most encouraging, provided it is not due to random fluctuation (apparently the cause of a small drop in 1999), ascertainment delay, or seasonality. But even a slow-down could argue against the explosive subsequent increases needed to produce an extremely large epidemic. Quantitative analyses using additional data may help elucidate the likely future course of the epidemic, but only by making crucial assumptions that must be open to scrutiny.
1 CJD Surveillance Unit. CJD statistics. Available at http://www.cjd.ed.ac.uk/figures.htm, accessed Nov 19, 2000.
2 Cousens SN, Vynnycky E, Zelder M, Will RG, Smith PG. Predicting the CJD epidemic in humans. Nature 1997; 385: 197-98.
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4 Donnelly CA, Ferguson NM. Statistical aspects of BSE and vCJD: models for epidemics. London: Chapman & Hall/CRC, 2000.
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6 Brookmeyer R, Gail MH. Minimum size of the acquired immuno-deficiency syndrome (AIDS) epidemic in the United States. Lancet 1986; 2: 1320-22.
7 Bacchetti P, Segal MR, Jewell NP. Backcalculation of HIV infection rates. Stat Sci 1993; 8: 82-119.
8 Bacchetti P, Moss AR. Incubation period of AIDS in San Francisco. Nature 1989; 338: 251-53.
9 Bacchetti P. Estimating the incubation period of AIDS by comparing population infection and diagnosis patterns. J Am Stat Assoc 1990; 85: 1002-08.
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11 Verity CM, Nicoll A, Will RG, Devereux G, Stellitano L. Variant Creutzfeldt-Jakob disease in UK children: a national surveillance study. Lancet 2000; 356: 1224-27.
MH Creutzfeldt-Jakob Syndrome/epidemiology/*prevention & control; Human; Incidence; Time Factors
AD Peter Bacchetti (e-mail: pbacchetti@epi.ucsf.edu), Department of Epidemiology and Biostatistics, University of California, San Francisco, CA 94143-0560, USA
SP englisch
PO England