Kuru is a transmissible spongiform encephalopathy (TSE), or prion disease, that had a very high incidence in the Fore population in Papua New Guinea. 1 Epidemiologic investigations indicated that the epidemic of kuru arose through transmission of the infectious agent during ritual endocannibalistic funeral feasts. 2,3 It is thought that most individuals were infected orally, although the possibility of other routes of transmission cannot be excluded. The funeral customs of the Fore resulted in adult women and young children of both sexes being more exposed than adult men to the infectious agent. 4
Endocannibalism ceased in the late 1950s, and no cases of kuru have been identified in persons born after 1959. However, approximately 2500 kuru deaths occurred between 1957 and 1976. 4 Since then, small numbers of cases have continued to occur, suggesting that the incubation period of kuru can be longer than 40 years.
A recent study found that kuru cases who were methionine-valine heterozygotes at codon 129 of the prion protein gene (PRNP) were older at death than those homozygous for methionine or valine at this codon. 5 A similar phenomenon has been observed in iatrogenic Creutzfeldt-Jakob disease (CJD) acquired from contaminated human growth hormone. In France, cases homozygous at codon 129 of the PRNP gene appeared some 5 years before the first case in a heterozygote. 6 These findings suggest that the incubation periods of human TSEs depend upon the PRNP genotype at codon 129.
Variant Creutzfeldt-Jakob Disease (vCJD) is a new human TSE caused by an agent that is presently indistinguishable from the agent responsible for bovine spongiform encephalopathy (BSE). 7–9 As with kuru, the favored hypothesis is that vCJD patients were infected orally. All vCJD cases tested up to November 2001 were methionine-methionine homozygotes at codon 129 of the PRNP gene. 10 Either those with other genotypes are not susceptible to the disease or, as in kuru and iatrogenic CJD, they have longer incubation periods. Another intriguing feature of vCJD is that all but 1 of the first 94 cases identified in the United Kingdom to date have been less than 55 years of age at disease onset 10 (median 28 years). This age distribution might reflect age-dependent exposure or susceptibility and/or a longer incubation period in older individuals.
It has been reported that the average duration of clinical disease is shorter in young kuru patients (about 15 months in adults and 9 months in children and adolescents). 11 We analyzed the kuru data further to see whether there was evidence that incubation period also varied with age at infection, as this variation may have relevance to the interpretation of the age distribution of vCJD cases.
We analyzed data, extracted from a database of all known kuru cases in Papua New Guinea, on the annual numbers of kuru deaths by sex and age for the period 1957–1978. Methods of data collection and case ascertainment have been described previously. 12 The data for this analysis come from the records of the kuru file at the National Institute of Neurological Disease and Blindness. These records are based on regular census reports (yearly or semiyearly), which since 1960 have recorded all current clinical cases and death of kuru. For patients who were not seen by a medical research worker, the community’s diagnosis of the disease, on which the census reports are based, has been accepted. This diagnosis has been shown to correlate very well with diagnoses made by medical research workers. 12 Mortality from kuru over this period is given in Table 1. The annual number of deaths declined progressively from the late 1950s to 1978 but the pattern of decline varied in different age groups 4,12 and was most rapid in the youngest age group. Between 1960 and 1978, no deaths occurred in children born after 1959, suggesting that transmission ended with the cessation of traditional funeral rites. Overall, there were about 4 times as many deaths among females as among males. The female-to-male death ratio increased sharply with age, from 1.1 in those under the age of 20 years to 22.7 in individuals 40 years of age and older.
The Fore population has been extensively studied in the last 50 years. A detailed demographic study was published in 1964. 13 Survival rates by age and sex are available for the South Fore and for the Gimi, a separate language group adjacent to the South Fore population. These data show a large discrepancy in mortality between men and women in the South Fore population; life expectancies at 10 years of age were 33 years for males and 22 years for females. This difference is probably attributable to the very high incidence of kuru among adult females in the South Fore in the late 1950s. Such a large difference in life expectancy was not present in the Gimi population, in which there was a much lower incidence of kuru.
More recent data on the incidence of kuru from 1994 to 1998 are also available (M Alpers, personal communication, 2000). These data have not been used in model estimation but have been used to compare predicted and observed numbers of cases for model validation.
The back-calculation method is widely used for modelling infectious diseases with long and variable incubation periods. 15,16 The observed numbers of cases of disease or deaths, together with a known or assumed incubation period distribution, are used to estimate patterns of past infection. 14 To apply the method, it is necessary to specify: (1) a probability density function for the incubation period of the disease; and (2) a pattern for the risk of infection over time.
The incubation period is usually defined as the interval between infection and disease onset. In this study, we have used death as the endpoint instead of onset, because data on disease onsets were not available. However, for the sake of brevity we refer to the interval from infection to death as the “incubation period”. We compared the results obtained using three mathematical forms for the incubation period distribution (Weibull, lognormal, and gamma). For each mathematical form, we first estimated the incubation period distribution assuming that it did not vary with age at exposure. Then, to examine a possible relation between age at infection and incubation period, we fitted models in which the length of the incubation period was assumed to be different in those infected at less than 20 years of age compared with those infected at older ages.
Experimental studies on TSEs indicate that the length of the incubation period is reduced if the infecting dose is high. 17 Because women may have been exposed to higher levels of infectivity than men, we also investigated whether incubation periods differed for men and women.
Computation of the risk of infection was not possible because the number of persons at risk is unknown. Hence, the model focused on the number of new infections per year (ie, the numerator of the risk). We assumed that, for a given age and sex group, the case reproduction number (ie, the number of new infections caused by one kuru case) was constant from the beginning of the kuru epidemic until the year 1958, approximately the time when traditional funeral rites are believed to have ceased.
We assumed that the kuru epidemic began in 1900 with the death of a single primary case, perhaps an individual with sporadic CJD. There is no direct evidence to support this precise choice of starting point; however, it has been reported that kuru was present among the Fore population for at least 25 years before the first investigations in the 1950s. At that time, older members of the Fore population stated that the illness was not present during their youth. 1 We also examined models in which the primary case was assumed to have occurred between 1870 and 1930. We further assumed that transmission occurred only during funeral rites and, consequently, that no new infections occurred after the cessation of these rites. We assumed that these rites ceased at the beginning of 1959.
Our model took account of competing risks (ie, that some infected individuals will have died from other causes before developing kuru). For this purpose, we used age- and sex-specific mortality rates obtained for the Gimi population, on the assumption that South Fore mortality would have been similar in the absence of kuru. Thus, we assumed that infant mortality was about 20% and life expectancy at birth and at 10 years of age were 24 years and 35 years, respectively. We assumed further that infected (but asymptomatic) individuals who died did not transmit the disease during funeral rites if they died from causes other than kuru. The detailed model formulation and parameter-estimation procedure are described in the appendix.
Table 2 presents parameter estimates for the incubation period distributions, assuming these are neither age nor sex dependent. Estimates of the median incubation period varied from 8.5 years (95 % confidence interval [CI] = 7.5–9.6) with the Weibull model to 9.2 years (95% CI = 8.8–9.8) with the log-normal model. Ninety percent of infected individuals were estimated to have died within about 21 years of infection under the Weibull and gamma models compared with 27 years under the log-normal model.
The chi-square test values indicate that the best fit was obtained by assuming that the incubation period followed a Weibull distribution. Therefore, the analysis of the relation between age at infection, sex, and incubation period was performed using this model. The median duration was 12.3 years in males of all ages and 8.7 years in females with 90th percentiles of 22.5 years and 19.0 years, respectively. Table 3 shows the estimates of the mean, median, and 90th percentile of the incubation period distribution according to age at infection and sex, based on the Weibull model. For individuals less than 20 years of age, there was substantial overlap in the CIs for each parameter in males and females. Among those 20 years of age or more, the median incubation period appeared shorter in women than in men with no overlap in their CIs. Among women, the incubation period appeared to be shorter in those infected after 20 years of age. The reverse was the case in men. The longest median incubation period was in adult males, the shortest in adult females.
Figure 1 shows the estimated average numbers of persons infected in different age and sex groups arising from each kuru case before 1959. Most infections in males were estimated to have occurred when they were under the 10 years of age. Among females, two groups appeared to have experienced most infections: those under the age of 10 years and those between 15 and 39 years of age. The number of individuals infected between 10 and 14 years of age in both sexes was estimated to be low, suggesting that adolescent boys and girls were not much exposed to the infectious agent. We estimate the average number of secondary infections arising from one kuru case to have been 2.0 females and 0.5 males, of whom 1.4 went on to develop the disease (the remainder dying of some other cause before developing kuru).
Figure 2 shows the observed annual numbers of kuru deaths by age group and sex for the period 1957–1978, together with the numbers of deaths predicted by the model used in this study, assuming that the incubation period follows a Weibull distribution with parameter estimates depending on sex and age at infection. The fit of the model is generally good, as shown by the approximate 95% prediction intervals, with the poorest fit being observed in the group 20–39 years of age towards the end of the period. Similar figures were obtained using the log-normal and the gamma models.
The estimates of the incubation period parameters (Table 4) and case reproduction numbers by age and sex (data not shown) were not much affected by the assumed start date of the kuru epidemic. Although the best fit was obtained by assuming that the first case occurred in 1900, the results do not provide decisive evidence as to when the epidemic started (the data are almost equally compatible with a wide range of start dates). Modifying the endpoint of the period (ie, the year of the cessation of funeral rites) by 1 or 2 years did not materially alter the findings either (results not shown).
Table 5 shows the numbers of kuru deaths predicted by this study’s model to occur in the period 1994–1998. It should be emphasized that the observed numbers of kuru deaths for this period have not been used in parameter estimation. All models tend to overestimate the observed incidence (particularly in old individuals). Of the three distributions used to model the incubation period distribution, the Weibull distribution provides the best fit to the observed data. This distribution also provided the best fit to the 1957–1978 data.
The estimates of the “incubation period” distribution of kuru that we have derived are consistent with previously estimated incubation periods based on smaller series of cases. 18 The average duration of clinical disease has been reported to be about 10 months, so true incubation periods (ie, time from infection to onset) will have been that much shorter than study estimates. There is some evidence that duration of illness was shorter in young individuals, 11 but this variation is on the order of a few months and is small compared with the spread of the overall distribution.
We estimate that about 50% of incubation periods exceed 10 years and that 15% exceed 20 years. The spread is greater than that estimated for iatrogenic CJD related to human growth hormone (hGH). 6 This difference in incubation period spread is not unexpected for three reasons. First, in experimental transmission of scrapie in hamsters, it has been reported that the oral route of infection is associated with greater variability in incubation periods compared with parenteral routes. 19 Second, in kuru, the infectious challenge is likely to have been more variable than in hGH-related CJD, resulting in a more variable incubation period distribution. Third, increased variability in kuru cases might be expected because of genetic factors. It is well established from mice models that incubation periods vary with PrP genotype. 7 Genetic analyses of recent kuru cases found nearly half to be methionine-valine heterozygotes at codon 129, with this proportion rising to 70% in older age groups. These findings suggest that the polymorphism at codon 129 is likely to play a key role in the incubation period of kuru. The kuru cases on which this analysis is based are a mixture of codon 129 genotypes, whereas the analysis of hGH-related iatrogenic CJD cases was restricted to methionine-methionine and valine-valine homozygote subjects. Hence, this study’s estimates correspond to the average incubation period over all PRNP genotypes. In addition, it is likely that there are other unknown genetic factors that influence the incubation period of kuru and other human TSEs. 20,21
To use the back-calculation method, we made several assumptions. We assumed that the Fore population was exposed to the kuru agent from 1900 until 1958. These dates, especially the beginning date, are approximate. However, varying the start and end dates for the exposure period did not alter our findings sub-stantially.
We further assumed a constant net case reproduction number during the period of exposure. However, in reality, the case reproduction number will have been time-dependent for at least one of two reasons. First, the high incidence and prevalence of infection among the Fore would certainly have led to a decrease in “susceptibles” in the population. Second, there may have been changes in funeral rites over the period considered (about 40 years), leading to variation in the net case reproduction number. It was not practical to estimate different time-dependent functions for each age group and sex, mainly because no data on kuru incidence before 1957 are available (and thus the corresponding models were not identifiable). It is difficult to evaluate what impact the failure to take account of these phenomena may have had on the estimated values of the incubation period of kuru. On the one hand, not taking account of the decrease in “susceptibles” in the population may have led to an underestimation of the mean incubation period, because the model used will have tended to shift dates of infection to later years. On the other hand, if the practice of ritual endocannibalism increased during the period, our failure to account for this will have led to an overestimation of the mean incubation period.
We took account of competing risks by applying age- and sex-specific mortality rates derived for the period 1950–1960. However, overall mortality from causes other than kuru has declined since 1960. An increase in life expectancy during the study period (late 1950s to 1976), not accounted for in this model, may have led to an overestimation of the incubation period. Overestimating competing death rates would lead to the prediction of a smaller number of cases than that observed. To compensate for this, the incubation period would have to have been overestimated to produce predictions consistent with the observed incidence.
Our model assumes that over the study period, the risk of infection was proportional to the number of kuru deaths, and thus it does not take into account the possible transmission of the infectious agent from asymptomatically infected individuals. However, we believe that this assumption is likely to have had a minor impact on our estimates. It is likely that, as in other TSEs, the proliferation of the infectious agent occurs relatively late in the disease process. 22 This model suggests that 50%–60% of infected individuals died of kuru. Thus, most infectivity to which uninfected individuals were exposed is likely to have come from symptomatic individuals. Even if one allows a substantial amount of infectivity to have come from individuals dying 1 or 2 years before clinical onset, this will not greatly change the pattern of exposure of the population over time and thus will not have a large effect on the estimates of when people became infected. If an important amount of transmission did occur from asymptomatic individuals earlier in the course of infection than this, our model would probably underestimate the incubation period of the disease by shifting the hazard of infection to later dates.
We have also assumed that over the whole epidemic, the incubation period distribution has remained unimodal and unchanged, which may not be verified. If, for example, individuals of a given genotype with shorter incubation period died in great majority before the beginning of 1957, then the estimates based on cases since 1957 may overestimate the mean incubation period. Assuming a time-dependent incubation period distribution in the model would require very strong unverifiable assumptions.
Despite these limitations, our models fit the observed data well and were consistent with more recent incidence data on kuru. The results are fully consistent with the epidemiologic data showing that, whereas young boys and girls were at similar risk of infection, the risk of infection among adults was much higher among women.
We also found some differences in the median incubation period distribution by sex and age at infection. In particular, the median incubation period in adult males was nearly twice that in adult females. The shorter incubation period in females may reflect higher levels of exposure among females rather than any difference in susceptibility. We found no convincing evidence that incubation periods increase with age at infection. Indeed, in females, the incubation period was shorter in the older age group. This shorter incubation period may be the result of variation in exposure, with older women, who were most likely to be exposed to brain material, 23 being exposed to the largest amounts of infectivity. The fact that the estimated incubation period in young boys and girls is similar is consistent with this explanation.
The absence of a consistent age pattern across both sexes suggests that the observed variation reflects either chance or variation in exposure, rather than a pure age-related dependency. This result is consistent with data from experimental mice models in which incubation period appears to have at most a very weak association with age at inoculation. 24,25
In summary, the mathematical-modelling approach we have adopted has allowed the examination of the relation between sex, age at infection, and incubation period of kuru. We did not find any evidence that incubation period increases with age, which might have offered some explanation for the age distribution of vCJD cases. Our model suggests that about 50% of kuru deaths occurred within about 10 years of infection whereas 15% of deaths occurred more than 20 years after infection. It is likely, therefore, that cases of vCJD and of hGH-related iatrogenic CJD will continue to occur for decades after the end of exposure.
The expected number of kuru cases at time t in individuals aged a was calculated using the following formula:MATH
with the following notation and functional form specification:
- ▪k (u,s) represents the number of new infections at age u and time s attributable to one kuru case. Because we assumed that no new infection occurred after 1959, k (u) was set to 0 for s ≥ 1959. For s < 1959, we assumed that k (u) varied with age as a step function. Six age groups were chosen: 0–9, 10–14, 15–19, 20– 29, 30–39 and ≥40 years. Because k (u) was also assumed to vary with sex, 12 parameters had to be estimated.
- ▪ñ (t) represents the total number of kuru deaths at calendar time t. Before 1959, ñ (t) was set to expected number of deaths ˆ;n(t) assuming an index death in 1900. After 1959, ñ (t) was set to the observed numbers of deaths n (t).
- ▪F (x) is the cumulative probability density function of the incubation period and was successively chosen to be a log-normal, a Weibull and a Gamma distribution.
- ▪S (u, a) is the proportion of survivors up to age u that survive up to age a. Given the function G(a) expressing the proportion of survivors up to time a (which can be derived from census data), S(u,a) was calculated as G(a)/G(u).
Model parameters were estimated by minimizing the quantity MATH
where g represents age groups (ieMATH
Numerical estimates were obtained using the SAS™ software statistical package. The algorithm used for the χ2 minimisation was Dual Quasi-Newton Optimisation with function gradient and hessian matrix (matrix of partial second derivatives) approximated by finite differences. The algorithm was applied using several different starting values for the parameters, to ensure that estimates were not local optima. Additionally, the estimates were verified using a purpose-designed program in C implementing the derivative-free Powell optimisation algorithm. Approximate confidence intervals were computed by fitting the model to 100 parametric bootstrap samples of the case data (Poisson distribution).
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