1Demographic analyses of human mortality are based on models of the age pattern of mortality. In a context of rapidly declining mortality, all variations in the rate of progress by age are of crucial importance for population projections. Another way to address this question is to use mortality shocks as “natural experiments” to see if the shock has the same impact at all ages, or if mortality increases more at some ages than at others. In this article, Virginia Zarulli analyses the effects on mortality of two shocks, the 1933 famine in Ukraine, and internment in a Japanese prison camp during the Second World War. By comparing the age patterns of mortality before and after the shock, she is also able to test opposing hypotheses of survivor selection or of negative longterm effects on survival.
2Environmental conditions affect mortality of populations. Life expectancy can be extended or contracted either by lowering or raising the mortality curve proportionally at all ages, or by changing the slope of the mortality curve, i.e. the rate at which mortality increases with age. Both phenomena may also operate simultaneously. The debate is open as to which of the three mechanisms actually occurs.
3To answer this question, a setting typical of natural experiments is needed in order to compare a control group with a case group that is subject to random assignment of the treatment, or, as in casecrossover studies, to analyse the effect of exposure to the treatment for a certain period of time, after which the treatment is withdrawn.
4Such experimental conditions are not achievable in studies on human mortality, but abundant research has been performed on laboratory organisms. Several experiments have been conducted to investigate whether the slope of the age trajectory of mortality is affected by abrupt changes in external conditions, such as sudden dietary restriction or exposure to desiccating air flows in the case of Drosophila, but the results are contradictory (Johnson, 1990; Aziz, 1995; Flurkey et al., 2001; Mair et al., 2003; Magwere et al., 2004; De Magalhães et al., 2005). Transposition to human mortality could be operated by focusing on population groups that undergo external shocks and by studying the mortality risk of the survivors after the shock.
5The aim of this article is to shed light on how a brusque worsening of the environmental conditions might act on human mortality. To analyse this question, the investigator has to look for documented cases of sudden change in environmental conditions – mortality shocks – that resemble a natural experiment as much as possible. A famous example, though representing a positive shock, is the reunification of Germany in 19901991, when the death rates of the East quickly converged with the lower death rates of the West (Vaupel et al., 2003). Other historical events like famines, deportations and internments represent negative mortality shocks. These events are an appropriate analysis tool because the shock is applied to the study population in a nonselective way, thereby reducing the risk of bias due to confounding factors in the evaluation of the shock’s effects. Other shocking events, like flu epidemics for example, depending on the specific disease or virus, might affect some specific age groups more than others. The 19181919 influenza epidemic, for instance, killed mainly at young ages (Simonsen et al., 1998).
6However, even in cases when, at least in principle, the shock is supposed to act on the population unselectively, such events never completely satisfy the conditions required by a natural experiment. Systems of values and social interactions, such as solidarity or competition, could distort the purely biological effect of the shock, modifying the final outcome of mortality increase by age. Unfortunately, the available data can seldom be used to investigate these factors.
7Famines are a good example of mortality shock and the literature about them is wide. Depending on the availability of data, they have been more or less extensively analysed. Examples of sadly famous famines are the great Finnish Famine in 18661868 (Pitkänen, 1992; Pitkänen and Mielke, 1993), the Dutch Famine in 19441945 (Lumey and Van Poppel, 1994), the 19411944 Greek Famine (Hionidou, 1995), the Ukrainian Famine in 19321933 (Meslé and Vallin, 2003; Meslé and Vallin, 2012), the Irish Potato Famine in 1840 (Guinnane, 2002) and the devastating famine that accompanied the Chinese Great Leap Forward in 19581961 which caused around 30 million excess deaths (Ashton, Hill et al., 1984; Peng, 1987; Song, 2009). There are also numerous studies on imprisonment in war camps (Dent et al., 1989; Williams et al., 1993; Costa, 2011) or in cities under siege (Stanner et al., 1997; Sparén et al., 2004), that represent another good example of mortality shocks.
8The great majority of research is concerned with assessing whether the cohorts born during a famine suffer from a higher late life mortality than the cohorts born immediately before and after (Kannisto et al., 1997; Song, 2009; Myrskylä, 2010; DoblhammerReiter et al., 2011), with contradictory results. Other studies look at the effect of starvation and malnutrition early in life on specific health outcomes in adulthood, such as blood pressure and diabetes (Stanner et al., 1997; Sparén et al., 2004; Painter et al., 2005; Chen and Zhou, 2007; Lumey et al., 2007).
9Another example of mortality shocks is represented by Australian veterans surviving Japanese Second World War camps. The survivors showed higher overall mortality rates than nonprisoners in the years after release (Dent et al., 1989), although the difference was more pronounced in the years immediately following release and diminished afterwards. A similar pattern has also been found for Holocaust survivors, whose initial excess mortality, due to the longlasting deleterious effect of imprisonment, gradually disappeared compared to nonprisoners (Williams et al., 1993). Costa (2011), on the other hand, finds that for the survivors of the Andersonville military camp during the American Civil War, what mattered in determining better or worse health outcomes compared to noninternees, was age at imprisonment.
10However, there is no systematic assessment of the contingent effect of the shock on the population rate of mortality increase with age. The study of this effect is important in order to shed light on the way a population may react to the unfortunate circumstance of a mortality shock. Moreover, studying the effect of catastrophic events on human mortality can help to determine whether the rate of ageing is biologically determined and stable (Vaupel, 2010), or sensitive to sudden environmental changes.
11In the presence of a transitory, relatively brief shock, laboratory experiments have shown that the overall level of mortality in the case group returns rapidly to that of the control group, not affecting the rate at which mortality increases with age (Khazaeli et al., 1995). This article aims to investigate the process that occurs among humans at adult ages.
12When external conditions suddenly worsen, the population under shock experiences a sharp increase in mortality rates and a temporary contraction of life expectancy. Technically, three different scenarios can occur:
 Scenario A: mortality is raised proportionally at all ages and the rate of mortality increase with age is unchanged (Figure 1A);
 Scenario B: mortality increases more at older ages and the rate of mortality increase by age is accelerated (Figure 1B);
 Scenario C: the rate of mortality increase by age slows down because the increase is relatively higher at younger ages (Figure 1C).
13Scenario A would take place under the hypothesis proposed by Vaupel (2010) whereby the rate of ageing has a biological basis and is not affected by environmental changes. The second and third scenarios, on the contrary, would contradict such a hypothesis. On the one hand, as illustrated by scenario B, it is biologically plausible that some age groups are weaker than others: older adults, for instance can be considered as weaker and a shock might affect them more than other groups. On the other hand, as shown by scenario C, the shock may also have a similar absolute additive impact on mortality by age, which would result in a larger relative increase in mortality among younger people who have lower initial mortality. In this case, the log mortality curve during the shock converges at old ages towards the log mortality curve under the normal regime.
14Scenario C, especially in cases of exposure to multiple years of harsh living conditions, must also be considered in the light of the wide literature on unobserved heterogeneity (Vaupel et al., 1979; Vaupel et al., 1983; Vaupel and Yashin, 1985). According to this literature, phenomena like old age mortality deceleration or convergence of hazards, are an artefact of selection processes due to unobserved heterogeneity of frailty: frailer individuals die at a faster pace and survivors are more selected towards robustness. If the exposure to a sudden shock is prolonged, selection might have the time to eliminate frailer individuals first. As individuals can plausibly be considered as weaker at older ages, this could produce the pattern depicted in Figure 1C, with a convergence at old ages of the mortality curve during the shock.
Three mortality shock scenarios
Three mortality shock scenarios
Notes: A: the shock raises the mortality level proportionally at all ages, as shown by the parallel upward shift of the curve on a logscale.B and C: the increase in mortality is not proportional at all ages.
B: older ages are more affected than younger adult ages and the slope of the logmortality curve is steeper.
C: the log mortality curve is less steep because the relative mortality increase is bigger at younger ages than at older ones. In all cases, mortality risk is increased and life expectancy contracted by the shock.
15We will analyse the effect of a mortality shock on human populations by investigating the various hypotheses using two examples of natural mortality experiments. The first example concerns Australian civilian prisoners of war during the Second World War who were held captive in a Japanese prison camp from March 1944 to August 1945. The second example is the Great Ukrainian Famine of 1933.
I – Data
1 – Australian prisoners of war in the Japanese Tjimahi camp,19441945
16Mortality data for these prisoners are published and available in Bergman (1948). Ten thousand Australian male civilians aged 1085 were interned in the Japanese camp of Tjimahi from the end of February 1944 until August 1945. They were exposed to extremely harsh dietary and living conditions.
17Bergman’s paper contains male monthly death counts by 5year age group, from ages 1115 to 8185, and the number of interned individuals by age group in March 1944 and January 1945. No individuallevel data are available so it is not possible to follow individual prisoners over the period. Moreover, the paper indicates that the camp population was not closed and that small movements of prisoners occurred throughout the period. For example, there was a sharp rise in dysentery cases in March 1944, but the Japanese authorities did not allow anybody to die in the camp and sent sick prisoners to nearby hospital camps where deaths were not registered. The exclusion of these individuals is likely to have lowered the mortality level recorded in the camp, but not its agepattern. There is no compelling reason to think that a rise in dysentery would affect some age groups more than others or that those sent away were concentrated in these age groups.
18Bergman [1] compared the agespecific death rates in the camp with those of the Australian civilian population in 1941, considered as the reference mortality level under a normal mortality regime, and noticed that they were extremely high at all ages (Figure 2A).
Death rates for two natural mortality experiments (log scale)
Death rates for two natural mortality experiments (log scale)
A. Australian prisoners in the Second World WarDeath rates for two natural mortality experiments (log scale)
Death rates for two natural mortality experiments (log scale)
B: Ukrainian famine in 19332 – The Ukrainian famine in 1933
19The Ukrainian data are drawn from reconstructed mortality trends in twentiethcentury Ukraine produced by Meslé and Vallin (2003 and 2012).
20In the twentieth century, Ukraine experienced major demographic crises that were mostly covered up by the authorities. With the implementation of openness and transparency policies in more recent years, researchers were finally able to access the archives and reconstruct data series by combining different sources. [2]
21In Meslé and Vallin (2012), genderspecific period life table probabilities of death q(x) by oneyear age group from ages 0 to 89 were reconstructed for the years 19272002. However, only data from 1927 to 1939 are considered in this analysis because the Second World War and the Ukrainian border changes after 1940 are likely to have created discontinuities in the series of deaths.
22These data show the severe impact of the Great Famine on Ukrainian mortality. Probabilities of death started to rise in 1932, peaked in 1933 and fell again in 1934. For this analysis, probabilities of death were converted into death rates using the following formula:
24The rates are presented in Figure 2B.
25The Australian data points are more fluctuating than those for the Ukrainian famine. They cover a smaller population (about 10,000 prisoners), while in the Ukrainian case, the reconstructed series of probabilities of death cover the whole country.
26Among adults, overall mortality under shock conditions is much higher. In the case of the Australian prisoners, the data points appear to follow lines with similar slopes while for the Ukrainian famine the lines converge, and the slope is less steep than under the normal mortality regime. The food shortages and mortality increase had already started in 1932, but only in 1933, at the peak of the crisis, can the convergence be clearly seen.
27In the case of the Australian prisoners, mortality seems to be raised proportionally at all ages, while for the Ukrainian famine, the change in the slope of the mortality curve shows a relatively smaller impact at old ages, although only in the second year of exposure to the shock. This could result from a similar absolute increase at all ages, which would imply a higher relative increase for the young, who had a lower mortality level under the normal regime. However, the absolute increase in the death rates in the year of the crisis was not the same at all ages (see Appendix Figure A.1). As discussed in the introduction, the convergence at old ages and the fact that it only becomes visible in the second year of the shock, could be an artefact of the selection process due to unobserved heterogeneity of frailty (Vaupel et al., 1979; Vaupel and Yashin, 1985).
28Clearly, the same reasoning could be applied to the prisoners of war, but the converging pattern is not visible in their case. Two possible explanations can be imagined. First, the small sample size and the highly fluctuating data might prevent a clear pattern from emerging. Second, to see a sign of selection due to hidden frailty would require observation of a closed population, which was not the case in the prison camp. From Bergman’s paper (Bergman, 1948) we know that small prisoner movements occurred throughout the period and, from the data, it is not possible to identify the population of individuals who were imprisoned from the beginning.
II – Methods
1 – Prisoners of war
Analysis of the slope of the mortality curves
29Figure 2A shows that imprisonment produced a parallel upward shift in the mortality curves. This is one of the three possible scenarios in case of a mortality shock. So the analysis here focuses on investigating whether this pattern is statistically detectable and whether the slopes of the logmortality curves remain similar under a normal mortality regime and during imprisonment.
30A Gompertz mortality model (1825), known to accurately describe adult mortality, has been fitted to the death rates of the captive population at ages 30 and above for the years of imprisonment, and to those of the Australian male civilian population in 1941 (from the Human Mortality Database) used as the reference normal mortality regime. [3]
31Previous analyses used these data to illustrate the parallelism of the prisoners’ mortality curves in different years (Jones, 1959; Jones, 1961; Finch, 1994; Rozing and Westendorp, 2008) by performing linear fitting on the empirical logdeath rate. However, the logarithmic transformation tends to flatten and level out possible differences. By contrast, to assess whether this pattern is statistically detectable we performed a weighted (with the inverse of the variance) nonlinear least squares regression on the empirical agespecific death rates. [4] Weighted least squares regression gives less weight to the less precise measurements and more weight to more precise ones, so is particularly effective with small data sets.
32According to the Gompertz model, at any age x, the force of mortality ?(x) is expressed by an initial mortality level, a, and by an exponential mortality increase by age, the parameter b, which is also defined as the rate of ageing (Shock, 1967; Finch, 1994) and represents the slope of the mortality curve on a logarithmic scale. To assess whether the estimates of the parameter b in the situation of imprisonment and in a normal mortality regime are statistically different, two models were estimated with the nonlinear least squares method:
34where t represents the different years (1941, 1944 and 1945). An Ftest based on the residual sum of the squares was used to compare the models and to test whether model 2, which estimates different b for each year, statistically improves the fit.
Analysis of the monthly variation in mortality
35To strengthen the analysis, further evidence could also be obtained from the slope of the mortality curves in the different months. All age groups show a similar dominant pattern that reflects the seasonal variation typical of tropical areas: mortality in dry months (from May to September) is lower than in the wet months (Shek and Lee, 2003). These fluctuations can also be considered as changes in external conditions and, especially for a population weakened by imprisonment, they are likely to represent a shock (although milder than the shock represented by the imprisonment itself).
36A Poisson regression was performed. The Poisson distribution is the most appropriate distribution for modelling rates (King, 1988; Cameron and Trivedi, 1998), based on counts of events occurring over a certain period of time.
37Model 3 includes an age variable, and 18 variables for each month spent in the camp. Model 4 introduces the interaction term between age and month. Both models include the agespecific exposure time as an offset term in the equation. For every month i, with i = 1 … 18:
39In this regression setting, exp(?_{0}) can be interpreted as the a term of the Gompertz equation, ?_{1} as the b term and the coefficients exp(?_{2,i}) as multiplicative terms with proportional effects on the baseline hazard. The two models were compared with an Anova test in order to investigate whether the interaction terms between age and months are significant, which would indicate that the age profile of mortality was influenced by the effect of the months.
2 – Ukrainian famine
Analysis of the slope of the mortality curves
40The analysis aims first to assess whether the slope of the mortality curve during the famine year 1933 is significantly different and lower than the slope during the other years.
41Gompertz models (Gompertz 1825) were fitted to the death rates, from age 50 on [5] for the different years and compared, following the same logic illustrated in equations 1 and 2 in the previous section. Two models where compared: model 1 estimated three different a parameters for the years 1932, 1933, 1934, one a parameter for all the other years and one b parameter common to all years under scrutiny; model 2 introduced a separate b parameter for 1933, the year when the mortality curve seems to converge at all ages towards the levels of the other years, to investigate whether the slope of the curve for year 1933 is significantly different (and lower) than in other years.
Analysis of pre and postcrisis cohort mortality
42Secondly, we investigated if the convergence of the curve could be considered as a selection artefact due to unobserved frailty (Vaupel et al., 1979; Vaupel et al., 1983; Vaupel and Yashin, 1985). Direct investigation of this selection would require longitudinal and cohort observation but the available data are in period format. We therefore adopted an indirect approach, aiming to look for some signs, even indirect ones, of the presence of selection processes in the Ukrainian population under the shock. [6]
43Results from a study that simulated heterogeneous human populations under shock show that selection due to unobserved heterogeneity leads to a specific cohort mortality pattern in which the mortality observed after the shock is lower than would have been experienced if there had been no shock (Vaupel et al., 1988). If such a pattern can also be found among the cohorts forming the Ukrainian population during the shock, then this suggests that the population underwent the kind of selection related to unobserved heterogeneity that, as shown in the demographic literature, can lead to converging logmortality curves at old ages.
44To perform a longitudinal cohort analysis, the diagonals of the data matrix of the probabilities of death were used. Since the data were available from 1927 to 1939, a 13year longitudinal observation period was obtained for cohorts of different ages at the beginning of the observation. The probabilities of death were transformed into death rates using the formula in equation 1.
45A cohort mortality model was then fitted on the precrisis cohort data. Cohort agespecific mortality for the years after the crisis was extrapolated based on the fit of the model for the precrisis years.
46A total of 28 cohorts aged 5077 were analysed. The age limits were chosen for two main reasons: age 50 was chosen to avoid the estimation problems related to the hump at the young adult ages, as discussed in the previous section; the upper limit of 77 was due to the fact that the cohort aged 77 in 1927 was the last one that could be observed longitudinally over the entire 13year period (given that period data cover years 19271939 and ages up to 89 years). Figure 3 shows a simplified scheme of the data processing. Analysis is performed along the diagonals of the period data matrix in order to follow several cohorts longitudinally.
Observation and extrapolation zone on a Lexis diagram
Observation and extrapolation zone on a Lexis diagram
47The model used for fitting was the gammaGompertz model that, unlike a simple Gompertz model, takes account of selection in the cohort due to unobserved heterogeneity of frailty. In addition to the Gompertz parameters a (initial level of mortality) and b (rate of mortality increase by age), this model controls for unobserved heterogeneity of frailty by estimating an additional parameter for the variance of frailty in the population, ?, at the initial age of observation (Vaupel and Yashin, 1985).
48The older the initial age at which a cohort starts to be observed, the lower the expected variance of frailty, as the cohort has undergone selection (that reduces heterogeneity) for a longer time, and the higher the a parameter that represents the initial level of mortality. In this analysis, each cohort was observed from a different age (one cohort was observed from age 50, one from age 51 and so on), so both the initial mortality level a and the variance of frailty ? are cohortspecific.
49In performing the estimation, this was taken into account by estimating a gammaGompertz model (Vaupel and Yashin, 1985) with cohortspecific a and ? parameters but only a common b. A prior investigation showed that the logdeath rates of different cohorts have the same slope, so a single b parameter was estimated.
50To simplify the procedure, the 28 cohorts were grouped into seven groups and for each group i, where i = 1 … 7
52By aggregating the different cohorts into groups, a possible bias might be introduced in the estimation. However, aggregation simplifies the procedure and reduces the number of parameters to be estimated from a limited number of data points.
III – Results
1 – Australian prisoners of war
The slope of the mortality curves
53Figure 4 shows the estimates of the Gompertz coefficients a and b. Model 1 fitted a Gompertz model with a common b for the three years in analysis, while model 2 allowed each year to have its own b (Appendix Table A.1 reports the results of the regression analysis). The confidence intervals of the b estimates in model 2 widely overlap, indicating that they are not significantly different in the three years. On the contrary, the a parameters are significantly different in the three years and this result is obtained with both models. An Ftest between model 1 and model 2 (Appendix Table A.1) indicates that the second model does not improve the fit significantly. It can thus be said that mortality during the period of internment was significantly higher overall, and the increase was proportional at all ages, so the rate of mortality increase by age remained unchanged.
Australian prisoners of war in the Second World War. Estimates for the a and b parameters of the Gompertz force of mortality
Australian prisoners of war in the Second World War. Estimates for the a and b parameters of the Gompertz force of mortality
Monthly variations in mortality
54Additional evidence comes from the Poisson regression analysis. The results of the Anova test between model 3 and model 4 reveals that the second model, which includes an interaction term between the ageslope of mortality and the monthly effect, does not improve the fit significantly, showing that there is no significant interaction between the months and the age term and that the monthly fluctuations affect mortality by shifting the level up and down proportionally at all ages but have no effect on the rate of mortality increase by age.
55The Anova test and the regression coefficients of model 3 are reported in Appendix Tables A.2 and A.3.
2 – Ukrainian Famine
Slope of the mortality curve during the famine
56The analysis shows that the slope of the mortality curve in the peak year of the crisis is significantly lower than in the other years. Appendix Table A.4 gives the results of the two Gompertz models fitted on the data. Their comparison via an F test shows that the model that estimates a specific b parameter for 1933 and another b for all other years, significantly improves the fit. Moreover, the estimated b for year 1933 is lower than in all the other years, for both men and women (0.06 versus 0.093 for men and 0.061 versus 0.095 for women).
Cohort mortality before and after the crisis
57Figure 5 shows the observed (black solid line) and predicted (green dashed line) mortality values after the crisis for cohorts of different ages in 1927. The xaxis shows the longitudinal observation in years since 1927. The yaxis reports the death rate of the cohort; we see that it follows a Gompertztype increase as the cohort ages.
Effect of the Ukrainian famine in 193234
Effect of the Ukrainian famine in 193234
Note: The curve represents the observed force of mortality (black solid line) for different cohorts followed up for 13 years (192739); the longitudinal observation includes the 3 years of the crisis, showing the mortality peak in 1933, six years after 1927. Predicted mortality (green dashed line) shows the mortality regime as if there had been no crisis. The predicted values are the results of a gammaGompertz fit for the years before the crisis and of an extrapolation, from this fit, for the years after the crisis.58For some cohorts, the predicted postcrisis mortality based on the extrapolation from precrisis mortality is higher than the observed one. For other cohorts there is no difference between the two. However, the difference tends to be bigger among older cohorts and can be observed in both sexes from the cohort aged 6265 on.
59Among younger cohorts, there is no difference between predicted and observed mortality for women, while men show a small difference in the 23 years following the crisis, which subsequently disappears. Men in older cohorts also consistently show this pattern.
60Among women, the cohorts aged 6265 and 6669 in 1927 show higher predicted mortality for the five years of observation after the crisis, while the cohorts aged 7073 and 7477 present a very small difference immediately after the famine which quickly disappears.
61The results of the gammaGompertz model are consistent with what was expected from the theory of unobserved heterogeneity of frailty. The a parameter increases from cohort 1 to cohort 7, because the age at which each cohort starts to be observed is increasingly old and, consequently, the respective initial level of mortality for that cohort, represented by the a parameter, has to be increasingly high.
62The estimates for the ? parameter also behave in line with theory and decrease from cohort 1 to cohort 7. This parameter, in fact, represents the variance of frailty at the initial age of observation. The older the initial age at which a cohort starts to be observed, the lower the variance of frailty should be, as the cohort has undergone selection (that reduces heterogeneity) for a longer time. As the 7 cohorts are observed from different (and older and older) starting ages, the estimated variance of frailty should decrease. Although the estimates for ? are not significant, the model captures the trend predicted by the theory. The estimates of the parameters are given in Appendix Tables A.5.
IV – Discussion
63This article uses data for Australian civilian prisoners in a Japanese camp during the Second World War (Bergman, 1948) and for the Ukrainian Famine in 1933 (Meslé and Vallin, 2003; Meslé and Vallin, 2012) to analyse the effect of a sudden and temporary exposure to extremely harsh conditions on the mortality curve at adult ages.
64In the case of the Australian prisoners of war, the results show that the prisoner death rates were spectacularly higher than those of a similar population under a normal mortality regime, but the increase in mortality proved to be proportional at all ages. The rate of mortality increase by age did not show an acceleration, only the initial mortality level parameter changed significantly.
65The fit of the Gompertz model to the death rates shows that the rate of mortality increase by age was not accelerated by the imprisonment period. The estimates for the b term of the exponential equation were not significantly different during imprisonment and under the normal mortality regime. On the contrary, the a parameter changed significantly. This term represents the baseline mortality level and was significantly higher during imprisonment than under the normal regime. Analysis of the monthly death counts also provides further evidence. The monthly oscillations due to the usual seasonality of mortality typical of tropical areas caused the mortality curve to fluctuate but left its slope unchanged.
66The captive population was not completely closed. Throughout the internment period, small movements of prisoners occurred, mainly due to the Japanese policy of not letting anybody die from diseases like dysentery in the camp. The very sick people were sent to nearby hospital camps but no information about their age distribution and their deaths is available. However, there is no compelling reason to think that a rise in dysentery would hit some age groups more than others and, consequently, that the prisoners sent away were concentrated in those age groups.
67In the case of the Ukrainian Famine, the analysis found that the logmortality curve in 1933 had a significantly lower slope than all the other years, showing convergence towards the mortality curves in the faminefree years. This suggests a relatively smaller impact of the famine at old ages than at younger ones.
68However, as highlighted by the wide demographic literature about unobserved heterogeneity of frailty, such a pattern may also be due to selection processes (Vaupel et al., 1979; Vaupel et al., 1983; Vaupel and Yashin, 1985).
69As the investigation of this type of selection would require a longitudinal observation, while the available data were in period format, the analysis used an indirect approach. Portions of 13year cohort observations were constructed with the aim of finding evidence of selection due to unobserved frailty among the cohorts that formed the Ukrainian population at the time of the famine. The analysis looked for signs of selection by checking whether the cohorts’ postcrisis mortality was lower than the mortality they would have experienced in the absence of the crisis. A simulation study (Vaupel et al., 1988) suggests that this pattern reveals the action of unobserved heterogeneity and selection.
70The results highlight gender and cohort differences. Observed male postcrisis mortality was consistently lower than the predicted one only in the two or three years following the famine, although the difference tended to be more pronounced among older cohorts (aged above 61 in 1927).
71Women showed a more heterogeneous picture. Younger cohorts displayed no difference between observed and predicted mortality, while among older cohorts such a difference was present but with different patterns. Two groups of cohorts showed a lower than expected mortality for the entire postcrisis observation period and two groups showed a pattern similar to the one found among men.
72Although the picture is ambiguous, a general pattern emerges: when observed and predicted mortality differ, the observed mortality is lower than the predicted one. This finding is consistent with the results of simulation studies about the effect of selection processes on the mortality of cohorts exposed to a shock (Vaupel et al., 1988). This could suggest that mechanisms of selection might actually have taken place in the Ukrainian case.
73However, the evidence provided by this analysis is too fragmentary to draw conclusive findings about the role of selection due to unobserved heterogeneity in the Ukrainian case. It is important to consider that other mechanisms could lead to the same pattern. The observed reduction in cohort mortality after the famine may be due to hormesis (Calabrese and Baldwin, 2002) rather than selection. In other words, what does not kill you strengthens you and lowers your subsequent death rates. However, while this could be true among some female cohorts, whose postcrisis mortality remained lower throughout the observation period, it is difficult to imagine that the same can apply to the other cohorts and especially to men, who experienced a lower mortality only for a short period immediately after the famine. This suggests the presence of a harvesting effect (Smith, 2003) rather than hormesis.
Conclusion
74How sudden changes in environmental conditions affect human mortality and, above all, whether they have an impact on the rate of mortality increase by age are crucial questions for understanding ageing processes. Contrary to what is possible with laboratory organisms, in the case of humans it is impossible to investigate these questions with controlled and randomized experiments. Our only option so far is to rely on documented mortality shocks.
75In the two cases of mortality shocks analysed in this article, older ages were not affected more than younger ones, in relative terms, by the mortality shock. In the case of the Australian prisoners of war, the mortality curve shifted upward in a parallel fashion during the imprisonment period, leaving the slope of the curve unchanged and affecting all ages proportionally. In the case of the Ukrainian famine, mortality at older ages increased proportionally less than at younger ages.
76The analysis found weak evidence that this pattern could be attributed to the possible presence of selection due to unobserved heterogeneity of frailty (Vaupel et al., 1979; Vaupel et al., 1983; Vaupel and Yashin, 1985). However, as pointed out in the discussion, other possible mechanisms could have caused the observed pattern.
77More cases of natural morality experiments need to be analysed and more evidence needs to be collected in order to assess which mechanisms play a major role.
Acknowledgments
I would like to thank Jutta Gampe for her technical support in the analysis and for her substantial comments in the writing of the manuscript. I am also grateful to Jim Vaupel, Graziella Caselli and Jim Oeppen for their encouragement and precious advice. Finally I would like to express my thanks to the participants of the 1^{st} International Biodemography Network Meeting, 34 May 2011, at Duke University for their useful opinions and remarks.Male and female death rates in 1931, the year preceding the beginning of the famine, and in 1933, the peak famine year
Male and female death rates in 1931, the year preceding the beginning of the famine, and in 1933, the peak famine year
Note: The dashed lines between the two curves show the absolute increase in mortality at different ages.Parameter estimates of a Gompertz fit for Australian male death rates under an internment regime in the Tjimahi camp in 1944 and 1945, and under a normal mortality regime in 1941
Parameter estimates of a Gompertz fit for Australian male death rates under an internment regime in the Tjimahi camp in 1944 and 1945, and under a normal mortality regime in 1941
Note: Model 1 fits a Gompertz model with three a parameters for the three different years and a common b parameter. Model 2 allows each different year to have its own b parameter.Australian male civilian prisoners of war in the Second World War
Note: Anova test between two Poisson regression models for the monthly death rates in the internment camp of Tjimahi (Java), from March 1944 to August 1945. Model 3 regresses death rates on age and months, while model 4 also includes an interaction term between age and months.Australian male civilian prisoners of war in the Second World War
Australian male civilian prisoners of war in the Second World War
Note: Estimated coefficients from Poisson regression of the monthly death rates in the camp of Tjimahi (Java), from March 1944 to August 1945.Parameter estimates of a Gompertz fit for Ukrainian death rates from age 50 during the famine years, 1932, 1933 and 1934, and in the years before (19271931) and after (19351939)
Parameter estimates of a Gompertz fit for Ukrainian death rates from age 50 during the famine years, 1932, 1933 and 1934, and in the years before (19271931) and after (19351939)
Note: Model 1 fits a Gompertz model with different a parameters for the three famine years, one a parameter for the other years and one b parameter common to all years. Model 2 introduces a separate b parameter for 1933, the peak of the crisis, when the mortality curve seems to converge at all ages towards the levels of the other years.Ukrainian men in 19271931. GammaGompertz fit for the death rates of cohorts aged 5077 in 1927, divided into 7 groups of 4year age groups
Ukrainian men in 19271931. GammaGompertz fit for the death rates of cohorts aged 5077 in 1927, divided into 7 groups of 4year age groups
Note: The a parameters denote the initial level of mortality, the ? parameters the heterogeneity level at the initial age for each group; b is the rate of mortality increase with age that is the same for all the cohorts.Notes

[*]
Max Planck Odense Center on the Biodemography of Aging and Institute of Public Health, University of Southern Denmark • Max Planck Institute for Demographic Research, Laboratory of Survival and Longevity, Rostock, Germany.
Correspondence: Virginia Zarulli, J.B. Winsløws Vej 9, DK5000 Odense C, Denmark, tel.: +45 6550 4087, email: vzarulli@health.sdu.dk. 
[1]
Bergman calculated probabilities of death in the camp, although he called them death rates.

[2]
Meslé and Vallin (2003, 2012) estimate that the great famine of 1933 led to about 2.9 million missing individuals because of excess mortality, 1.1 million due to lower fertility and 0.9 million who migrated or were forcibly deported or exiled. They also show an incredibly low life expectancy at birth during the crisis. It fell to just 7.3 years for men and 10.9 years for women in 1933, versus 43.5 years and 47.9 years, respectively, in 1931, a level to which it returned in 1935.

[3]
Bergam (1948) used male death rates in 1941 as “normal” death rate against which he compared the death rates registered in the camp. To follow Bergman’s comparison, the death rates for the same year have been analysed in this article. They were taken from the Human Mortality Database that contains reliable and high quality data.

[4]
The weights of the agespecific death rates in the years 1944 and 1945 are inversely related to their monthly variation, information contained in Bergman’s paper. For the year 1941, no additional information on the variability of the agespecific rates was available and a weight of 1 was assigned to each of them. This is not a particular problem because these data come from the Human Mortality Database, a source of highquality populationbased data.

[5]
Estimations from age 30 were tried with a Makeham model, which includes an extra parameter c to account for the nonexponential pattern of mortality at younger adult ages (with the clearly visible hump in the death rates before age 50, a Gompertz fit would be inappropriate). Due to computational problems related to matrix singularity, it could not be estimated for some years. Therefore, in order to compare the slope of the mortality curve in all the available years, a simple Gompertz model was fitted from age 50 on.

[6]
The selection component could not be investigated in the case of the Australian prisoners of war, not even via an indirect approach, due to data issues. Death rates by 5year age groups, for only a very limited number of ages and years, represented an insufficient quantity of data to permit rearrangement with a view to partial longitudinal observation, such as that required for the analysis of selection.