Taking multi-morbidity into account when attributing DALYs to risk factors: comparing dynamic modeling with the GBD2010 calculation method

In this section we will outline the calculation of the DALY, the conceptual problems with the method for attribution of the DALY to risk factors and describe the alternative method using dynamic modelling.

The DALY is a measure for the burden of disease, which aims to “quantify loss of healthy years of life due to dying prematurely or to living with the health consequences of diseases, injuries or risk factors” [2]. Figure 1 shows the concept behind the DALY: the figure depicts the numbers lived in a population with and without disease related disability (area D and H respectively). In order to calculate the DALY, one first defines an envelope (here the thick black line) indicating the ideal situation: a situation without any burden of disease. In this ideal situation, the envelope would be completely filled with healthy years. In reality, however, there is a burden of disease, represented by the area M (the sum of years of life lost (YLL)) and the area D (the sum of years of life lost due to disability (YLD)). Now the aim of calculating a DALY for a particular disease or injurie is to attribute the areas M and D to the different diseases that cause the loss of health. As every person only dies once, the years contributed to M can be uniquely assigned to the primary cause of death of those dying prematurely. The GBD2010 developed a method (described in Appendix A) to attribute the years in D uniquely to each disease.

The DALY thus is operationalized as the sum of years of life lost (YLL) and years of life lost due to disability (YLD), where the latter is calculated as:where YD are the years that will be spend living with disease, and DW the disability weight.

There are two ways to calculate YD. The first, named the incidence-based method, estimates the YD by multiplying the incidence and the average period that an incident case is expected to live with the disease (to which we will further refer to as “duration of disease”). This method was initially used [1, 9]. The second, named the prevalence-based method, also referred to as the hybrid method [10], assumes a stationary situation. In that case the odds of the prevalence of the disease is equal to incidence times duration. Thus, when the prevalence is not too high, the YD can be estimated directly by using the prevalence of the disease in the population. This method is used in the GBD2010 and the current GBD2013. This latter method has the advantage of not requiring data on disease duration, which is hard to come by. Also the problem of multi-morbidity is more easily tackled.

In order to attribute DALYs to risk factors, a counterfactual approach based on PAFs is generally used. In a counterfactual approach one calculates the reduction in the burden of disease when exposure to a risk factor would have been at a theoretical minimum level. The PAFs are based on relative risks from the epidemiological literature on the associations of the risk factor with disease incidence or mortality. In the prevalence-based method, exposure refers to the past exposure, as the current prevalence of the disease is the result of past exposure of the risk factor. In the incidence-based method, exposure refers to the exposure that determines the incidence.

In a counterfactual approach, the question is: what would happen if a disease or risk factor exposure would be eliminated? Such an counterfactual approach is conceptually different from a attribution approach, where the goals is to attribute each pixel in D and M in Fig. 1 uniquely to a single risk factor. Both approaches differ in the way they handle multi-causality. If, for instance, a disease only occurs when two causes are simultaneously present, the disease can be prevented by removing one cause, but just as well by removing the other cause. An attribution method will attribute only part of this disease to each cause (adding up to attributing the disease exactly one time in the total of all attributions), while a counterfactual approach will fully attribute the disease to each risk factor, because removing each risk factor will fully remove the disease. In other words, in this situation a counterfactual approach will attribute the disease twice. This is the reason for the well-known fact that PAFs can add up to more than 100%, or, more generally, that PAFs (and thus DALYs due to risk factors) are not additive.

In applying the PAF (representing a counterfactual approach) to disease specific DALYs (representing an attribution approach), the GBD2010 method for calculating the burden of disease due to risk factors is a mixture of two conceptually different approaches. The result is a hybrid method, the result of which is difficult to interpret.

There are several reasons why the method does not correctly represent the effects of elimination a risk factor (that is, setting a risk factor at the theoretical minimum level). The first and most important one is that with regards to the YLL, the method assumes that all years gained by eliminating mortality due to the risk factor will be healthy years. It thus ignores substituting morbidity [11]. In an attribution approach, where the goal is to attribute current morbidity and mortality, this is justified, but not in a counterfactual approach. This is because in a counterfactual approach, the years gained by elimination will be partly years spent in less than full health. Second, with regards to the YLD, the GBD2010 calculation implicitly assumes that multi-morbidity will remain the same after elimination of the risk factor. However, if part of the multi-morbidity is also prevented (because diseases share the risk factor), this is not the case and the method overcorrects. Third, the years lived with disease (YD, that is, the duration for a single incident case) are assumed to be constant. However, elimination of the risk factor will decrease mortality from diseases that share the risk factor, and thus YD will increase after elimination of the risk factor. This means that -in theory- risk factor elimination by decreasing mortality could even increase the YLDs. Lastly, as we show in Appendix A, the methods developed to take multi-morbidity into account, do not work in case of partial elimination of diseases (which is the case by elimination of one risk factor of a disease).

Another criticism on the method to calculated DALYs for risk factors is that the PAF is applied to YLDs calculated using the prevalence method. The PAF itself, however, is calculated using relative risks derived from studies on the association between risk factor exposure and disease incidence (or disease mortality), not prevalence. Therefore, this PAF should only be applied to YLD from an incidence and not a prevalence method. Applying the PAF to YLDs based on prevalence means that the ratio of disease prevalence in exposed and unexposed is assumed to be the same as the ratio of disease incidence in exposed and unexposed. In case of low prevalence and equal mortality in both groups, this might be approximately true, but only if exposure and relative risks are constant over age. Many exposures differ in older and younger age groups, and also relative risks generally decline with age. In that case the PAF that should be applied to prevalence-based YLD at a certain age group should be based on the exposure and relative risks at lower ages, at the moment that the disease first occurred (moment of incidence).

In summary, given a mix of a counterfactual and an attribution approach, and applying incidence based relative risks to prevalence, it is not clear what exactly the DALYs attributed to a risk factor represent.

In dynamic modelling, the evolution of disease in a population is simulated over time. This kind of modelling has been developed to perform counterfactual (“what-if”) calculations: The amount of disease and mortality in a counterfactual situation (here called a scenario) can be determined simply by rerunning the simulation under this scenario.

Figure 2 presents such a model with two diseases. In this figure, the diseases are assumed to be irreversible, so no remission is included. Exposure to the risk factor influences the transition rate from a state without a particular disease to the state with a disease (the incidence rates i₁ and i₂, here assumed to be conditionally independent, that is, independent within those being equal with respect to risk factor status and presence or absence of disease). Furthermore, in every state subjects can die, governed by mortality rates m_x where the mortality rate depends on the state x (e.g. mortality is higher in those with the disease than in those without the disease). In this model, the probability of dying does not directly depend on the exposure, but does so indirectly, as exposure increases the incidence, and mortality is higher in those with a disease. The mortality in those without the disease is calculated from the population all-cause mortality by subtracting the disease-related mortality, which is calculated from the prevalence of the disease at baseline and the disease related mortality. The incidence rate of an individual with a certain risk factor exposure is calculated as a baseline incidence times the relative risk (RR) for that risk factor exposure. The relative risks are obtained from the literature, the incidence rates are based on data from GP or cancer registries.

Given a particular exposure, the accompanying incidence rates, and the effect of exposure on the incidence rates, the model can be used to simulate the future health states in a population.

DYNAMO-HIA is software (downloadable from www. Dynamo-hia.eu) simulating such a model for a single risk factor with a particular number of diseases [12, 13]. DYNAMO-HIA simulates the development of risk factor exposure over time using micro-simulation. Given the simulated exposure, it calculates the incidence rates and from that the probability of each health state over time. Part of the incident cases can die immediately when getting the disease (acute mortality).

In this model, a state is characterized by the presence or absence of each of the diseases that are modelled. Thus the number of states is 2 ^N were N is the number of diseases in the model, so multi-morbidity is explicitly modelled. After simulating the entire future development of disease states and death, the number of years lived within each health state in the population can be obtained by adding the probabilities of being in the state over all simulated individuals. These years then are multiplied by the appropriate disability weight. For each combination of diseases, a disability weight is calculated using a multiplicative formula, conforming to the same choice for a multiplicative effect as was made by the GBD2010 project:where d is the index for the disease, DW_s the disability weight for the health state and DW_d the disability weight for someone with disease d only.

A change in the initial risk factor exposure, as for instance the complete elimination of exposure, changes disease incidence and in turn future disease prevalence and mortality. The gain in life years and in disability weighted life years from such elimination can be calculated by subtracting the (disability weighted) life years in a simulated population where the risk factor has been eliminated from those in a simulation where the exposure is equal to the observed exposure.

Such a calculation gives the gain for every person in the population over his or her entire future lifespan. In such a simulation one has to specify the exposure not only at the start of simulation, but also in future life years. If exposure is eliminated not only for the present, but also in the entire future, the gain will be much larger than that calculated by the DALY, that only aims to calculate the gain of eliminating exposure in a particular calendar year. In order to obtain a measure on the same scale as the DALY, therefore exposure is eliminated only in the current calendar year, and afterwards returns to what it would have been in the situation without the elimination. This is somewhat similar to the 10-year intervention suggested in 2003 in WHO-CHOICE’s generalized CEA methodology (WHO 2003) [14].

Our objective is to compare the dynamic modelling approach with the method used by the GBD2010 in order to obtain further insight in the magnitude of the differences between the two methods.

For illustration purposes we use smoking, in relation to four diseases: lung cancer, Chronic Obstructive Pulmonary Disease (COPD), Coronary Heart Disease (CHD) and stroke.

In order to make a fair comparison, we used the same data (incidence, mortality, relative risks etc.) in both methods. This means that the GBD method in this paper does not yield DALY comparable to those calculated by the GBD project, as they use different relative risk, mortality and prevalence data. For the same reason, we use the remaining life-expectancy for the Netherlands as calculated from the mortality rates used as basis for the YLL.

DYNAMO-HIA requires input on 1) demography (population numbers, all-cause mortality); 2) epidemiological information on disease incidence, prevalence, excess mortality (defined as the difference in mortality rate between those with and without the disease) and acute mortality for relevant diseases; 3) initial risk factor exposure and transition probabilities for risk factor exposure (in order to simulate future risk factor trajectories for the case with current exposure), and 4) relative risks linking exposure to disease. All these data are differentiated by age and sex.

In the illustration for this paper we used data estimates for the Dutch population with 2011 as the calendar year to which the calculations apply. Lung cancer incidence (1989–2011) and survival data (1989– 2010) were available from the Netherlands Cancer registry, and Poisson models (including time-trends) were used to model age- and gender specific incidence and excess mortality rates in 2011.

Stroke and coronary heart disease (CHD) incidence rates were taken from the Netherlands Information Network of General Practice (LINH) for 2011. For stroke and CHD, patients were linked to hospital records (1995–2010) in order to obtain only incident cases in those without previous CHD and stroke respectively, and linked to cause-of-death records from the national mortality register in order to include immediately fatal cases. Both prevalent and incident cases were linked to death records in order to obtain mortality for those with disease compared to those without the disease. For stroke and CHD, mortality was split into short term (less than 1 year) and long term mortality. Acute mortality was calculated by subtracting long-term mortality from the observed one-year mortality. COPD incidence data were from the same GP registration. Again both prevalent and incident cases were linked to death records in order to determine excess mortality rates.

Calculating death rates from differences between those with and without the disease has the advantage of including excess mortality where the disease is not registered as the cause of death. However, it might overestimate mortality in case there is confounding from risk factors (other than smoking, as that effect is adjusted for in our modelling). However, this potential overestimation will not disturb our comparison of methods, as this is used in both cases.

Although we also had current prevalence data for all diseases, for the purpose of this exercise we want to use a population in equilibrium, as we did not want our results to be influenced by time trends. In order to derive input data representing a population at equilibrium, we used the incidences and mortality rates described above and simulated the prevalence of disease in a cohort of newborns, who were all disease free at birth. The simulated future prevalence rates in this cohort were used as starting prevalence rates.

We used the smoking prevalence as obtained from a 2011 smoking survey from the Dutch Foundation on Smoking and Health in the population aged 16 and older. Smoking data comprised the proportion of current smokers, former smokers and never smokers. Smoking rates were assumed zero until and including age 10 and afterwards we let the rates increase linearly with age towards the observed prevalence rates at age 16. We used a multinomial spline model (package VGAM in R) to smooth the smoking rates over age. Again, as we want to use an equilibrium situation, we used transition rates that keep the age- and sex specific smoking probabilities constant over time.

We used the relative risks that were used for previous chronic disease modelling in the Netherlands, which smoothly change over age and are presented in Appendix A; we considered using the GBD2010 Relative risks [15] instead, but those are only available for smokers and non-smokers, while we prefer to distinguish former smokers from never smokers. Our relative risks differ by age. For cardiovascular disease they decrease with age, as is also the case in those used for the GBD2010 [5]. This is due to the fact that the same absolute risk difference translates to a lower relative risk when the baseline risk (that is, the risk in never smokers) increases with age. For COPD and lung cancer, the relative risks first increase with age, reflecting higher average cumulative exposure with age, but at high ages the effect of increasing baseline risk takes over and relative risks decline with age [16].

In order to obtain insight in the causes of the differences between methods, we additionally performed analyses using an artificial situation (artificial data instead of the empirical data described above) in which:

In this last artificial situation, the prevalence method and incidence method are expected to deliver more or less similar results, so the difference between the dynamic modeling and the GBD2010 method will not be due to these differences.

We used the following disability weights: cancer of the lung: 0.285; stroke 0.609, CHD 0.288 and COPD 0.314. The values were derived assuming that the distribution over severity states of each disease is fixed and are equal to those used in the 2014 PHSF report [8].

In the DYNAMO-HIA model, also a disability weight is given to those without one of the diseases in the model, as these persons will have disabilities due to diseases that are not modelled, or simply due to old age. We both ran the analyses with and without these extra disability weights. In the latter case perfect health is assumed for anyone without one of the four diseases in the model.

In order to have a fair comparison, the data used in the GBD2010 method should be the same as those used in the DYNAMO modelling. Below we describe how we obtained such data.

Disease specific mortality in the DYNAMO model is not obtained from statistics on cause-specific mortality, but from the difference in mortality between those with and without a disease (which DYNAMO-HIA names “excess mortality”), adjusted for effects of risk-factor related multi-morbidity from other modelled diseases [17]. In order to use mortality rates in the GBD2010-type calculation equal to the data used in the DYNAMO-HIA modelling, we used this attributable mortality.

The mortality rate used was calculated as follows: First, the attributable mortality rate in the prevalent population was taken from the model. From this the one-year probability of dying was calculated as 1-exp(- m _a ) + i * (1-(1-exp(- m _a ))/m _a ), where i is the incidence rate (excluding fatal cases), and m _a the attributable mortality rate. The last term in this expression represents the mortality from those who acquire the disease during the simulated year, and die before the beginning of the next year. For diseases with acute mortality (stroke, CHD) we added the mortality of newly diagnosed cases to this mortality rate.

As the number of life years lost for each death we took the remaining life expectancy for that age and gender. By doing so we deviate from the GBD2010 method, which used a normative life table. For this exercise, however, our choice makes for a better comparison between methods, as the same life table is used in both methods.

The disease prevalence was the same as used as initial prevalence in the DYNAMO-HIA model.

We multiplied the disease prevalence in our population with the PAF calculated based on the relative risks and risk factor exposure prevalence and the disability weights as used in the DYNAMO-HIA model. The disability weight was adjusted for multi-morbidity using the same method as applied in the GBD2010, and described above. However, as we only used four diseases, we could do so by straightforward enumeration instead of simulation.