What if dependent causes of death were independent?

Introduction

Timing of death is determined by one’s genetic predisposition to diseases, lifestyle, social environment, and proneness to external adversities [1]. The extension of human life, particularly in Western Europe and North America after World War II, has been driven by significant declines in infant and adult mortality [2], leading to a concentration of deaths in the oldest age groups [3]. However, research consistently shows that extending lifespan often comes with an increase in the number of years lived with disease or disability [4], 5]. As diseases accumulate over a person’s lifetime, it is rarely a single health condition that causes death [6]. In Sweden, 60 % of deaths are attributed to at least two causes [7]; in France, 65 % [8]; in the USA, 80 % [9], comparable to Canada [10] and Australia [11]. In Czechia, nearly 90 % of deaths result from multiple causes [12]. Consequently, the approach of considering only the single underlying cause of death – defined as the condition that initiates the chain of morbid events leading to death – overlooks the majority of health conditions listed on the death certificate, providing only a limited understanding of the lethal disease process and interplay between causes of death in aged societies [13]–22]. Some authors suggest that the timing of death is influenced more by the presence of multiple coexisting diseases than by a single dominant cause that “wins” in the conventional competing risk framework [23]–26]. Understanding how diseases interact is therefore crucial not only for more accurate estimation of mortality risks in multimorbid populations but also for preventing the emergence of such interactions, because multimorbidity is strongly associated with rapid negative changes in health status, including functional decline and increased frailty [27], 28].

Rising prevalence of multiply caused deaths has led to increased interest in pairwise associations between causes of death [29], [30], [31]. However, most of these studies face important limitations. First, they often focus on causes of death associated with selected diseases, for example diabetes [32], [33], [34], Alzheimer’s disease and dementia [35], [36], [37], sepsis [38], [39], [40], [41], or heart diseases [42], 43]. Second, they explore relationships between the underlying cause of death and contributory causes (non-underlying conditions), frequently neglecting the connections solely among contributory causes [6], 44], 45]. However, these non-underlying conditions are often essential components of the lethal process, potentially driving translation of “a disease” into “the underlying cause of death”. Among the contributory conditions, physicians frequently record diabetes, dementia, sepsis, hypertension, and other cardiovascular diseases [9].

Several studies have moved beyond the narrow focus on pairwise associations between causes of death [16], 46], 47]. Egidi et al. [16] address the complexity of relationships between causes of death by applying network analysis, providing an innovative visualization of the complex relationships between major cause of death groups in an intuitively understandable manner. However [16], focus solely on measuring strength of relationships between cause of death groups and the authors do not examine the potential impacts of their changes, which is the focus of the current study. Above that, as highlighted by [30], studies focusing on identifying clusters of causes of death involving more than two causes often lack reliability, as application of different clustering algorithms leads to identification of different clusters [30], 31].

While the dependence between causes of death is hard to be denied, regardless of the research focus and methods applied, to date, no study has explicitly delved into the question of how the architecture of relations between causes of death would change if certain disease pairs that are known to co occur non randomly suddenly become independent. This is particularly important because, for instance, in the USA, the strengths of associations between leading pairs of causes of death have undergone substantial changes since the year 2000 (Figure 3). If there is a change in the association between diseases i and j, how could this affect the relationships between other diseases related to i? Understanding how changes in the relationship between disease i and disease j influence the relationship between disease i and disease k provides insight into the complexity of disease interdependencies and the far-reaching effects of altering associations between just one pair. This might be valuable for the early detection of newly emerging comorbidities, which, consequently, might contribute to both the rapid functional declines and the increased costs of health care, which are associated with treatment of complex multimorbid patterns [48], 49].

To explore the effect of disruptions in associations between diseases, we work with the US multiple cause of death data in 2019 [9] and measure the strength of association between pairs of diseases with odds ratios (OR). Then, we identify the most frequent cause of death (COD) pairs and make them independent by adjusting the marginal distributions of the respective contingency tables. Setting dependent COD to be independent has ripple effects on the associations with the remaining CODs. The primary objective of this study is to investigate the effects of such disruptions introduced into the structure of cause of death dependencies.

Data

The US Multiple Cause-of-Death Mortality Data was obtained from the National Bureau of Economic Research, which compiles microdata on mortality from the National Vital Statistics System of the National Center for Health Statistics (NCHS). Each record in NCHS Mortality Multiple Cause Files corresponds to one death which occurred during a single year in the USA and consists of sociodemographic variables as well as of two types of variables for recording the causes of death. The first type contains “Entity Axis Codes” which are recoded to the second type, “Record Axis Codes”, to eliminate inconsistencies, such as redundant codes, diagnoses incompatible with the sex of the deceased person, dual codes, etc. [50]. In the present paper we use the “Record Axis Codes” to study relations between causes of death. We create all possible combinations of codes recorded on the death certificate, which are coded in accordance with the Shortlist of causes of death provided by the Human Cause-of-Death Database [51]. We introduce the disruptions to leading COD pairs, which accounted for nearly 70 % of deaths in the USA in 2019. The selected pairs are highlighted in blue in Figure 3. The ICD codes included in each leading disease group are listed in Table 1, and the complete classification of diseases is provided in the Supplementary material.

In 2019, there is a total of 2,861,523 death records in the USA. Among these records, approximately 80 % were attributed to at least two causes of death. Consequently, of all the medical information recorded on death certificates, the single underlying causes of death accounted for only 30 %. The highest average number of conditions (exceeding 4) was mentioned with diseases of blood and blood-forming organs (D50–D89), diseases of the skin, subcutaneous tissues, musculoskeletal system and connective tissue (L00–M99) as well as with endocrine, nutritional and metabolic disorders (E00–E90). At the other end, neoplasms (C00–D48) are the only diseases, whose average number of additional diagnoses is lower than three.

Table 1 illustrates the most frequent cause-of-death pairs, collectively representing nearly 70 % of all deaths. Notably, among the leading causes of death, there is a recurrent presence of heart diseases (I00–I52), other respiratory diseases (J30–J98), and symptoms and signs (R00–R99, excluding R95), the latter sometimes referred to as ill-defined causes of death. Next, Table 1 shows odds ratios (OR) as well as the percentage of self-loops, which indicate how often a disease is recorded with another disease from the same disease group on the death certificate. These figures illustrate the extent to which cause-of-death pairs are excluded from our analysis, given that we do not investigate relationships within the major cause-of-death groups. Notably, there is considerable variation among causes of death, with the percentage of self-loops ranging from 1 % for acute respiratory diseases to as high as 48 % for symptoms and signs.

It is important to note how we address cases where deaths result from two identical causes. This becomes more common when causes of death are grouped into broader categories, as done in this paper. As recommended, a single death should not be attributed to multiple identical causes. Therefore, after the causes of death were aggregated following Shortlist of COD [51], the duplicities have been excluded from the analysis.

Methodology

Various measures have been proposed to assess the association between diseases, including the odds ratio (OR), relative risk (RR), and conditional probabilities. Specifically for analyzing associations between multiple causes of death, the cause of death association indicator (CDAI) has been developed, which is a standardized measure of the OR. Here, we use the OR for several reasons. Firstly, RR is unsuitable when the true exposure is unknown [52], and since we are working with period data, our exposure is not known. Secondly, conditional probabilities do not account for the number of individuals without the disease (or without a pair), which might introduce additional biases. Thirdly, we do not use CDAI because it can be distorted by the need to calculate age-specific associations. In our study, we include all associations involving diseases in leading cause of death pairs and do not exclude rare disease pairs from the analysis. It can be shown, that OR and CDAI are highly correlated (see Supplementary material).

We quantify the strength of associations between causes of death using odds ratios (OR). The OR are calculated by the formula [53]:

where the D _i,j is the number of deaths due to both causes i and j. The negation sign ¬ expresses the absence of cause i or j. For example, D _¬i,¬j is the number of deaths due to neither i, nor j. The odds ratio higher than one indicates significantly increased risk of co-occurrence of causes of death i and j.

We calculate 95 % confidence intervals (CI) for the OR by using normal distribution approximation, as in [54]:

where σ is the standard error of the odds ratio:

The measure of association described above detects non-randomly connected CODs. The significance of these associations is evaluated using the chi-squared (χ ²) test (see [55] for more details). After identifying significant associations among leading cause of death pairs, we optimize the marginal distributions of the corresponding contingency tables, ensuring that the χ² test statistic suggests independence between the causes of death in each pair. The process of optimizing the χ ² test statistic for two factors is illustrated in Figure 1.

Figure 1:

The process of adjusting the results of χ ²to achieve independence between diseases, example of heart disease and metabolic diseases. Source: data: [9]; authors calculations. X ²=test statistic for each cell of 2-way table; sum X ²=total test statistic; constrain: enforced on the total number of deaths, ensuring that the death counts in the optimal solution always sum to the total population death count. Note: Starting with the original distribution of deaths within the contingency table highlighted in green, we can perform the chi-squared (χ ²) test to measure the association between two factors (Table “Former χ ² Test” on Figure 1). In this illustrative example, the resulting p-value is lower than 0.05, leading to the conclusion that the null hypothesis of independence between the factors can be rejected. The corresponding odds ratio (OR) is 3.8010. Next, we optimize the marginal distributions of the original contingency table (Table “χ ² Test Adjusted for Independence” on Figure 1) to search for p-values that indicate independence (p-value >0.05). This process is iteratively applied to varying D _i and D _j and the results of the χ2 Test are recorded after each iteration. The sequences of D _i (and similarly D _j ) begin at 0, assuming no deaths occur with cause i (or j), and progress to the total number of deaths, assuming all deaths are attributed to cause i (or j). Each step in the sequence increments by 0.1 D _i,j .

The key purpose of this approach is to explore how the disruption of significant associations between leading causes of death might impact associations with their neighboring diseases. Therefore, the process involves adjustments to the marginal distributions of the contingency tables. To initiate this optimization, we first assume the number of deaths involving both causes i and j (D _i,j ) to be fixed. Then, we calculate the χ ² statistic while varying the sequences of the number of deaths due to cause i (D _i ) and the number of deaths due to cause j (D _j ). These sequences begin at D _i,j , signifying the assumption that all individuals who died due to at least one of the diseases i or j also died due to the other disease from the pair i, j. The sequences conclude at N, representing the total number of deaths within the population. By employing this upper bound, we assume that all deaths are attributed exclusively to either disease i or disease j. In addition, we impose a natural constraint that the sum of D _i and D _¬i,j should be less than N. To examine all resulting pairs of values for D _i and D _j , we implement a loop for the sequences specified above. Note that we do not test for independence with each potential number of deaths within these sequences individually, as it would be highly time-consuming. Instead, we set the intervals (increments) for the loops to be equal to 10 % of D _i,j.

Using the sequences of varying D _i and D _j , while keeping D _i,j at its original value, we recompute the remaining elements in the contingency tables. Then, we conduct χ ² tests and extract all cases that indicate independence at a confidence level of 99 %. We will refer to this selection as “independence scenarios.” As shown in Figure 2, for each pair of leading causes of death, the marginal distribution combinations that indicate independence tend to cluster around the yellow line. This line exhibits a characteristic shape of 1/x -hyperbola (Figure 2).

Figure 2:

Independence scenarios between causes of death, USA, 2019. Source: data: [9]; authors calculations. Both axes plot number of deaths from causes marked on the axes. Units on both axis are in 10⁶ (for instance, 1=1 000 000 deaths); black dot: original combination of D _i and D _j ; red dot: independence scenario applied here.

In the next step, we integrate the “independence scenarios” into the cause-of-death structure. We take each adjusted marginal distribution for causes i and j and implement it in order to calculate adjusted OR for all cause of death pairs that include either disease i or disease j. These OR represent the associations between diseases i and k (or j and k) that would exist if diseases i and j were independent. Here, k stands for all other causes of death under consideration, excluding causes i and j, respectively.

As a result, for each pair of causes of death, we obtain a distribution of adjusted OR, each corresponding to a different optimization solution or, in other words, an independence scenario. The next step is to determine what “independence scenario” to consider for studying the influence of the inserted independence on the other cause-of-death associations. We select the “independence scenario” corresponding to the relocation of the minimum number of deaths in the contingency table. The rationale behind this criterion is that it could be considered the one closest to reality as reaching independence requires minimal distortions in the distribution of deaths. In Figure 2, we depict two dots; the coordinates correspond to the original values of D _i and D _j (black dots) and their modification according to “minimum relocation scenario” (red dots). In summary, the red dots represent the solution that is further interpreted, and the distance between the dots signifies how much change is needed to dissolve the association between leading cause-of-death pairs.

The analysis was performed in R Studio version 4.3.1 and the preprocessing of raw NCHS data was done in SAS version 9.4.

Findings

Figure 3 shows the odds ratio (OR) between cause of death groups, with higher values indicating stronger associations. The leading cause of death pairs are highlighted in blue, where we also apply the distortions.

Figure 3:

Odds ratios between major cause-of-death groups, USA, 2019 (left) and index of odds ratios (base=2000), leading cause of death pairs, USA, 2000–2019 (right). Source: data: [9]; authors calculations.

Tables 2a and 2b summarize the effects of the dissolution of leading disease pairs containing diseases i and j on the association between i and k (or j and k), where k represents all other diseases except those involved in the pair (i, j) that undergoes dissolution. As mentioned earlier, these tables illustrate the effect under the minimum relocation scenario. Certain disease pairs exhibit only mild associations, requiring minimal distortion to render them independent. Examples include the association of mental and behavioral disorders with ill-defined causes of death, as well as heart diseases paired with other respiratory diseases or diseases of the genitourinary system.

Table 2a shows the adjusted OR between diseases in rows and the first diseases in the pairs, that are made independent. These pairs are in the column headings. Table 2b presents the same information but in relation to the second disease in the column headings. In both tables, adjusted OR that significantly differ from the original values are highlighted in pink. Additionally, in brackets, we provide the ratio between the adjusted and original OR. For example, if the adjusted odds ratio between infectious diseases and metabolic disorders is 1.15, the figure 0.88 indicates a 12 % decrease in the association between infectious and metabolic diseases if metabolic diseases and other respiratory disorders were independent.

Disrupting associations between leading cause of death pairs would lead to substantial changes in the architecture of cause of death relations. In most cases, the associations would decrease. However, disrupting the association between heart diseases and mental disorders would increase the odds ratios with heart diseases and all other cause-of-death groups except for mental disorders. It is noteworthy that achieving independence even under the minimum relocation scenario requires substantial distortions in the marginal distribution of deaths to make heart diseases and mental disorders independent (Figure 2, Panel A).

However, the diseases exhibit varying degrees of decrease in their associations. The most pronounced decreases are observed in pairs of mental and other respiratory diseases (Figure 2, Panel G), heart and metabolic diseases (Figure 2, Panel B), or heart and mental diseases (Figure 2, Panel A). The specific role of mental and metabolic diseases in the structure of disease interrelations has been previously identified [56], [57], [58]. These diseases are referred to as bridging diseases, indicating that they do not belong to any specific cluster of diseases but rather mediate relationships between seemingly unrelated diseases. The widespread impact of distortions involving mental and metabolic diseases might reflect their unique position within the architecture of disease dependencies.

Furthermore, there are several disease pairs for which the effect of disruption would lead to the same outcome as for pair being disrupted, resulting in their independence as well. This applies to associations such as mental with heart and mental with cerebrovascular diseases if mental and other respiratory diseases are disrupted. A similar effect would occur with the disruption of metabolic and other respiratory diseases on nervous and metabolic diseases, or on digestive and respiratory diseases. This effect might again point to transitive nature of relations involving mental and metabolic diseases, where making them independent of disease i also yields independence from disease k.

Lastly, the impact of disruption of cerebrovascular and heart diseases is quite specific, as introducing their hypothetical independence would not affect relations between heart diseases and other major disease groups (Table 2b, last column). Similarly, assuming independence between heart diseases and respiratory or metabolic disorders would not substantially alter the overall structure of relationships involving heart diseases (Table 2a, column Heart diseases + Other respiratory diseases).

Discussion

In this paper, we quantify the strength of associations between pairs of major CODs in the USA in 2019. We introduce disruptions into the respective contingency tables while searching for marginal distributions that reflect independence between the two causes. We propose different “independence scenarios” for each of the most frequent COD pairs and incorporate in the structure of cause-of-death dependencies the scenario corresponding to relocating the minimum number of deaths in the respective contingency table. In this setting, we examine the effect of this dissolution on associations of other pairs of diseases.

Our results indicate significant changes, mostly decreases, in the strength of association between diseases i and k (or j and k). The most pronounced effects would be observed (i) on mental and behavioral disorders if these would be independent on heart diseases, next (ii) on endocrine, nutritional and metabolic diseases if these would be independent on heart diseases and (iii) on other respiratory diseases if no dependence would exist between them and mental disorders. On the other hand, the dissolution of the association of heart diseases with mental and behavioral disorders leads to increased association of the former with all other causes, especially with neoplasms and endocrine and metabolic diseases. We identified pairs, in which achieving independence in one pair would imply independence in another. For instance, independence between mental and other respiratory diseases would lead to independence between mental and cerebrovascular as well as with mental and heart.

The outcomes are to some extent predictable. The most notable change occurs when the imposed independence is far from reality. Some of our findings are less intuitive, as for example, the ones for pairs involving heart diseases and other respiratory diseases, genitourinary diseases, and endocrine, nutritional and metabolic conditions. Even if the total amount of relocation for these pairs is comparable to (or greater than) pairs such as endocrine, nutritional metabolic diseases with other respiratory diseases or mental and behavioral disorders with ill-defined conditions, the dissolution does not have a significant effect on the associations with other diseases. Thus, the results are not predictable based on distinct D _i,j .

Our results showed that the dissolution of heart diseases and mental diseases could increase the association between heart diseases and almost all other disease groups. While there is a large body of literature discussing the links between heart and mental diseases, to our knowledge, no medical explanation exists about how changes in this link affect other diseases. For this analysis, we propose the following explanation: Deaths with mental diseases are usually associated with oldest-old ages. Therefore, dying with mental disease, might be interpreted as a condition for long lifespan. If this condition is cancelled, we might see increased associations between heart diseases and other causes of death, simply because some individuals would die sooner, where the associations between heart and other diseases is much more common.

Next, we observed a significant weakening of connections when disrupting associations related to endocrine, nutritional, and metabolic diseases. For example, such disruptions affected connections with respiratory diseases or mental and behavioral disorders. Previous studies have demonstrated that endocrine, nutritional and metabolic diseases develop more widespread connections with other diseases compared to other major disease groups that tend to cluster within their respective organ systems. Our analysis has revealed that connections with these diseases might exhibit a high degree of transitivity. This is due to their heightened sensitivity to disruptions in one connection, significantly impacting other connections with endocrine and metabolic diseases.

In other words, the independence of pairs with mental and metabolic diseases, which leads to a decrease in associations with other diseases, might reflect the fact that these frequently co-occurring chronic conditions “open the doors” for developing complex multimorbid patterns. However, further analysis is needed to determine if increasing the dependence in pairs with metabolic and mental diseases would have a similar effect on the dependence between mental, metabolic, and other diseases.

We also identified dependencies that primarily exist in pairwise associations, meaning that disrupting their association does not affect relationships with other diseases. This was particularly evident in the case of leading pairs involving heart diseases.

Our study has several limitations. First, we only allow the relocation of deaths to have an impact on the nodes that are direct neighbors of the disease pairs whose associations are disrupted. However, in reality the relocation of deaths can potentially influence the associations between other diseases as well. For example, changes in the association between heart and cerebrovascular diseases could potentially impact associations between other circulatory and blood diseases (as other circulatory diseases are frequently associated with both heart and cerebrovascular), as well as other disease pairs not directly involving either heart or cerebrovascular diseases. Second, we use only odds ratios, even though there are more sophisticated measures for the analysis of cause-of-death relations, such as the cause-of-death association indicator [6]. This measure is standardized for different distributions of deaths by age and cause. However, we do not use it because it is extremely time-consuming to calculate it for all possible combinations of D _i and D _j . Computation time increases dramatically if the age dimension, required to calculate cause-of-death association indicators, is added to the calculation process. Nevertheless, age certainly must play an important role, and further research is needed to evaluate how the results change if we relocate deaths occurring only in selected age groups. Third, there are limitations in the artificial approach to searching for independence between diseases. In the present paper, we were searching for an optimum by testing sequences of D _i and D _j . However, independence in contingency tables might be achieved in other ways, too. Lastly, we need to acknowledge the limitations that stem from the data we use. Multiple cause-of-death datasets are notorious for their lack of international comparability. Therefore, we should incorporate data from other countries into our future analyses. Last, the current findings do not explore in detail the specific interventions made in the contingency tables – that is, which deaths are being relocated in the minimal relocation scenario. This naturally limits the ability to derive practical implications from the findings. Future research could address this by focusing on only selected disease pairs and investigating in greater detail the optimal strategies for reducing their dependence.

Conclusions

In conclusion, studying pairwise associations between diseases without considering the complexity of cause-of-death interrelations might produce an incomplete picture of the overall COD structure. This study attempts to show that distortions introduced in the cause-of-death structure have an impact beyond the diseases under study. Changes in odds ratios between leading cause of death pairs do not happen in isolation from other diseases.

Our results can provide valuable insights for optimizing strategies aimed at preventing multimorbidity, which is recognized as one of the most significant challenges for healthcare systems in developed societies due to the complexity of treating multiple health conditions simultaneously [59]. Further steps in unveiling the robustness of the COD architecture, which are out of the scope of this paper, include incorporating the age dimension in the analysis, as well as studying the effect of introducing the reverse: adding statistically significant associations where they are not present or strengthening weak associations.