There are six main perspectives that should be considered in the measurement of multimorbidity and comorbidity. First, the Nosological perspective, the classification of diseases, is important in defining the boundaries between disease entities that are of interest. Second, the etiological perspective, the causes of the co-existence of the diseases, is useful to establish meaningful relationship between the diseases (6, 7). Third, the chronological perspective, both the time sequence of occurrence of diseases and time span of assessment, is critical in the analysis and interpretation of multimorbidity and comorbidity data (8).

Fourth, the reference population considered in the measurement of multimorbidity and comorbidity can affect the results. A measurement of multimorbidity or comorbidity may consider the total population or sub-populations with a specific disease. Fifth, the orientation of the health system under which measurements are conducted can influence the selection of the index disease in comorbidity measurement. Finally, the professional orientation of the measurement – epidemiological/public health, clinical, or management – could affect the measurement, interpretation, and utilization of multimorbidity and comorbidity data (8).

Different aspects of multimorbidity and comorbidity can be measured from different perspectives. This review focused on measurements of magnitude, severity, pattern and burden of multimorbidity and comorbidity. When there are differences between the measurements of multimorbidity and comorbidity, these are highlighted under each section. Central to the analysis of any multimorbidity and comorbidity data is the case-by-disease matrix. In this matrix, cases make the rows and diseases make the columns.

There are two major approaches in the measurement of multimorbidity and comorbidity. The first and the most common approach is reduction of the measurement values of the coexisting diseases in to a single summary variable that can undergo any analysis similar to single disease conditions. In this approach, disease counts, severity weights, risk of death, proportion of life years lost, and disability weights of the coexisting diseases are combined in to a single summary variable. The second approach treats the coexisting diseases as multiple entities and tries to identify non-random clusters based on similarities and proximities. Cluster analysis and factor analysis are the main pattern analysis techniques that apply this approach. However, there were only few studies that have used these methods.

There are many studies that have reported the prevalence of multimorbidity and comorbidity. The overall prevalence of multimorbidity is the proportion of people with multimorbidity (more than one disease) at the time (during the period) of measurement (9). This can also be limited to a specific set or number of diseases. In the case of measurement of prevalence of multimorbidity, a case-by-disease matrix of unweighted disease scores (disease present=1; disease absent=0) is used. Most of the indicators of prevalence of multimorbidity can be derived from this matrix.

Let’s consider there are m cases and n diseases in the table below. D is the total number of diseases for each case, obtained by adding the disease variables. T is the total number of disease events in the study population. It is a simple sum of the scores of all the diseases. Variable D is the most important variable in the measurement of prevalence of multimorbidity. The frequency (FREQ) table for the variable D is the main source of the prevalence indicators of multimorbidity.

Figure 1

Table 1: The case-by-disease matrix of multimorbidity (Prevalent cases)

The main measures of prevalence of multimorbidity are:

Overall = [m-FREQ (D=1)]/m

Any Y diseases = FREQ (D=Y)/m; given Y>2

Y specific diseases=FREQ of Y in sum of specific diseases/m

More than Y diseases = 1- Cumulative FREQ (D<Y) (cumulative FREQ in proportion)

Average number of diseases per person = T/m

The prevalence of comorbidity measures the proportion of people with the index disease who have comorbid disease(s) (10). Note that the reference population is people with the index disease. The prevalence of comorbidity may be specific to a single comorbid disease, or a defined set of multiple comorbid diseases. The same method used in the prevalence of multimorbidity can be applied to prevalence of comorbidity, except that the index disease scores (which should be present=1 for all cases) are not included in summation of the scores to obtain D. As one additional disease coexisting with the index disease is enough to define a comorbidity, the overall prevalence of comorbidity will be [m-FREQ (D=0)]/m. Once the study subjects are limited to those with the index disease and scores of the index disease are not added to the total score, calculation of all the other indicators of prevalence of comorbidity will be similar to that of multimorbidity.

For two co-occurring diseases, the prevalence of multimorbidity and comorbidity can be estimated from the prevalence ratio (11) and the prevalence of one of the diseases in the general population. Consider the following two-by-two table for the prevalence of two diseases.

Figure 2

Table 2: Two-by-two table for prevalence of two diseases

The prevalence of multimorbidity among all cases from the above 2X2 table is the number of cases with both diseases (a) divided by the total number of cases (a+b+c). If the total population is considered as a reference, the prevalence of multimorbidity will be a/n. on the other hand, the prevalence of comorbidity (disease 2) among those with the index disease (disease 1) will be a/(a+b). If the prevalence ratio (PR) of prevalence of disease 2 among those with disease 1 as compared to those without it is known, the prevalence of comorbidity (P_C) will be: P_C=PR*P₂ where P₂ is the prevalence of disease 2 among those without disease 1 (c/(c+d)).

The incidence of multimorbidity is the development at least two disease entities in a healthy individual or the development of at least one additional disease in an individual with a pre-existing disease (12). The same case-by-disease matrix for incident diseases and incident cases can be used to measure the incidence of multimorbidity. The final score for analysis in this case will be the difference between the total score for new diseases (D) and the score of pre-existing diseases at baseline (B).

Figure 3

Table 3: Case-by-disease matrix of multimorbidity (incident cases)

Let’s consider that m1 and m2 are the number of cases with pre-existing disease and without pre-existing disease respectively, and m is the total number of new diagnoses. The main incidence indicators of multimorbidity will be:

In those with pre-existing disease) = [m-FREQ (D-B=0)]/m₁

In those without pre-existing disease) = [m-FREQ (D-B<2)]/m₂

Any Y diseases = FREQ (D-B=Y)/m; for Y>2

Y specific diseases = FREQ of Y in D-B of specific diseases

More than Y diseases = 1- Cumulative FREQ (D-B<Y); cumulative FREQ is in proportions

Average number of new disease per person = D-B total /m

The incidence of comorbidity is the development of comorbid condition(s) among people with an index disease (13). A similar case-by-disease matrix and indicators as the prevalence of comorbidity can be used but in this case with incident cases of comorbid conditions.

For two diseases, disease 1 and disease 2, the incidence of multimorbidity is the sum of the incidence of disease 2 among those with disease 1, the incidence of disease 1 among those with disease 2, and the incidence of disease 1 and 2 (both newly diagnosed during follow up period) among those free from disease 1 and disease 2 at baseline.

For the incidence of a single comorbid disease, the two-by-two table will be useful. The incidence of the comorbidity will be a/a+b. The relative comorbidity risk (RcR) of the comorbid disease can be computed using the same method as exposure and disease relationships (RcR= [a/(a+b)/ c/(c+d)]. This relative risk shows the risk of the comorbid disease among those with the index disease as compared to those without the index disease.

Figure 4

Table 4: Two-by-two table for incidence of comorbidity

The purpose of analysing the pattern of diseases is generally to identify relevant multimorbidity groups from a set of diseases (20, 21). The underlying characteristic for a cluster of diseases could be epidemiological, pathogenetic or management related similarities. Identification of diseases that tends to occur together has important clinical and public health implications (22).

From the axis of cases, analysis of patterns using either cluster analysis or Q-factor analysis yields clusters of cases/patients with similar underlying disease conditions (23). The technique will identify sub-groups of populations of complex patients with specific combinations of coexisting diseases. The patterns of diseases within each group can then be described. This is important for more targeted management of patients with complexities.

Both cluster analysis and factor analysis can be used to identify non-random groups of cases and diseases. Commonly, cluster analysis is used for cases (rows) and factor analysis for variables (columns). But a dataset can be transposed to fit with either of the methods.

In case of patterns of comorbidities, the same techniques can be used. But the application of these methods will be limited to the comorbid conditions (additional diseases) among those people with the index disease.

Disease-specific mortality risk, the number of deaths among people with a specific disease divided by the total cases of the same disease in a defined period, can be used to estimate mortality risk from multimorbidity/comorbidity. For the calculation of disease specific mortality risk, the number of deaths from a disease (the numerator) can be easily obtained from available data or can be estimated from the cause-specific mortality rate (CSMR). The total number of cases of the disease (the denominator) is usually available from reports or can be estimated from prevalence figures.

This disease-specific mortality risk (DSMR) shows the risk (probability) of death from a specific disease in an individual with that specific disease in a defined period. Deaths among cases of a disease can be due to the disease itself (confirmed deaths) or due to other causes (other cause of deaths). The DSMR considers only the deaths that are due to or attributed to the disease.

Figure 6

Table 6: The case-by-disease matrix of disease-specific mortality risks

As death is a single time event, and there is usually one primary case of death, risk of mortality of death from competing causes of death can be considered to be additive (cumulative). The fact that a single disease ultimately claims life even though other coexisting disease can have important roles favors additive approach. Assuming that competing risks of death are independent, the total risk of death of an individual from multimorbidity will be the sum of all the DSMRs of the coexisting diseases. This sum will be in the form of DSMR. This mortality risk will be unique to specific combinations of diseases i.e. the DSMR for a person with two diseases is different from a person with three and so on. In general: DSMR (multimorbidity) = DSMR₁ + DSMR₂+ ….DSMR_n.

The total DSMR multiplied by the number of cases of multimorbidity of the specified disease combination will provide the estimated number of deaths among those cases during a specified period. This number of deaths can be used to estimate the cause-specific mortality rate of the multimorbidity among the total population.

After the DSMR values are added, every individual with multimorbidity will have a single summary risk of mortality from all the diseases he or she have. The summary variable can be considered as an outcome variable for further analysis. However, it should be noted that a constant risk of mortality from coexisting diseases is assumed in the estimation of DSMR.

Years of Life lost (YLL) due to death from a disease is the difference between life expectancy (LE) and age at death (24). Proportion of life years lost (PLL) due to premature death from a disease as calculated by dividing the YLL by LE (PLL=LL/LE) can be considered as an indicator of the Severity of a disease in causing premature death. The YLL should be discounted and adjusted accordingly before being used for calculating PLL.

Assuming independence between coexisting diseases, there are two main possible apparoaches of combining PLL: additive approach and Multiplicative approach (25). The additive approach assumes the PLLs are additive. The PLL of a patient with multimorbidity will be the sum of the PLL of each of the coexisting diseases. The resulting PLL will be unique to specific combination of diseases.

With the same assumption of independence between coexisting diseases, the multiplicative approach provides an adjusted value that is less than the sum but greater than each of the individual diseases (26). In this approach, the PLL of multimorbidity will be between the PLL of the more severe disease and the sum of the PLL of all the co-occuring diseases. However, a synergy (interaction) factor may be considred if the assumption of independence is not considered. The general formula for the multiplicative approach is one minus the product of the complements of the weights: PLL (multimorbidity) = 1-(1-PLL₁)*(1-PLL₂)*…(1-PLL_n)

Figure 7

Table 7: The case-by-disease matrix for PLL

Once the PLL of the multimorbid situation is determined, it can be multiplied by the LE to find the YLL of the multimorbidity (YLL= PLL*LE) (4). The resulting value can be multiplied by the total number of deaths in a specific age to estimate the PYLD at population level.

Expected years of survival (EYS) for an individual with multimorbidity can be estimated from the combined PLL of the coexisting diseases. The EYS is the difference between life expectancy (LE) and PYLL (EYS=LE-PYLL).

Specific disability weights have been developed for different diseases (27). In the scale of disability weights, 1 corresponds to death and 0 shows ideal health free from any disease. The disability weights shows the fraction of years lived with the disease that are lost due to the effect of the disease. Assuming indepedence between coexisting diseases, the disability weights can be combined using the additive and multiplicative approach to estimate the disability weight(Dw) of a multimorbid condition. In the additive approach Dw (combined)=Dw₁+Dw₂+….Dw_n; and in the multiplicative appraoch Dw (combined) = 1-(1-Dw₁)*(1-Dw₂)*…(1-Dw_n).

Figure 8

Table 8: The case-by-disease matrix of PYLD

The PYLD of multimorbidity can then be obtained by multiplying years lived with disability (YLD) by the combined disability weight. The total PYLD of multimorbidity at population level will be: PYLD=YLD*Dw* Prevalence.

Prevalent years lived in full health (PYLH) for an individual with multimorbidity can be estimated from the combined Disability of the coexisting diseases. The PYLH is the difference between total years lived with disability (TYLD) and PYLD (PYLH=TYLD-PYLD).

Total years Lived in full health (TYLH) for an individual with multimorbidity can be estimated from EYS and PYLD. The TYLH is the difference between expected years of survival (EYS) and PYLD (PYLH=EYS-PYLD).

The total burden of multimorbidity can determined by DALY, the sum of Potential Years of Life Lost (PYLL) and Prevalent Years Lived with Disability (PYLD) (28). The sum of DALYs for all individuals with the comorbidity during a year will constitute the total burden of the multimorbidity in a population. The DALY of multimorbidity will be the sum of PYLL and PYLD obtained in the above estimations: DALY= PYLL+PYLD

Healthy life years (HLL) will be the difference between life expectancy and disability adjusted life years: HLL=LE-DALY. This will be the total number of healthy years that an individual is expected to live.

In the estimation of burden of comorbidities, the same principles of as the estimation mortality risks, PYLL, PYLD and DALY that are applied in multimorbidity can be used. But in this case, the estimation will be limited to the burden of comorbid conditions (additional diseases) among those people with the index disease.