Association of Multimorbidity and Excess Mortality After Fractures Among Danish Adults

Key Points Question Are there associations between multimorbidity and excess mortality among older adults with fractures? Findings This nationwide cohort study of 307 870 adults 50 years or older with an incident fracture found chronic health disorders were common and grouped into distinct multimorbidity clusters, providing additional stratification beyond simple additive summation of diagnoses. The combination of specific multimorbidity clusters and proximal fractures was associated with a compounding mortality, conferring much greater risk of mortality than either event alone. Meaning The compound contribution of multimorbidity to postfracture mortality highlights the need for more comprehensive approaches in patients with multimorbidity; the analytical approach used for fracture can be applied to other sentinel health events.


Latent class analysis
A latent class analysis (LCA) 1 is a cluster analysis that groups binary objects so that objects in the same group are more similar to each other than those in other groups using their estimated probabilities of belonging to a specific group. This statistical clustering technique utilises maximum likelihood estimation to assimilate the observed specific comorbidities into unobserved classes that are statistically distinct and clinically meaningful 2 . Importantly, LCA allows the comparison between all possible combinations of the variables of interest, which were the specific health conditions in our analysis to be statistically tested, making the selection of optimal clusters rigorous, objective and reproducible. 2 Latent class analysis has been shown to be superior to the counts-based methods of measuring multimorbidity, which are usually not possible to distinguish between individuals with the same number but different types of diseases 3 . LCA is also more robust than the conventional clustering techniques 2 4 as not only does LCA provide rigorous statistical tests to assess model fit, class separation, but also formal criteria to make decisions to select the optimal clusters. LCA has been found to be also associated with significantly lower rate of misclassification than the k-means method, one of the most commonly used clustering methods (1.3% vs. 8%, P< 0.01) 5 . However, as LCA assigns the participants to cluster based on their probability of being in the clusters 1 2 , a risk of misclassification bias in LCA, though lower than the conventional clustering techniques cannot be completely eliminated.
Additionally, the name of the identified clusters, usually assigned by researchers for convenience in interpretation sometimes leads to a "naming fallacy" 6 wherein the cluster name might not accurately or fully reflect the cluster nature due to complexity of the cluster.
We conducted LCA 1 to determine the unique clusters of comorbidities presented at the time of fracture. Technically, we first developed a series of models in which we varied the number of latent classes from 2 to 10. We optimized the number of latent classes to provide the best fit for the data and the best separation among classes. Latent class enumeration was conducted without covariates to prevent problems related to class overestimation 7 . The optimal number of classes was chosen based on three criteria: (i) data fit, (ii) separation capacity and (iii) smallest meaningful class. We used the statistical model fit indices including log likelihood plot where the log likelihood starts to level off and other criteria, such as adjusted Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) in which the smaller value indicates better fit 8 . An entropy statistic was used to quantify the degree of separation between latent classes, with the level of ≥ 0.6 suggesting good between-group separation 9 , whereas the smallest meaningful estimated class proportion was expected to be at least 5% 8 . Once the optimal latent class model was selected, each participant was assigned to the "best-fit" cluster for which he or she had the highest computed probability of membership.

Relative survival analysis
Relative survival analysis was originally developed to determine excess mortality attributable to a specific cancer by comparing the observed all-cause mortality rate in the cancer cohort with the expected mortality rate in a comparative age-, sex-and calendar period-matched general population. All-cause deaths in the cancer cohort result from two sources: the cancer per se and other causes; whereas the expected background time-related mortality rate in the comparative general cohort is assumed to reflect the contribution of "other causes" to mortality over time. As a result, the excess mortality is then considered a robust measure of mortality attributable to the cancer or a disease of interest 10 . Cause-specific mortality data are not needed in a relative survival analysis, making it especially relevant for examining the contribution of fracture to mortality as a fracture is rarely recognized as a contributing cause of death 11 12 .
We performed relative survival analysis to quantify excess mortality attributable to the interaction between specific multimorbidity clusters and individual fracture sites under similar assumptions originally used in oncology research 10 . Excess mortality for patients in a specific multimorbidity cluster who fractured at a specific site, calculated as 1 minus its relative survival ratio can be interpreted as the proportion of patients who would die due to the combination between the specific comorbidity cluster and the individual fracture site. The relative survival ratio is the ratio of observed survival among the cohort of individuals in a specific multimorbidity cluster who fractured at a specific site to the expected survival in a comparative age-, sex-and calendar period-matched general population 10 . The observed survival was calculated using all-cause deaths of the fracture cohort; whereas the expected survival is the survival probability of similar individuals from the general population of the same age, sex and calendar period as the fracture cohort 10 . We used the Ederer II method 13 to estimate the expected mortality rate from the Danish population life tables stratified by sex, age and calendar period from the Human Mortality Database 14 . An excess mortality of zero indicates that the mortality rate observed in the cohort of patients with specific fracture in a specific cluster of comorbidities is not different from that in a comparative background population and hence that no excess mortality is attributable to the combination of the cluster of comorbidity and the fracture site.