Using latent class analysis to model prescription medications in the measurement of falling among a community elderly population

Latent Class Analysis (LCA) is a statistical method for finding subtypes of related cases (latent classes) from multivariate categorical data [1]. The most common use of LCA is to discover case subtypes (or confirm hypothesized subtypes) based on multivariate categorical data [1–4]. LCA is well suited to many health applications where one wishes to identify disease subtypes or diagnostic subcategories [1–4]. LCA models do not rely on traditional modeling assumptions (normal distribution, linear relationship, homogeneity) and are therefore, less subject to biases associated with data not conforming to model assumptions [1–4]. In this paper, we demonstrate the utility of LCA for the prediction of falls among community dwelling elderly.

Falls among the elderly are a major public health concern. Research on falls and fall-related behavior among the elderly has found that falls are the leading cause of injury deaths among individuals who are over 65 years of age [5–11]. Research has shown that sixty percent of fall-related deaths occur among individuals who are 75 years of age or older [5–11]. Demography research estimates that by 2030, the population of individuals who are 65 years of age or older will double and by 2050 the population of individuals who are 85 years of age or older will quadruple [5–11].

Predicting elderly falling can be complex and often involves heterogeneous markers. Therefore, the identification of more homogeneous subgroups of individuals and the refinement of the measurement criteria are typically inter-related research goals. Appropriate statistical applications, such as latent class analysis, have become available for researchers to model the complex heterogenous measurements.

Latent class models are used to cluster participants. This type of model is adequate if the sample consists of different subtypes and it is not known before-hand which participant belongs to which of the subtypes [2]. The latent categorical variable is used to model heterogeneity. In the classic form of the latent class model, observed variables within each latent class are assumed to be independent, and no structure for the covariances of observed variables is specified [2].

LCA is one of the most widely used latent structure models for categorical data [12]. LCA differs from more well-known methods such as K-means clustering which apply arbitrary distance metrics to group individuals based on their similarity [13–15]. LCA derives clusters based on conditional independence assumptions applied to multivariate categorical data distributed as binomial or multinomial variables [16, 17]. Using statistical distributions rather than distance metrics to define clusters helps in evaluating whether a model with a particular number of clusters is able to fit the data, since tests can be performed to observed (ni) versus model expected values (mi), using exact methods as recommended [18, 19]. This comparison gives rise to a χ ² test of global model fit, in which significant values indicate lack of fit [20]. Here lack of fit means deviation of (model) predicted (m) frequencies from observed frequencies (n) [16].

where ${\mathrm{\pi }}_{\mathrm{t}}^{\mathrm{X}}$ denotes the probability of being in a latent class (t = 1,2,…,T) of latent variable X; ${\mathrm{\pi }}_{\mathrm{it}}^{\mathrm{A}|\mathrm{X}}$ denotes the conditional probability of obtaining the i th response from item A, from members of class t, i = 1,2,…,I; and ${\mathrm{\pi }}_{\mathrm{jt}}^{\mathrm{B}|\mathrm{X}}{\mathrm{\pi }}_{\mathrm{kt}}^{\mathrm{C}|\mathrm{X}}{\mathrm{\pi }}_{\mathrm{lt}}^{\mathrm{D}|\mathrm{X}}{\mathrm{\pi }}_{\mathrm{mt}}^{\mathrm{E}|\mathrm{X}}{\mathrm{\pi }}_{\mathrm{nt}}^{\mathrm{F}|\mathrm{X}}{\mathrm{\pi }}_{\mathrm{ot}}^{\mathrm{G}|\mathrm{X}}$, j = 1,2,…,j k = 1,2,…,k l = 1,2,…,l m = 1,2,…,m n = 1,2,…,n O = 1,2,…,O are the corresponding conditional probabilities for items B,C,D,E,F, and G respectively.

We are testing the hypothesis that a two-class distal relationship (fall/no fall) can explain the relationship among the biomedical, pharmacological and demographic variables. Proper analysis of this data requires the understanding of two interdependent outcomes.² First, the binary outcome is whether or not the event occurred (fall or no fall) and second what covariates increase or decrease the likelihood of this occurrence. The four specific aims of the study are to identify items that indicate classes, estimate class probabilities, relate the class probabilities to covariates, and predict a distal outcome (fall/no-fall) based on class membership. We model this process through the application of latent class analysis (Figure 1).

The data set was taken from the State of Florida’s Elder Affairs Office. All variables were physician diagnosed and recorded in an electronic dataset using appropriate ICD-9 codes. Variables included in the database were:

This paper demonstrated the utility of LCA in the measurement of falling among community-dwelling elderly. The basic idea underlying LCA is that variables differ across previously unrecognized subgroups [24]. These subgroups form the categories of a categorical latent variable. Given the potential for confounding among the study variables, latent class analysis holds great promise.

The six-class solution was statistically sound and provided a relatively straightforward interpretable number of classes. The interpretation of a LCA relies on both the statistical indices and the practical interpretation of the classes. In our example, the statistical indices strongly point toward a six factor model. The classification accuracy for the model was very good. Furthermore, we were able to define each latent class, which provides researchers and practitioners practical implications of the analysis.

Medication usage helped differentiate the latent classes. Subjects in latent class one have higher probabilities of possessing the seven medical conditions than subjects in latent class two; yet, subjects in latent class two possess similar rates of falling. This may be explained by the number of medications that class two is taking (7.5 vs. 4.7). Similarly latent class three and six are both defined as the healthy groups. Differentiating the two groups is the number of medications taken by subjects in latent class three vs. latent class six (7.8 vs. 4.3).

It also true that the type of medications subjects are taking is impacting their probability of falling. This can be demonstrated for latent class one. Holding age and number of medications at their means, females with a drug falling measure of 1.50 [i.e., Thioridazine & Amoxapine] have a 80% greater chance of falling than the same subjects with a drug falling measure of -0.50 [i.e., Imipramine & Methadone] (p < 0.05). We stress that the latent classes are composite variables, so one should not look at medications in isolation. As one would expect, the two latent classes with the highest probability of falling also possess the highest drug falling measure and the worst medical conditions.

As was demonstrated in past research correspondence analysis is a useful tool for researchers examining prescription medication data [25]. Combining LCA with CA provides researchers a powerful tool for data reduction analysis. We demonstrated that this approach was effective for finding relevant subgroups with a heterogenous at-risk population for falling. Nevertheless, the results may not be relevant to other countries, with different lifestyles and different socio-economic status.

LCA and CA possess limitations which make its application to this type of modeling dependent on replication studies. The specific limitations include (1) Classes not known prior to analysis, and (2) Class characteristics not know until after analysis. Both of these problems are related to LCA being an exploratory procedure for understanding data. Furthermore, the items were not designed for a LCA approach. A latent class study designed a-priori may offer better solutions. We would also suggest that additional items (medical) be used which have demonstrated to impact falling among elderly community dwellers--such as eye disease and pain.