26 uniform development of the whole drug market or diverse developments in market segments are assumed, it is essential to scrutinise whether the drug market must be subdivided. For this we apply principal components and cluster analysis in the following. 2.4.1. Data All pharmaceutical consumption and expenditure data used stem from the SHI Drug Index, which distinguishes not only between gender and 19 age groups but also between the 88 indication areas of the “Red List”: the pharmaceutical catalogue of certi- ? ed drugs in Germany.10 Each indication area represents a group of drugs with the same main application ? eld, i.e. they are used against similar disturbances of health. Because some of the groups are unoccupied and, due to changes in the classi? cation of the indication areas for the observed period between 1988 and 2004, persistent data for only 50 groups are available – covering around 95 % of whole consumption and 90 % of total drug expenditure, respectively. Hence the analysis has been divided for men and for women by considering data differentiated into 50 indication areas and 19 age groups from 1988 to 2004. For this reason, it is based on 16,150 observations in each case. All data have been standardised by use of mean values and standard deviations. Since expenditure is highly affected by various parameters which could conceal the in? uence of ageing, the analysis does not refer to drug expenditure but directly to consumption, using De? ned Daily Dosages (DDDs). A DDD represents “the assumed average maintenance dose per day for a drug used for its main indication in adults” (WHO 2006). Taking DDD as a technical scale unit instead of drug expenditure offers the substantial advantage that a de? ned quantity of an active substance is directly measured. It enables the observation of drug consumption broadly unattached from alterations in package sizing, prices or dose rates. 2.4.2. Principal Components Analysis The idea is that it should be possible to compose groups of pharmaceuticals whose members are characterised by similar demand attributes. Since there exists a great variety of different causes for the occurrence of diseases, a theoretical method is needed to explicitly extract the in? uence of ageing. Therefore, we use principal components analysis (PCA) – a mathematical technique used to reduce the number of variables and diseased persons as well as the number of long term care patients increases. As a result, the expenditure pro? les would develop somewhere between the predictions of medicalisation and compression theses. 10 The “Red List” is published annually on behalf of the “German Pharmaceutical Industry Association” (BPI), the “German Association of Research-Based Pharmaceutical Companies” (VFA), the “German Generics Association” and the “Federal Association of Pharmaceutical Manufacturers” (BAH). 27 without losing much information by means of identifying structural patterns in data.11 Table 2.1 shows the results of the PCA. Table 2.1: Results of Principal Components Analysis (First 12 Components, Rounded Values). Men Component 1 2 3 4 5 6 7 8 9 10 11 12 Eigenvalue 30.63 7.30 3.30 1.62 1.49 0.99 0.61 0.52 0.41 0.35 0.33 0.29 Variance Proportion 0.61 0.15 0.07 0.03 0.03 0.02 0.01 0.01 0.01 0.01 0.01 0.01 Cumulative Proportion 0.61 0.76 0.82 0.86 0.89 0.91 0.92 0.93 0.94 0.94 0.95 0.96 Women Component 1 2 3 4 5 6 7 8 9 10 11 12 Eigenvalue 28.82 8.07 3.88 2.12 1.45 1.15 0.69 0.66 0.46 0.42 0.33 0.26 Variance Proportion 0.58 0.16 0.08 0.04 0.03 0.02 0.01 0.01 0.01 0.01 0.01 0.01 Cumulative Proportion 0.58 0.74 0.82 0.86 0.89 0.91 0.92 0.94 0.95 0.95 0.96 0.97 Sample: 16,150 observations in each case (consumption pro? les 1988 - 2004; 50 indication areas; 19 age groups). Both cases (men and women) show fairly similar outcomes: the ? rst component achieves a variance proportion of around 60 %, and an eigenvalue of around 30 is suf- ? ciently satisfying. With a cumulative proportion of around 75 %, only two components are necessary to explain three-quarters of drug consumption. From the third component, the additional variance proportion decreases signi? cantly and reaches 0.01 after seven components. Consequently, the ? rst two components contain the most information and therefore can be used as a summary of the consumption data. In other words: there exist two variables which are suf? cient to explain three-quarters of drug consumption. But what kind of in? uences do these two variables represent? The ? rst supposition is self-evident: the per capita age-related drug consumption pro? le (in the following referred to as “consumption pro? le”) suggests “age” as the most important determinant for drug demand.12 Hence it must be guessed that “agedependency” is the variable that causes the high variance proportion of the ? rst component. To check this hypothesis, we take a look at the component matrix (? gure 2.4a and 2.5a for the ? rst component; graphic presentation). The entries in this matrix, loadings, are correlations between the components and the indication areas consi- 11 All applied econometric and statistic methods in this chapter have been compiled with the statistical software package “EViews” and the computer language “R”. For more information about principal component analysis see e.g. Hartung and Elpelt (1999). 12 The consumption pro? le shows a shape comparable to the expenditure pro? le. See ? gures A.2.1 and A.2.2 in the appendix to this chapter. 28 dered. This means that if “age-dependency” is, indeed, the most important explaining variable, component 1 should possess high loadings on indication areas consisting of drugs which are primarily prescribed in higher ages and low loadings on indications areas which members are not, in general, more consumed by older people. Therefore, we compare the loadings of component 1 with the DDD consumption ratio between the age groups 80 - 84 and 20 - 24 of each indication area. High values of the consumption ratios indicate strong age-dependency in consumption of the respective indication area. Figure 2.4 shows the results.13 As a matter of fact, both component loadings and consumption ratios exhibit fairly close results, i.e. most indication areas with high values on component 1 also show high consumption ratios. Consequently, it can be assumed that “age-dependency” represents the underlying explaining variable of component 1. 13 List of abbreviations on pages 13 - 14. 29 F ig ur e 2.4: C om po ne nt 1 ( M en ). a. Loa di ng s. -0 ,1 -0 ,0 50 0, 050, 1 0, 150, 2 Analg. Antiall. Antianae. Antiarr. Antibio. Antico. Antidia. Antiem. Antiep. Antihyper. Antihypo. Antimigr. Antimyc. Anti-Park. Antiphl. Antisp. Antithr. Antitus. Beta Bl. Blood C. Bronch. Cardiac Caries Coronar. Corticos. Cytok. Dermat. Diuret. Gastro. Gynec. Haem. Hypnot. Influen. Infusions Laxat. Lipid Low. Minerals Muscel R. Nasal Ophtal. Oroph. Otolog. Podagr. Psycho. Sex H. Thyroid Urolog. Venous Vitam. Wounds b. C on su m pt io n R at io s (80-84 / 20-24) . 0246810 Analg. Antiall. Antianae. Antiarr. Antibio. Antico. Antidia. Antiem. Antiep. Antihyper. Antihypo. Antimigr. Antimyc. Anti-Park. Antiphl. Antisp. Antithr. Antitus. Beta Bl. Blood C. Bronch. Cardiac Caries Coronar. Corticos. Cytok. Dermat. Diuret. Gastro. Gynec. Haem. Hypnot. Influen. Infusions Laxat. Lipid Low. Minerals Muscel R. Nasal Ophtal. Oroph. Otolog. Podagr. Psycho. Sex H. Thyroid Urolog. Venous Vitam. Wounds 30 F ig ur e 2.5: C om po ne nt 1 ( W om en ). a. Loa di ng s. b. C on su m pt io n R at io s (80-84 / 20-24) . -0 ,1 -0 ,0 50 0, 050, 1 0, 150, 2 Analg. Antiall. Antianae. Antiarr. Antibio. Antico. Antidia. Antiem. Antiep. Antihyper. Antihypo. Antimigr. Antimyc. Anti-Park. Antiphl. Antisp. Antithr. Antitus. Beta Bl. Blood C. Bronch. Cardiac Caries Coronar. Corticos. Cytok. Dermat. Diuret. Gastro. Gynec. Haem. Hypnot. Influen. Infusions Laxat. Lipid Low. Minerals Muscel R. Nasal Ophtal. Oroph. Otolog. Podagr. Psycho. Sex H. Thyroid Urolog. Venous Vitam. Wounds 0246810 Analg. Antiall. Antianae. Antiarr. Antibio. Antico. Antidia. Antiem. Antiep. Antihyp… Antihypo. Antimigr. Antimyc. Anti-… Antiphl. Antisp. Antithr. Antitus. Beta Bl. Blood C. Bronch. Cardiac Caries Coronar. Corticos. Cytok. Dermat. Diuret. Gastro. Gynec. Haem. Hypnot. Influen. Infusions Laxat. Lipid … Minerals Muscel … Nasal Ophtal. Oroph. Otolog. Podagr. Psycho. Sex H. Thyroid Urolog. Venous Vitam. Wounds 31 At ? rst sight component 2 shows a more heterogeneous picture (see ? gure A.2.3 in the appendix). To speculate about the underlying in? uencing variable, we concentrate on indication areas which possess particularly high or low component loadings. We take a look at indication areas with loadings beyond 0.1 and below -0.1. This apportionment displays a surprisingly clear pattern (see table 2.2). With the exception of antiallergics (Antiall.) for men and cardiac agents (Cardiac) for women, all indication ? elds with loadings of more than 0.1 represent disturbances of health which typically occur erratically: antibiotics (Antibio.), antiemetics (Antiem.), antitussives (Antitus.), in? uenza and common cold agents (In? uen.), laxatives (Laxat.), otologicals (Otolog.), nasal preparations (Nasal), and vitamins (Vitam.) are usually used against viral infection, ? u and temporary sickness. The main indication area of antimycotics (Antimyc.) and dermatological preparations (Dermat.) are fungal infections of the skin, whereas dental care preparations (Caries) and oropharyngeal agents (Oroph.) are against oral infections. Infusions and wound care material (Wound) are often associated with accidents. Table 2.2: Indication Areas with Low or High Loadings on Component 2. Men Women < -0.1 > 0.1 < -0.1 > 0.1 Antico. Antiall. Antiep. Antibio. Antiep. Antibio. Lipid Low. Antiem. Lipid Low. Antiem. Bronch. Antimyc. Antimigr. Antimyc. Cytok. Antitus. Thyroid Antitus. Gynec. Cardiac Caries Antimigr. Caries Dermat. Sex H. Dermat. Infl uen. Thyroid Infl uen. Infusions Infusions Laxat. Laxat. Oroph. Oroph. Otolog. Otolog. Nasal Nasal Vitam. Vitam. Wounds Wounds In contrast to these, indication areas with very low loadings represent chronic diseases such as epilepsy (Antiep.), hyper- and hypothyroidism (Thyroid), cardiovascular diseases (Antico., Lipid Low.), migraine (Antimigr.), asthma (Bronch.) and cancer (Cytok.) or are usually continuously applied like sex hormones (Sex H.) and gynecologics (Gynec.).14 Consequently, there is a strong indication that variable 2 represents 14 For more information on the main application areas see Schwabe and Paffrath (2006). 32 chronic and non-chronic diseases respectively. Since higher values stand for nonchronic diseases, we call this variable “acuteness”. 2.4.3. Cluster Analysis Referring to the results of the PCA, each indication area can be displayed in a twodimensional space with “age-dependency” on the x-axis and “acuteness” on the yaxis. The scatter-plot (? gure 2.6) gives the reason for the presumption that the indication areas can be classi? ed into different groups. For this a cluster analysis based on the component loadings was conducted. This was done by using the Euclidean distance as the distance measure and Ward’s method as the linkage rules.15 Gynecologicals for men as well as antiallergics, antianaemics and sex hormones for women have been excluded as outliers. Applying the Milligan/Cooper criterion, we respectively identi? ed 6 groups for men and 5 for women.16 For comparability reasons an unoccupied female group 3 has been included. Figure 2.6: Indication Areas and Results of Cluster Analysis in a Two-Dimensional Space. Men -0,3 0,4 -0,1 0,2 Co m po ne nt 2 (a cu ten es s) Component 1 (age-dependency) 1 2 4 5 3 6 15 For more information about cluster analysis see e.g. Hartung and Elpelt (1999). 16 Originally the Milligan/Cooper-Criterion suggested 8 groups for men and 9 for women. After pooling of close adjoining clusters, 6 groups for men and 5 for women remain. The hierarchical tree plots (Dendrogramms) are presented in the appendix (? gure A.2.4).