Case study using data mining to find potential customers for an orthopedic client.

1. Sales of Orthopedic Equipment
Xiaomeng (Mina) Chai
11/25/2014

2. Client’s Background
• Client:
a large manufacturer of orthopedic
equipment in the United States
• Customer base:
almost all hospitals over the 50 states

3. Client’s Products
• Orthopedic parts and equipment
• Medications administered in the process of
surgery, rehabilitation, and recovery

4. The Company Thinks …
• SALES!
– High sales
– Moderate sales (further sales potential)
– Little or no sales (substantial potential gain)

5. Imagine …

6. We think…
• ORTHOPEDIC ACTIVITIES!
– Small general hospitals (little or no interest)
– Large general hospitals (moderate interest)
– Specialized hospitals (main target group!)

7. Objective
• Increase sales...
…in the more desirable groups!
• How?
– Identify target hospitals
– Study them individually
• Another objective: other ways to classify
hospitals?

8. Dataset
All U.S. hospitals are in the dataset:

9. Variables
A subset of variables is already selected

10. Variables

11. Methodology
• Data Mining
– Dimension Reduction
• Factor Analysis
• Principal Component Analysis
– Cluster Analysis
• Hierarchical Clustering
• Centroid Methods
• Regression analysis

12. Data Mining
• Overall goal—to extract information from a data set and
transform it into an understandable structure for further
use. (Wikipedia)
• The objective of data mining is to identify nuggets, small
clusters of observations in these data that contain
unexpected, yet potentially valuable, information. (The
author)

13. Data Mining

14. Approach to data mining
1. Dimension (variable) reduction
– Principle components
– Factor analysis
1. Data segmentation and selection
– Cluster analysis
– Tree methods
– Neural nets
1. Data analysis of interesting segments

15. This case study

16. PART 1:Select Market Segments
• Find state or group of states (at least 300 hospitals)
– IL, IN, MI, WI are selected (590 hospitals)

17. Transformation
Log or square root transformations are performed

18. Transformation
Before After

19. so far…

20. Dimension Reduction
• Two stages factor analysis
– Operational factor (HIP95, KNEE95, HIP96, KNEE96,
and FEMUR96)
– Size factor (BEDS, OUTV, ADM, SIR, TH, and TRAUMA)
and rehab factor (RBEDS and REHAB)

21. Factor Analysis--stage1

22. Factor Analysis—stage2

23. Factor Analysis: Rotate?
• More interpretable results.
• Orthogonal rotation methods (VARIMAX) is commonly
used.
e.g. Look at variable X33 here:

24. Factor Analysis—stage2

25. Principal Component Analysis--stage 1

26. Principal Component Analysis--stage 2

27. R

28. Factor Analysis in R

29. Factor Analysis in R

30. Factor Analysis in R

31. PCA in R

32. PCA in R

33. PCA in R

34. PCA in R

35. PCA in R

36. Factor Analysis
13 variables are divided into 3 factors:

37. Textbook Question:
Graph the main principal components. Are there any visible clusters?
The banding is relatively vertical, REHAB is affecting factor 2 (RBEDS and REHAB).

38. so far…

39. Cluster Analysis
• To determine the best cluster to concentrate on
for improving sales.
• Two popular methods
– Hierarchical Clustering (interpoint distance)
• Single linkage
• Average linkage
• Ward
– Centroid Methods
• K-means algorithm
• Partitioning Around Medoids (PAM)

40. Cluster Analysis
• Hierarchical Clustering:
1. Start with a cluster at each sample point
2. At each stage of building the tree the two closest clusters joint
to form a new cluster

41. Cluster Analysis
• Centroid Methods (K-means algorithm)
1. K seed points are chosen and the data is distributed
among k cluster
2. At each step, switch a point from one cluster to
another if the R2
is increased
3. Clusters are slowly optimized by switching points
until no improvement of the R2
is possible

42. Cluster Analysis
• Centroid Methods (K-means algorithm)

43. Cluster Analysis
• Partitioning Around Medoids (PAM)
1. Search for k representative medoids
2. K clusters are constructed by assigning each point
to the nearest medoid
3. The goal is to find k medoids which minimize the
sum of the dissimilarities of the observations to their
closest representative medoid.

44. Cluster Analysis
• PAM VS K-means
– PAM operates on the dissimilarity matrix
– PAM minimizes a sum of dissimilarities instead of a
sum of squared Euclidean distances
– Silhouette plot (select the optimal number of clusters)

45. Cluster Analysis
• To determine the best cluster to concentrate on
for improving sales.
• Two popular methods
– Hierarchical Clustering (interpoint distance)
• Single linkage
• Average linkage
• Ward
– Centroid Methods
• K-means algorithm
• Partitioning Around Medoids (PAM)

46. Cluster Analysis
…
…

47. Cluster Tree

48. PAM in R

49. PAM in R
• Silhouette width:
si=(bi-ai)/max(ai,bi)
Large Si (almost 1) are very well clustered

50. PAM in R

51. Cluster Analysis

52. Cluster Analysis

53. Cluster Analysis in R

54. Cluster of Interest

55. so far…

56. Part 2-Estimate Potential Sales
• Part1 – Select Market Segments : DONE
• Part2 – Estimate Potential Sales

57. Regression Analysis

58. Regression Analysis

59. Regression Analysis
• Hospitals with large negative residuals:
HID CITY STATE RESIDUAL Gain
087043 Chicago IL -2.8766 68.590
915042 South Bend IN -1.7989 16.440
016045 Beloit WI -2.5633 24.893
020042 Columbus IN -2.5146 34.710
078045 Madison WI -2.2309 59.362
109043 Chicago IL -1.9317 47.980
262043 Peoria IL -2.5952 90.593

60. Thank you and Happy Holiday!