Bivariate Displays for Categorical Data, Contingency ...
Bivariate Displays for Categorical Data, Contingency Tables and Correspondence Analysis
EXAMPLE - HISTOLOGICAL TYPE of HODGKIN’S DISEASE and
RESPONSE TO TREATMENT
Data File: Hodgkins.JMP
Key Words: Contingency table, conditional probabilities, mosaic plot, correspondence analysis
Topics: Medicine
The purpose is to understand the relationship between histological type and response to treatment.
The variables in the data file are:
o Histological type - LP = lymphocyte predominance, NS = nodular sclerosis, MC = mixed cellularity, and LD = lymphocyte depletion
o Response - Positive, Partial, None
o Freq - number of patients in a given histological type and response category
Interest centers on the relationship, if any, between histological type of Hodgkin’s disease and response to standard treatment.
Analysis in JMP
By using the Distribution option we begin by examining univariate displays for both histological type and response to treatment. The resulting bar graphs from JMP is shown on the following page. We have clicked on the patients with lymphocyte predominance to observe their response to treatment distribution. All graphical displays in JMP are “linked”, i.e. when we highlight certain observations in one plot they are automatically highlighted in any other plots or graphs that we currently have open. Even plots in different windows are linked.
[pic]
From the above display we can see that the most common response to treatment for patients with lymphocyte predominance is positive. The frequency distribution tables for both variables are also shown.
Will now use the Fit Y by X option to examine the relationship between Histological Type (X) and Response (Y). The mosaic plot and contingency table for these data are shown below.
Mosaic Plot of Response vs. Histological Type
[pic]
From the mosaic plot we can clearly see that individuals with LP or NS have the highest proportion of subjects with positive response to treatment, while the LD has the largest percentage of patients with no response to treatment. The contingency table for these data is shown below with only Row% added to each cell (i.e. the Total % and Col % options have been unselected.). These percentages can be interpreted as the conditional chance /probability of each response type given the histological type, i.e.
P(Positive| LP) = “Probability of positive response to treatment given the patient has lymphocyte predominant Hodgkin’s (LP)” = .7115
P(None|LD) = “Probability of no response to treatment given the patient has lymphocyte depletion Hodgkin’s” = .6111
We will introduce conditional probabilities more formally in Chapter 3.
Contingency Analysis of Response By Histological type
[pic]
Finally we use correspondence analysis to examine the relationship between response to treatment and histological type. To do this select Correspondence Analysis from the pull-down Contigency Table menu. The results are displayed below.
Correspondence Analysis for Hodgkin’s Data
[pic]
From the above plot we can see that no response and LD are most closely associated while MC is associated with either partial or positive response and LP/NS individuals are most closely associated with positive response to treatment.
-----------------------
|LD is least treatable. |
MC, LP & NS are the most treatable forms of Hodgkin’s Disease.
LD is the least treatable.
This pull down menu allows you to select what numbers will be displayed in each cell of the table. Here only Count and Row % are selected.
This pull-down menu allows you to choose which numbers will be displayed in each cell of the table. Here only Count and Row % have been selected.
|Treatable forms of Hodgkin's |
|Disease |
|(MC,LP & NS) |
| |
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