Ординатура / Офтальмология / Английские материалы / Principles Of Medical Statistics_Feinstein_2002

Figure 16.29 is a counterpart, in two groups, of the useless display of complementary proportions shown earlier in Figure 9.1 for one group. The information for both groups could have been communicated more simply and directly with a straightforward comparison of the constituent numbers.

Figure 16.30 has been nominated for an “Oscar” in malcom-

16.3 Displaying Binary Variables

The frequency counts for a binary variable in two groups form a 2 2 table, and each group’s results are easily summarized as a binary proportion. The main visual decision is how to orient the rows and columns of the table itself.

16.3.1Orientation of 2 × 2 Table

If the research has the cause–effect architectural structure of a randomized trial, observational cohort, or etiologic case-control study, the most scientific arrangement places the alleged causal agents in the rows and the outcomes in the columns. This format is used because readers are accustomed to looking at horizontal scientific symbols for the sequence of cause → effect. Table 16.2 is organized in this “longitudinal” direction of observation and reasoning. In longitudinal studies, the rows indicate the

© 2002 by Chapman & Hall/CRC

© 2002 by Chapman & Hall/CRC

Comparison of 119 autopsy and cancer-associated breasts.

FIGURE 16.32

Reproduction of histograms and tabular data for a comparison of “atypical lobules per breast” in two groups.

denominator groups, n1 and n2, that have been exposed or nonexposed to the alleged “cause”; and the columns show frequencies for the outcome fates, f1 and f2, for the forward direction of observation.

In an etiologic case-control study, however, the groups are chosen according to presence or absence of the outcome event. They are then “followed backward” to determine previous exposure to the alleged “cause.” To keep a scientific format, the table can still have the same horizontal orientation with “causes” in the rows; but the n1 and n2 totals for the “sampling” are now listed in the columns for the selected outcome groups that are the appropriate denominators. The arrangement is shown in Table 16.3.

16.3.2Individual Summaries

Because of structural differences in the research, the n1 and n2 denominators for longitudinal and casecontrol studies have different locations in the tables and must be expressed with different binary proportions.

For the longitudinal data of Table 16.2, n1 and n2 are marginal totals for the rows. The proportions of success, which would be p1 = a/n1 and p2 = c/n2, could then be compared as an increment pl − p2 or as a “risk” ratio, p1/p2. (If “risk of success” seems like an inappropriate phrase, it can be replaced by the risk ratio for failure, expressed as q2/q1.)

For the case-control study shown in Table 16.3, the analogous calculation of a /f1 and c/f2 in the rows is forbidden, as noted earlier (in Section 10.7.3), because patients were not chosen according to their exposure or nonexposure. If two proportions in this table are to be compared directly, they would have to refer to antecedent exposure, as e1 = a/n1 and e2 = b/n2. Because these proportions have relatively little intuitive meaning and cannot be used to express risk, they are seldom given much attention. Instead, the odds ratio, ad/bc, is usually cited as a single index of contrast, with the hope that it will adequately approximate the risk ratio. (The topic, mentioned in Chapter 10, is further discussed in Chapter 17.)

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TABLE 16.2

TABLE 16.3

Architectural Structure of Etiologic Case-Control Study

16.3.3Graphic Displays

If graphic displays have any merit at all for a 2 × 2 table, their main role would be to show the direction of observation and to compare magnitudes for the appropriate proportions.

Figures 16.33 and 16.34 show the “tabular box-graphs” that have been proposed14 for this purpose.

squares.” The dividing lines, however, are arranged to show the different directions and interpretations of the research architecture. The proportions for the selected denominators of the two main groups are shown by the placement of thick horizontal or vertical lines, and the thinner perpendicular vertical or horizontal lines are then placed to show the appropriate proportions in each group of either success for the cohort study or exposure for the case-control study.

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To display each constituent of an odds ratio, Figure 16.35 has a “quadrant-hub” arrangement of four contiguous squares, whose magnitudes for each side are a, b, c, and d for the four cells of the 2 × 2 table. The substantial differences in magnitude of the ad vs. bc squares in Figure 16.35 is consistent with the odds ratio of 6.1 [= (20 × 46)/(10 × 15)].

3.9 = 15

46 = 6.8

FIGURE 16.35

Contiguous squares showing cell sizes in a 2 × 2 table. [Figure and legend taken from Chapter Reference 14.]

The graphical displays in the squares of Figures 16.33 through 16.35 do not communicate much beyond what is readily discerned from direct inspection of the corresponding table, but they can be used if you want tables to receive an artistic emphasis that might help compensate for the enormous visual attention given to dimensional graphs in statistical illustrations.

A visually esthetic but intellectually unattractive arrangement shows the spinning-top shapes of Figure 16.36. The implications of the shapes themselves are difficult enough to understand; but the legend — which is reproduced here exactly as published — is inscrutable.

16.4 Displaying Ordinal Data

Because of the problems of getting adequate summary indexes (discussed throughout Section 15.7), there is no single ideal method for visual display of ordinal categories. The available methods of arrangement will inevitably differ according to the goal of the display. Is it intended to compare the overall distribution of categories in the two groups, or to do a category-by-category comparison? Bar charts can be used for either purpose, but the organization of the bars will differ.

© 2002 by Chapman & Hall/CRC

16.4.1Overall Comparisons

The “divided bar-chart,” also called a “component bar-chart,” has been a standard method of showing the distribution of constituent categories for two groups. Figure 16.37 is a schematic drawing of the arrangement, with the ordinal categories arrayed in vertical tiers that obscure both the shape of the distribution, and the comparison of individual categories.

A preferable way of displaying this same information is the divided dot chart proposed by Cleveland and McGill.15 Figure 16.38, which shows their dot chart for the same information that appears in Figure 16.37, allows magnitude to be clearly identified for each category, while also displaying shape of the overall distributions.

FIGURE 16.37

Divided (or “component”) bar chart for ordinal categories in two groups. [Figure and legend taken from Chapter Reference 15.]

GROUP A TOTAL

A5

A4

A3

A2

A1

GROUP B TOTAL

B5

B4

B3

B2

B1

VALUES

FIGURE 16.38

Divided dot chart for data of Figure 16.37. [Figure taken from Chapter Reference 15.]

© 2002 by Chapman & Hall/CRC

16.4.2Category-by-Category (Side-by-Side) Comparisons

Perhaps the most effective way to show category-by-category comparisons, however, is to place the bars opposite one another on a single vertical stalk.16 If just a few categories are included, this type of arrangement resembles a traffic signpost, as in Figure 16.39. If the ordinal data have many categories that are shown without spaces, as in Figure 16.40, the portrait may look like the layers of the “Michelin man.” The latter tactic has often been used to construct a “population pyramid,” which compares demographic components for two regions. The tactic can also be used to construct a type of back-to- back histogram, shown in Figure 16.41 for the distributions of CD-4 counts in two groups of men.17

If the layered categorical-bar arrangements of Figure 16.39 are converted to dot charts, as shown in Figure 16.42, the results produce a “Christmas tree” effect.16

© 2002 by Chapman & Hall/CRC

16.5 Nominal Data

For two groups of nominal data, no visual structure improves the comparison that can be obtained with a well-organized table showing the frequency counts (or relative frequencies) for each of the nominal categories in each group. If visual adornment is desired, a side-by-side category dot chart is probably the best approach.

16.6 “Bonus” Displays

As a reward for your completing this chapter, here are two “bonuses” of interesting features in data display.

16.6.1New Haven–New York Timetable

In Edward Tufte’s second book, Envisioning Information,18 he denounces the visual display used for the schedule of Metro North trains from New York to New Haven. His critique is replicated in Figure 16.43.

In Figure 16.44, however, Tufte shows a revised improved schedule, done as a student project at Yale University in 1983. Whatever be the merits of the criticism and the new design, travelers on this railroad route will recognize that the old format is still being used almost 20 years later. (Tufte does not mention whether the improved version was ever brought to the attention of railroad officials.)

Edward R. Tufte’s critique18 of the Metro North Railroad schedule of trains from New York to New Haven.

© 2002 by Chapman & Hall/CRC