The
Longitudinal data is measured repeatedly at multiple time points for each object (Jeong and Choi, 2009). This data is present in several fields such as sociology, education, economics, meteorology, and especially in medicine. One of the multiple methods used to visualize longitudinal data for continuous response variables, the box plot was proposed by Everitt and Hothorn (2006). The box plot compares the change according to time points using the box plot of each time point. Another method is the growth curve introduced by Singer and Willett (2003). The growth curve is used for exploratory data analysis. It is useful for identifying patterns by mean or median over time.
For binary or categorical response variables, it is difficult to distinguish patterns by growth curve and cannot be expressed by the box plot. In this case, it can be visualized as a horizontal line plot, a correspondence analysis plot, and other such plots, as well as a dot plot and bar chart. However, there are some limitations in the existing visualization techniques of longitudinal data such as,
They tend to include simple visualization levels or are only applicable to particular sizes.
As the number of variables or categories increases, the techniques are complex even if they apply to all contingency table sizes.
It is difficult to visually identify the techniques at a glance and interpret the changes in time points.
The distance between the row and column coordinates is not geometrically meaningful.
Only variable information is utilized, as opposed to the information of objects.
The VLDA plot method (Lee, 2019) used in this study is a new method for graphical representation of multidimensional longitudinal data. This method is based on the projection method (Greenacre and Hastie, 1987; Lebart
The distance between the row and column coordinates can be used to identify the relative relationship between the two categories.
It has the ability to describe data in detail using distance and coordinate directions.
The multiple correspondence analysis, which uses the indicator matrix, enables us to cluster the objects, as well as to explain the relationships between categories and objects using object information.
The VLDA plot is a visualization technique for multidimensional longitudinal data and can be viewed as an extension of correspondence analysis plots, which are based on projection methods due to these properties. When using the statistical software R language, there is no package available for creating the VLDA plot.
Therefore, to implement the existing VLDA plot method, we implemented a new interactive visualization plot in R language. This implementation is organized according to an R (R Development Core team
This paper is organized as follows: Section 2 provides the theoretical background of this work. Section 3 simply describes the usage of the R function for package
Longitudinal data is measured repeatedly by multiple time points for each object (Jeong and Choi, 2009). This data is present in several fields such as sociology, education, economics, and meteorology, and is particularly easy to observe in medicine. For example, patients can be measured at monthly intervals to ascertain whether a drug treatment is successful. Long format presents
In the special case where the covariates do not change from time point 1 to
In this section, we provide an overview of the VLDA plot algorithm. For a detailed description of the algorithm, refer to Lee (2019). In general, the indicator matrix
Consider a long format consisting of
where
where
where
and the row and column coordinates of the
We note that Step 3 in Algorithm 2.1 can be described as follows, the
where
where
The solution is
Longitudinal data inevitably displays the characteristic of added supplementary data as per the following example,
Outcome variables measured at additional time points, such as
When new objects are added that have not been measured previously.
Other covariates that indicate the characteristics of objects.
Therefore, in this section, we review an algorithm for coordinates that represent objects and variables added in the VLDA plot already provided. This algorithm is proposed by Lee (2019).
Suppose that the
First,
Similar to (
Here, diag(
Next, recall the row and column coordinates
and
Similarly, by using this property we can obtain low-dimensional coordinates of the supplementary row and column profile matrices in (
Thus, the coordinates in the
consisting of
It supports visualization technology that can display changes over time more effectively.
It is convenient to plot by using a consistent calling method for the two types of longitudinal data.
Additional analyses can be performed by providing a new interactive implementation of the existing VLDA plot.
Due to the synergistic relationship between the existing VLDA plot and interactive features, the user is empowered by a refined observe the visual aspects of the VLDA plot layout.
Two coordinates are used to identify the relative relationship between the two categories using distance.
It identifies the relationship between categories and objects by using the indicator matrix with the information of objects, and the clustering of objects is also made possible.
It has the ability to project supplementary information (supplementary objects and variables) onto a graph.
We outline the
The
vlda(x, object, time, type = c(“long”, “wide”))
The
vlda_plot(fit, rename = NULL, interactive = TRUE,
title = NULL, title.col = NULL, title.size = 15, title.hjust = 0,
subtitle = NULL, sub.col = NULL, sub.size = 15, sub.hjust = 0,
labels = NULL, lab.col = NULL, lab.size = NULL, lab.face = NULL,
legend.position = “bottom”, legend.justification = NULL,
linetype = 2, line.col = “red”, font.size = 1.0, var.size = 2.5,
obs.col = “darkgray”, obs.size = 2.5, add.obs.col = “#666666”,
arrow.col = “orange”, arrow.size = 0.5, arrow.type = “closed”).
The
After the coordinates of the supplementary objects and variables are found, the
vlda_add(fit, add.col = NULL, add.row = NULL, time.name = NULL)
Figure 1 shows an overview of the basic steps in the data visualization pipeline provided by the
Step 1: The
Step 2: The
Step 3:
Step 4: The supplementary coordinates found in Step 3, are accepted as a
In Section 4, practical examples are provided to highlight the implemented methods of real applications.
We illustrate the capabilities of the
R> library(vlda)
R> data(“PTSD”)
R> str(PTSD)
’data.frame’: 948 obs. of 7 variables:
$ subject : Factor w/ 316 levels “15”,”18”,”19”,..: 1 1 1 2 2 2 3 3 3 4 ...
$ control : num 3.22 3.17 3.28 2.56 3.44 ...
$ problems: num 5.62 5.38 3.75 9.25 4.38 ...
$ stress : int 1 0 1 0 0 0 1 1 1 0 ...
$ cohesion: int 8 8 8 8 8 8 7 7 7 8 ...
$ time : Factor w/ 3 levels “1”,”2”,”3”: 1 2 3 1 2 3 1 2 3 1 ...
$ ptsd : Factor w/ 2 levels “0”,”1”: 1 1 1 2 1 1 2 2 1 1 ...
The primary question in this trial is whether or not PTSD occurs over time according to the conditions of control, problems, stress, and cohesion, which are covariate variables. We start loading
The below code fits
R> PTSD[,2:4] <- apply(PTSD[,2:4], 2, function(x) ifelse(x >= 3, 1, 0))
R> PTSD[,5] <- ifelse(PTSD[,5] >= 6 , 1, 0)
R> PTSD <- data.frame(lapply(PTSD, function(x) as.factor(x)))
R> fit <- vlda(x = PTSD, object = “subject”, time = “time”, type = “long”)
R> fit
$obs.coordinate
# A tibble: 57 x 3
# Groups: x [57]
x y obs_list
1 -1.49 -1.20 2 -1.26 -0.283 3 -1.03 -1.14 4 -1.03 -1.01 5 -1.02 -0.379 6 -0.92 0.233 7 -0.916 -0.784 8 -0.858 -0.808
9 -0.801 -0.21510 -0.799 -0.088
# ... with 47 more rows
$var.coordinate
x y
control.0 -2.215 -0.326
control.1 0.530 0.078
problems.0 2.549 -1.702
problems.1 -0.589 0.393
stress.0 0.081 0.326
stress.1 -1.292 -5.200
cohesion.0 -1.658-2.528
cohesion.1 0.373 0.568
time.1 -1.270 1.243
time.2 0.132 0.667
time.3 1.138 -1.910
ptsd.0 0.855 0.362
ptsd.1 -1.902 -0.805
$Eigen
Eigenvalue Percent Cumulative
1 0.289 24.8 % 24.8 %
2 0.184 15.8 % 40.6 %
3 0.169 14.5 % 55.1 %
4 0.165 14.1 % 69.2 %
5 0.133 11.4 % 80.6 %
6 0.116 9.9 % 90.5 %
7 0.110 9.5 % 100 %
$GOF
[1] “Goodness of fit : 40.6 %”
As a result of
R> fit$obs.coordinate$obs_list
$ “x = -1.488 y = -1.204”
[1] “127_1” “350_1”
$ “x = -1.259 y = -0.283”
[1] “57_1” “69_1” “71_1” “115_1” “141_1” “150_1” “155_1” “162_1” “178_1”
[10] “190_1” “244_1”“273_1”“284_1” “319_1” “331_1” “383_1” “393_1” “447_1”
[19] “523_1” “529_1” “566_1”
# ... with 46 more rows
This means that patients 127 and 350 are located at that coordinate three months after the fire.
R> vlda_plot(fit)
control (control.0 and control.1), problems (problems.0 and problems.1), stress (stress.0 and stress.1), and cohesion (cohesion.0 and cohesion.1), where 0 and 1 denote low and high respectively.
Time, where time.1, time.2, and time.3 denote three, six, and twelve months respectively.
PTSD, where ptsd.0 denotes that PTSD does not appear, and ptsd.1 denotes that PTSD appears.
In Figure 2, a total of 948 rows for 316 objects are grayed out at three time points. Gray dots indicate the number of category combinations for each variable. This refers to each row of obs.coordinate. The
Tooltip allows users to identify the time point and observations associated with the coordinate when the mouse hovers over the coordinates. The function visually displays the above-mentioned
The VLDA plot is used to understand trends in observations over time in addition to identifying relative relationships at a simple visualization level. Due to the synergistic relationship between the existing VLDA plot and interactive features, the user is empowered by a refined observe the visual aspects of the VLDA plot layout.
In the VLDA plot, each variable is separated according to a different color, and each category included in the variable is displayed in the same color. The default passed to the color argument in
R> G <- vlda_plot(fit, interactive = FALSE)
R> G + scale_color_discrete() + theme_grey()
Here, we explain the geometric interpretation of the VLDA plot. Coordinates in opposite directions on each axis can be considered separate groups. If the distance between the coordinates is close, it indicates that the group has a similar tendency. Even if the explanatory variable is not significant, a small tendency can be confirmed because the coordinate is placed in consideration to the relative influence.
As shown in Figure 2, control.0, problem.1, stress.1, cohesion.0, time.1, and ptsd.1 are placed on the left side of the first axis, indicating homogeneity. This indicates that patients have low self-control and family cohesion, and have experienced many life problems and stress-related events, which caused PTSD after 3 months. In contrast, control.1, problem.0, stress.0, cohesion.1, time.2, time.3, and ptsd.0 are placed on the right side of the first axis. Therefore, there was no sign of PTSD after 6–12 months because patients had greater self-control and family cohesion, fewer life problems, and fewer stress-related events.
Subsequently, we can consider supplementary data as per the characteristic of longitudinal data. PTSD row refers to control, problems, stress, and cohesion; PTSD would add rows for 316 patients after 18 months. PTSD column is the degree of alcohol consumed (low, high) that may affect PTSD, which can be added to the columns that correspond from the first to the third time point for 316 patients.
R> data(PTSD_row)
R> data(PTSD_column)
R> str(PTSD_row)
’data.frame’: 316 obs. of 13 variables:
$ control.0 : int 0 0 0 0 0 0 0 0 0 0 ...
$ control.1 : int 1 1 1 1 1 1 1 1 1 1 ...
$ problems.0: int 1 1 1 1 1 1 1 1 0 1 ...
$ problems.1: int 0 0 0 0 0 0 0 0 1 0 ...
$ stress.0 : int 1 1 1 1 1 1 1 1 1 1 ...
$ stress.1 : int 0 0 0 0 0 0 0 0 0 0 ...
$ cohesion.0: int 0 0 0 0 0 0 0 0 0 0 ...
$ cohesion.1: int 1 1 1 1 1 1 1 1 1 1 ...
$ time.1 : int 0 0 0 0 0 0 0 0 0 0 ...
$ time.2 : int 0 0 0 0 0 0 0 0 0 0 ...
$ time.3 : int 0 0 0 0 0 0 0 0 0 0 ...
$ ptsd.0 : int 1 1 1 1 1 1 1 1 1 1 ...
$ ptsd.1 : int 0 0 0 0 0 0 0 0 0 0 ...
R> str(PTSD_column)
’data.frame’: 948 obs. of 2 variables:
$ Drinking.0: int 1 1 1 0 1 1 0 0 0 1 ...
$ Drinking.1: int 0 0 0 1 0 0 1 1 1 0 ...
R> fit2 <- vlda_add(fit, add.row = PTSD_row, add.col = PTSD_column)
R> vlda_plot(fit2))
control (control.0 and control.1), problems (problems.0 and problems.1), stress (stress.0 and stress.1), cohesion (cohesion.0 and cohesion.1), and Drinking (Drinking.0 and Drinking.1), where 0 and 1 denote low and high respectively.
Time, where time.1, time.2, time.3, and time.4 denote three, six, twelve, and eighteen months respectively.
PTSD, where ptsd.0 denotes that PTSD does not appear, and ptsd.1 denotes that PTSD appears.
Figure 6 shows an added drinking column parameter and supplementary coordinates for 316 patients of the fourth time point in the VLDA plot. In the supplementary data, the number of categorical combinations of each variable has a total of 15 possibilities for the added fourth time point of the existing 316 patients. Therefore, Figure 6 shows 15 supplementary coordinates in dark grey. The center of the supplementary coordinates is placed on the right side of the first axis. Also, we observe that it draws nearer to ptsd.0 at the fourth time point than at the third time point.
That is, after 18 months, we know that the ratio of PTSD decreases over time, and that the same interpretation can be made after 6–12 months. Drinking.1 is located on the left side of the first axis, indicating homogeneity with control.0, problems.1, stress.1, cohesion.0, time.1, and ptsd.1. This shows that patients have low self-control and family cohesion, and experience many life problems and stress-related events, as well as heavy drinking, which caused an increase in PTSD after 3 months. On the contrary, Drinking.0 is located on the right side, which displays similarities with control.1, problems.0, stress.0, cohesion.1, time.2, time.3, and ptsd.0. In other words, after 6–12 months, self-control and family cohesion increased, and the number of life problems, stress-related events, and drinking decreased, and thus, showed no sign of PTSD.
In this section, we illustrate the capability of how to apply the package
In depression data, two drugs that treat patients suffering from depression are compared. This data has modified some of the data collected by Koch
R> data(Depression)
R> str(Depression)
’data.frame’: 800 obs. of 6 variables:
$ Case : Factor w/ 800 levels “1”,”10”,”100”,..: 1 112 223 334 ...
$ Diagnosis: Factor w/ 2 levels “1”,”2”: 1 1 1 1 1 1 1 1 1 1 ...
$ Drug : Factor w/ 2 levels “1”,”2”: 2 2 2 2 2 2 2 2 2 2 ...
$ 1week : Factor w/ 2 levels “1”,”2”: 2 2 2 2 2 2 2 2 2 2 ...
$ 2weeks : Factor w/ 2 levels “1”,”2”: 2 2 2 2 2 2 2 2 2 2 ...
$ 4weeks : Factor w/ 2 levels “1”,”2”: 2 2 2 2 2 2 2 2 2 2 ...
The focus is on drug levels, which is considered one of the most important treatments associated with depression. The key question in this trial is whether the new drug treatment group indicates a significantly more effective treatment of depression than the standard drug treatment group. Therefore, we consider whether the initial depression and drug levels affect drug treatment over time. In the call to
R> wide.fit <- vlda(x = Depression, object = “Case”,
+ time = c(“1week”, “2weeks”, “4weeks”), type = “wide”)
R> vlda_plot(wide.fit)
According to the depression data, the number of categorical combinations for each variable of 800 objects has a total of 32 unique possible combinations, and 32 observed coordinate points are grayed out. The yellow arrows that are connected between the same categories denote the trend of changes over time. In Figure 7, Drug.1, Diagnosis.1, and Normal (1week.2, 2week.2, and 4weeks.2) are placed on the left side of the first axis, indicating homogeneity. For example, patient 201 has the values of 1 in mild (Diagnosis.1), new drug (Drug.1), and normal (1week.2, 2weeks.2, and 4weeks.2); therefore, it is placed in the second quadrant.
R> Depression[201,]
Case Diagnosis Drug 1week 2weeks 4weeks
201 201 1 1 2 2 2
In contrast, Drug.2, Diagnosis.2, and abnormal (1week.1, 2weeks.1, and 4weeks.1) are placed on the right side of the first axis. For example, patient 600 has the value of 1 in severe (Diagnosis.2), standard drug (Drug.2), and abnormal (1week.1, 2weeks.1, and 4weeks.1), so it is placed in the fourth quadrant.
R> Depression[600,]
Case Diagnosis Drug 1week 2weeks 4weeks
600 600 2 2 1 1 1
Therefore, patients with mild initial depression (Diagnosis.1), who take a new drug (Drug.1), are more likely to be normal, and patients with severe initial depression (Diagnosis.2), who take a standard drug (Drug.2), are more likely to be abnormal. Also, regardless of the drug taken after one week, mild (Diagnosis.1) is close to normal (1week.2) and severe (Diagnosis.2) is close to abnormal (1week.1). This means that the drug has no effect after one week. However, as time passes, normal (1week.2 → 2weeks.2 → 4weeks.2) draws nearer to the new drug (Drug.1) and abnormal (1week.1 → 2week.1 → 4week.1) draws nearer to the standard drug (Drug.2). That is, the effect of the drugs is visible over time. In this way, it is possible to relate variables and objects, and to cluster objects by utilizing object information. Also, the VLDA plot shows that it is more suitable to the visualization of longitudinal data by dynamically illustrating the trend of change over time, unlike the existing visualization techniques of categorical data.
In the case of long format, coordinates with the same time points are illustrated on the graph in yellow to distinguish between patients with similar time points. However, in the case of wide format, when the mouse hovers over the observation coordinate points, the graph shows the hover effect in which the coordinate points of observations with the same covariate are displayed in yellow points on the graph. Figure 8 shows four graphs with yellow observation coordinate points according to the variable combinations of the covariates. For example, observations with a covariate of Diagnosis.1 and Drug.1 appear in the upper left of the graph. In this graph, the observations on the right side of the first axis appear abnormal for all three time points, and the more they move to the left, the more normal they appear. Conversely, observations with covariates Diagnosis.2 and Drug.2 appear in the lower right of the graph, and the observations on the left side of the first axis appear normal for all three time points, however, the more they move to the right, the more abnormal they appear. It is possible to visually examine the number of observation points, according to the covariate, which are close to the response variables.
Next, we consider applying the additional measured objects and variables to the depression data. In
R> data(Depression_row)
R> data(Depression_column)
R> str(Depression_row)
’data.frame’: 100 obs. of 10 variables:
$ Diagnosis.1: int 1 1 1 1 1 1 1 1 1 1 ...
$ Diagnosis.2: int 0 0 0 0 0 0 0 0 0 0 ...
$ Drug.1 : int 0 0 0 0 0 0 0 0 0 0 ...
$ Drug.2 : int 0 0 0 0 0 0 0 0 0 0 ...
$ 1week.1 : int 0 0 0 0 0 0 0 0 0 0 ...
$ 1week.2 : int 1 1 1 1 1 1 1 1 1 1 ...
$ 2weeks.1 : int 0 0 0 0 0 0 0 0 1 1 ...
$ 2weeks.2 : int 1 1 1 1 1 1 1 1 0 0 ...
$ 4weeks.1 : int 0 0 0 1 1 1 1 1 0 0 ...
$ 4weeks.2 : int 1 1 1 0 0 0 0 0 1 1 ...
R> str(Depression_column)
’data.frame’: 800 obs. of 4 variables:
$ 6weeks.1: int 0 0 0 0 0 0 0 0 0 0 ...
$ 6weeks.2: int 1 1 1 1 1 1 1 1 1 1 ...
$ sex.1 : int 1 1 1 1 1 1 1 1 1 1 ...
$ sex.2 : int 0 0 0 0 0 0 0 0 0 0 ...
The first example was already shown in Figure 6 in Section 4.1 by using the default command
The
R> Depression_row <- as.matrix(Depression_row)
R> Depression_column <- as.matrix(Depression_column)
R> wide.fit2 <-
+ vlda_add(
+ wide.fit,
+ time.name = “6weeks”,
+ add.row = Depression_row,
+ add.col = Depression_column
+ )
R> rownames(wide.fit2$var.coordinate)
[1] “1week.1” “1week.2” “2weeks.1” “2weeks.2” “4weeks.1”
[6] “4weeks.2” “6weeks.1” “6weeks.2” “Diagnosis.1”
[10] “Diagnosis.2” “Drug.1” “Drug.2” “Drug.3” “sex.1” “sex.2”
R> vlda_plot(
+ wide.fit2,
+ rename = c(“1week.Ab”, “1week.N”,
+ “2weeks.Ab”, “2weeks.N”,
+ “4weeks.Ab”, “4weeks.N”,
+ “6weeks.Ab”,”6weeks.N”,
+ “Mild”,”Severe”,
+ “New”,”Standard”,”Placebo”,
+ “Male”,”Female” ),
+ title = “Depression data”,
+ title.col = “#555555”, title.size = 25,
+ subtitle = “Supplementary objects and variables added”,
+ sub.size = 15, sub.col = “darkgrey”,
+ legend.position = c(0.15,0.15)
+ )
Figure 9 shows an additional representation of coordinates to the VLDA plot already provided in Figure 7. It illustrates sex and the fourth time point (after 6weeks) as columns parameters for 800 patients added by the
In the supplemental data added by the column indicator matrix, the fourth time point (after 6weeks) refers to the time that passes from 4 weeks to 6 weeks, normal (4weeks.N → 6weeks.N) draws closer to the new drug, and abnormal (4weeks.Ab → 6weeks.Ab) draws closer to the standard drug. That is, the effect of the drugs still increases over time. This can also be confirmed in Table 5 which shows the normal response proportion at the fourth time point (after 6 weeks) according to the combinations of diagnosis and drug. The drug effect according to diagnosis shows that 6 weeks increased normal proportion compared to after 4 weeks. Also, we observe that the new drug is more effective than the standard drug, and that mild is more effective than severe.
Next, we consider the combination of sex and the fourth time point added by the supplementary column indicator matrix. Normal at the fourth time point (6weeks.N) and male on the left side of the first axis shows homogeneity with new drug, mild, and normal (1week.2, 2weeks.2, and 4weeks.2). On the contrary, abnormal at the fourth time point (6weeks.Ab) and female on the right side of the first axis shows homogeneity with standard, severe, and abnormal (1week.Ab, 2weeks.Ab, and 4weeks.Ab, respectively). Therefore, if patients who take a new drug have mild initial depression and are a male, they are more likely to be normal. Contrarily, if patients who take a standard drug have severe initial depression and are female, they are more likely to be abnormal. Table 6 shows the normal response proportion at three time points by combining diagnosis, drug, and gender. In males, the proportion of all combinations increased, and the proportion of new drug was higher than standard drug, and the proportion of mild was higher than severe. Conversely, in females, the patients who took the standard drug showed no change or decrease, and the patients who tooke the new drug had a higher proportion of mild than severe.
This paper presents the R package
The generalized estimation equation (GEE) as introduce by Liang and Zeger (1986) is commonly used to analyze longitudinal data. It is possible to identically interpret the VLDA plot and the GEE result. In fact, the VLDA plot showed a relatively strong performance compared to the GEE results based on the real longitudinal data analysis from Lee (2019). As a result, the same interpretation as the GEE results is possible. However,
Arguments and descriptions in the vlda function
Arguments | Description |
---|---|
x | A data frame consisting of categorical data coded in numbers. The samples |
object | A vector of length |
time | A time point of longitudinal data. Accepts a character string that denotes the name of the time variable. |
type | A type of longitudinal data. Long format refers to each row that equals one time point per object, so each object has |
Arguments and descriptions in the
Arguments | Description |
---|---|
fit | An object returned by |
rename | Rename a variable. |
interactive | Use the interactive graphical elements (default TRUE). |
title | Plot title. If NULL, the title is not shown (default NULL). |
title.col | Title color (default color is black). |
title.size | Title font size (default size = 15). |
title.hjust | Alignment of title (Number from 0 [left] to 1 [right]: left-aligned by default). |
subtitle | Subtitle for the plot which will be displayed below the title. |
sub.col | Subtitle color (default color is black). |
sub.size | Subtitle font size (default size = 15). |
sub.hjust | Alignment of sub-title (Number from 0 [left] to 1 [right]: left-aligned by default). |
labels | Legend labels. |
lab.col | Legend labels color. |
lab.size | Legend labels size. |
lab.face | Legend labels font c( |
legend.position | The position of legends ( |
legend.justification | Anchor point for positioning the legend inside the plot “center” or two-element numeric vector) or the justification according to the plot area when positioned outside the plot. |
linetype | Line types can be specified as: An integer or name: 0 = blank, 1 = solid, 2 = dashed, 3 = dotted, 4 = dotdash, 5 = longdash, 6 = twodash, as shown below: |
line.col | Axis line color. |
font.size | Font size (left-aligned by default size = 1.0). |
var.size | Variable coordinate point size of plot. |
obs.col | Observation coordinate point color of plot. |
obs.size | Observation coordinate point size on plot. |
add.obs.col | Color of added observation coordinate points. |
arrow.col | Arrow color (default color = |
arrow.size | Arrow size (default size = 0.5). |
arrow.type | One of |
Arguments and descriptions in the
Arguments | Description |
---|---|
fit | An object returned by |
add.col | A data matrix, the type of indicator matrix. Additional data sets in column format. |
add.row | A data matrix, the type of indicator matrix. Additional data sets in row format. Supplemental data should have the same variable name as |
time.name | If the supplemental data to be added contains a time variable, enter the name of the time variable. |
Normal response proportion at each time point for the placebo
Diagnosis | Drug | Normal response proportion | ||
---|---|---|---|---|
1 week | 2 weeks | 4 weeks | ||
Mild | Placebo | 0.36 | 0.36 | 0.24 |
Severe | Placebo | 0.20 | 0.18 | 0.18 |
Normal response proportion at the fourth time point (after 6 weeks) according to combinations of diagnosis and drug
Diagnosis | Drug | Normal response proportion |
---|---|---|
6 weeks | ||
Mild | Standard | 0.57 |
New | 1.00 | |
Severe | Standard | 0.35 |
New | 0.94 |
Normal response proportion at each time point by combinations of diagnosis, drug, and gender
Diagnosis | Drug | Gender | Normal response proportion | ||
---|---|---|---|---|---|
1 week | 2 weeks | 4 weeks | |||
Mild | Standard | Male | 0.40 | 0.54 | 0.68 |
Female | 0.42 | 0.42 | 0.42 | ||
New | Male | 0.38 | 0.62 | 0.86 | |
Female | 0.36 | 0.44 | 0.54 | ||
Severe | Standard | Male | 0.22 | 0.26 | 0.46 |
Female | 0.20 | 0.24 | 0.16 | ||
New | Male | 0.22 | 0.30 | 0.46 | |
Female | 0.14 | 0.20 | 0.36 |