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Code of Conduct

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License

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Reporting Security Issues

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+

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+ + + + +
+
+ + + +

The packages used in this vignette are:

+ +
+

Variable Class Conversion +

+

rtables requires that split variables to be factors. +When you try and split a variable that isn’t, a warning message will +appear. Here we purposefully convert the SEX variable to character to +demonstrate what happens when we try splitting the rows by this +variable. To fix this, df_explict_na will convert this to a +factor resulting in the table being generated.

+
+adsl <- tern_ex_adsl
+adsl$SEX <- as.character(adsl$SEX)
+
+vars <- c("AGE", "SEX", "RACE", "BMRKR1")
+var_labels <- c(
+  "Age (yr)",
+  "Sex",
+  "Race",
+  "Continous Level Biomarker 1"
+)
+
+result <- basic_table(show_colcounts = TRUE) %>%
+  split_cols_by(var = "ARM") %>%
+  add_overall_col("All Patients") %>%
+  analyze_vars(
+    vars = vars,
+    var_labels = var_labels
+  ) %>%
+  build_table(adsl)
+#> Warning in as_factor_keep_attributes(x, verbose = verbose): automatically
+#> converting character variable x to factor, better manually convert to factor to
+#> avoid failures
+
+#> Warning in as_factor_keep_attributes(x, verbose = verbose): automatically
+#> converting character variable x to factor, better manually convert to factor to
+#> avoid failures
+
+#> Warning in as_factor_keep_attributes(x, verbose = verbose): automatically
+#> converting character variable x to factor, better manually convert to factor to
+#> avoid failures
+
+#> Warning in as_factor_keep_attributes(x, verbose = verbose): automatically
+#> converting character variable x to factor, better manually convert to factor to
+#> avoid failures
+result
+#>                                                A: Drug X    B: Placebo    C: Combination   All Patients
+#>                                                 (N=69)        (N=73)          (N=58)         (N=200)   
+#> ———————————————————————————————————————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                                                               
+#>   n                                               69            73              58             200     
+#>   Mean (SD)                                   34.1 (6.8)    35.8 (7.1)      36.1 (7.4)      35.3 (7.1) 
+#>   Median                                         32.8          35.4            36.2            34.8    
+#>   Min - Max                                   22.4 - 48.0   23.3 - 57.5    23.0 - 58.3     22.4 - 58.3 
+#> Sex                                                                                                    
+#>   n                                               69            73              58             200     
+#>   F                                           38 (55.1%)    40 (54.8%)      32 (55.2%)      110 (55%)  
+#>   M                                           31 (44.9%)    33 (45.2%)      26 (44.8%)       90 (45%)  
+#> Race                                                                                                   
+#>   n                                               69            73              58             200     
+#>   ASIAN                                       38 (55.1%)    43 (58.9%)       29 (50%)       110 (55%)  
+#>   BLACK OR AFRICAN AMERICAN                   15 (21.7%)    13 (17.8%)      12 (20.7%)       40 (20%)  
+#>   WHITE                                       11 (15.9%)    12 (16.4%)       11 (19%)        34 (17%)  
+#>   AMERICAN INDIAN OR ALASKA NATIVE             4 (5.8%)      3 (4.1%)       6 (10.3%)       13 (6.5%)  
+#>   MULTIPLE                                     1 (1.4%)      1 (1.4%)           0             2 (1%)   
+#>   NATIVE HAWAIIAN OR OTHER PACIFIC ISLANDER        0         1 (1.4%)           0            1 (0.5%)  
+#>   OTHER                                            0             0              0               0      
+#>   UNKNOWN                                          0             0              0               0      
+#> Continous Level Biomarker 1                                                                            
+#>   n                                               69            73              58             200     
+#>   Mean (SD)                                    6.3 (3.6)     6.7 (3.5)      6.2 (3.3)       6.4 (3.5)  
+#>   Median                                          5.4           6.3            5.4             5.6     
+#>   Min - Max                                   0.4 - 17.8    1.0 - 18.5      2.4 - 19.1      0.4 - 19.1
+
+
+

Including Missing Values in rtables +

+

Here we purposefully convert all M values to +NA in the SEX variable. After running +df_explicit_na the NA values are encoded as +<Missing> but they are not included in the table. As +well, the missing values are not included in the n count +and they are not included in the denominator value for calculating the +percent values.

+
+adsl <- tern_ex_adsl
+adsl$SEX[adsl$SEX == "M"] <- NA
+adsl <- df_explicit_na(adsl)
+
+vars <- c("AGE", "SEX")
+var_labels <- c(
+  "Age (yr)",
+  "Sex"
+)
+
+result <- basic_table(show_colcounts = TRUE) %>%
+  split_cols_by(var = "ARM") %>%
+  add_overall_col("All Patients") %>%
+  analyze_vars(
+    vars = vars,
+    var_labels = var_labels
+  ) %>%
+  build_table(adsl)
+result
+#>                A: Drug X    B: Placebo    C: Combination   All Patients
+#>                 (N=69)        (N=73)          (N=58)         (N=200)   
+#> ———————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                               
+#>   n               69            73              58             200     
+#>   Mean (SD)   34.1 (6.8)    35.8 (7.1)      36.1 (7.4)      35.3 (7.1) 
+#>   Median         32.8          35.4            36.2            34.8    
+#>   Min - Max   22.4 - 48.0   23.3 - 57.5    23.0 - 58.3     22.4 - 58.3 
+#> Sex                                                                    
+#>   n               38            40              32             110     
+#>   F            38 (100%)     40 (100%)      32 (100%)       110 (100%) 
+#>   M                0             0              0               0
+

If you want the Na values to be displayed in the table +and included in the n count and as the denominator for +calculating percent values, use the na_level argument.

+
+adsl <- tern_ex_adsl
+adsl$SEX[adsl$SEX == "M"] <- NA
+adsl <- df_explicit_na(adsl, na_level = "Missing Values")
+
+result <- basic_table(show_colcounts = TRUE) %>%
+  split_cols_by(var = "ARM") %>%
+  add_overall_col("All Patients") %>%
+  analyze_vars(
+    vars = vars,
+    var_labels = var_labels
+  ) %>%
+  build_table(adsl)
+result
+#>                     A: Drug X    B: Placebo    C: Combination   All Patients
+#>                      (N=69)        (N=73)          (N=58)         (N=200)   
+#> ————————————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                                    
+#>   n                    69            73              58             200     
+#>   Mean (SD)        34.1 (6.8)    35.8 (7.1)      36.1 (7.4)      35.3 (7.1) 
+#>   Median              32.8          35.4            36.2            34.8    
+#>   Min - Max        22.4 - 48.0   23.3 - 57.5    23.0 - 58.3     22.4 - 58.3 
+#> Sex                                                                         
+#>   n                    69            73              58             200     
+#>   F                38 (55.1%)    40 (54.8%)      32 (55.2%)      110 (55%)  
+#>   M                     0             0              0               0      
+#>   Missing Values   31 (44.9%)    33 (45.2%)      26 (44.8%)       90 (45%)
+
+
+

Missing Values in Numeric Variables +

+

Numeric variables that have missing values are not altered. This +means that any NA value in a numeric variable will not be +included in the summary statistics, nor will they be included in the +denominator value for calculating the percent values. Here we make any +value less than 30 missing in the AGE variable and only the +valued greater than 30 are included in the table below.

+
+adsl <- tern_ex_adsl
+adsl$AGE[adsl$AGE < 30] <- NA
+adsl <- df_explicit_na(adsl)
+
+vars <- c("AGE", "SEX")
+var_labels <- c(
+  "Age (yr)",
+  "Sex"
+)
+
+result <- basic_table(show_colcounts = TRUE) %>%
+  split_cols_by(var = "ARM") %>%
+  add_overall_col("All Patients") %>%
+  analyze_vars(
+    vars = vars,
+    var_labels = var_labels
+  ) %>%
+  build_table(adsl)
+result
+#>                A: Drug X    B: Placebo    C: Combination   All Patients
+#>                 (N=69)        (N=73)          (N=58)         (N=200)   
+#> ———————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                               
+#>   n               46            56              44             146     
+#>   Mean (SD)   37.8 (5.2)    38.3 (6.3)      39.1 (5.9)      38.3 (5.8) 
+#>   Median         37.2          37.3            37.5            37.5    
+#>   Min - Max   30.3 - 48.0   30.0 - 57.5    30.5 - 58.3     30.0 - 58.3 
+#> Sex                                                                    
+#>   n               69            73              58             200     
+#>   F           38 (55.1%)    40 (54.8%)      32 (55.2%)      110 (55%)  
+#>   M           31 (44.9%)    33 (45.2%)      26 (44.8%)       90 (45%)
+
+
+
+ + + + +
+ + + + + + + diff --git a/v0.9.2-rc1/articles/tables.html b/v0.9.2-rc1/articles/tables.html new file mode 100644 index 0000000000..15046f1450 --- /dev/null +++ b/v0.9.2-rc1/articles/tables.html @@ -0,0 +1,883 @@ + + + + + + + + +Tabulation • tern + + + + + + + + + + + Skip to contents + + +
+ + + + +
+
+ + + +
+

+tern Tabulation +

+

The tern R package provides functions to create common +analyses from clinical trials in R. The core functionality +for tabulation is built on the more general purpose rtables +package. New users should first begin by reading the “Introduction +to tern” and “Introduction +to rtables vignettes.

+

The packages used in this vignette are:

+ +

The datasets used in this vignette are:

+
+adsl <- ex_adsl
+adae <- ex_adae
+adrs <- ex_adrs
+
+
+

+tern Analyze Functions +

+

Analyze functions are used in combination with the +rtables layout functions, in the pipeline which creates the +rtables table. They apply some statistical logic to the +layout of the rtables table. The table layout is +materialized with the rtables::build_table function and the +data.

+

The tern analyze functions are wrappers around +rtables::analyze function, they offer various methods +useful from the perspective of clinical trials and other statistical +projects.

+

Examples of the tern analyze functions are +tern::count_occurrences, +tern::summarize_ancova or tern::analyze_vars. +As there is no one prefix to identify all tern analyze +functions it is recommended to use the the +tern website functions reference.

+
+

Internals of tern Analyze Functions +

+

Please skip this subsection if you are not interested in the +internals of tern analyze functions.

+

Internally tern analyze functions like +tern::summarize_ancova are mainly built in the 4 elements +chain:

+
h_ancova() -> tern:::s_ancova() -> tern:::a_ancova() -> summarize_ancova()
+

The descriptions for each function type:

+
    +
  • analysis helper functions h_*. These functions are +useful to help define the analysis.
  • +
  • statistics function s_*. Statistics functions should do +the computation of the numbers that are tabulated later. In order to +separate computation from formatting, they should not take care of +rcell type formatting themselves.
  • +
  • formatted analysis functions a_*. These have the same +arguments as the corresponding statistics functions, and can be further +customized by calling rtables::make_afun() on them. They +are used as afun in rtables::analyze().
  • +
  • analyze functions +rtables::analyze(..., afun = make_afun(tern::a_*)). Analyze +functions are used in combination with the rtables layout +functions, in the pipeline which creates the table. They are the last +element of the chain.
  • +
+

We will use the native rtables::analyze function with +the tern formatted analysis functions as a +afun parameter.

+
l <- basic_table() %>%
+    split_cols_by(var = "ARM") %>%
+    split_rows_by(var = "AVISIT") %>%
+    analyze(vars = "AVAL", afun = a_summary)
+
+build_table(l, df = adrs)
+

The rtables::make_afun function is helpful when somebody +wants to attach some format to the formatted analysis function.

+
afun <- make_afun(
+    a_summary,
+    .stats = NULL,
+    .formats = c(median = "xx."),
+    .labels = c(median = "My median"),
+    .indent_mods = c(median = 1L)
+)
+
+l2 <- basic_table() %>%
+    split_cols_by(var = "ARM") %>%
+    split_rows_by(var = "AVISIT") %>%
+    analyze(vars = "AVAL", afun = afun)
+
+build_table(l2, df = adrs)
+
+
+
+

Tabulation Examples +

+

We are going to create 3 different tables using tern +analyze functions and the rtables interface.

+ ++++ + + + + + + + + + + + + + + + + + + +
Table +tern analyze functions
Demographic Table +analyze_vars() and +summarize_num_patients() +
Adverse event Tablecount_occurrences()
Response Table +estimate_proportion(), +estimate_proportion_diff() and +test_proportion_diff() +
+
+

Demographic Table +

+

Demographic tables provide a summary of the characteristics of +patients enrolled in a clinical trial. Typically the table columns +represent treatment arms and variables summarized in the table are +demographic properties such as age, sex, race, etc.

+

In the example below the only function from tern is +analyze_vars() and the remaining layout functions are from +rtables.

+
+# Select variables to include in table.
+vars <- c("AGE", "SEX")
+var_labels <- c("Age (yr)", "Sex")
+
+basic_table() %>%
+  split_cols_by(var = "ARM") %>%
+  add_overall_col("All Patients") %>%
+  add_colcounts() %>%
+  analyze_vars(
+    vars = vars,
+    var_labels = var_labels
+  ) %>%
+  build_table(adsl)
+#>                       A: Drug X    B: Placebo    C: Combination   All Patients
+#>                        (N=134)       (N=134)        (N=132)         (N=400)   
+#> ——————————————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                                      
+#>   n                      134           134            132             400     
+#>   Mean (SD)          33.8 (6.6)    35.4 (7.9)      35.4 (7.7)      34.9 (7.4) 
+#>   Median                33.0          35.0            35.0            34.0    
+#>   Min - Max          21.0 - 50.0   21.0 - 62.0    20.0 - 69.0     20.0 - 69.0 
+#> Sex                                                                           
+#>   n                      134           134            132             400     
+#>   F                   79 (59%)     77 (57.5%)       66 (50%)      222 (55.5%) 
+#>   M                  51 (38.1%)     55 (41%)       60 (45.5%)     166 (41.5%) 
+#>   U                   3 (2.2%)      2 (1.5%)         4 (3%)         9 (2.2%)  
+#>   UNDIFFERENTIATED    1 (0.7%)          0           2 (1.5%)        3 (0.8%)
+

To change the display order of categorical variables in a table use +factor variables and explicitly set the order of the levels. This is the +case for the display order in columns and rows. Note that the +forcats package has many useful functions to help with +these types of data processing steps (not used below).

+
+# Reorder the levels in the ARM variable.
+adsl$ARM <- factor(adsl$ARM, levels = c("B: Placebo", "A: Drug X", "C: Combination")) # nolint
+
+# Reorder the levels in the SEX variable.
+adsl$SEX <- factor(adsl$SEX, levels = c("M", "F", "U", "UNDIFFERENTIATED")) # nolint
+
+basic_table() %>%
+  split_cols_by(var = "ARM") %>%
+  add_overall_col("All Patients") %>%
+  add_colcounts() %>%
+  analyze_vars(
+    vars = vars,
+    var_labels = var_labels
+  ) %>%
+  build_table(adsl)
+#>                      B: Placebo     A: Drug X    C: Combination   All Patients
+#>                        (N=134)       (N=134)        (N=132)         (N=400)   
+#> ——————————————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                                      
+#>   n                      134           134            132             400     
+#>   Mean (SD)          35.4 (7.9)    33.8 (6.6)      35.4 (7.7)      34.9 (7.4) 
+#>   Median                35.0          33.0            35.0            34.0    
+#>   Min - Max          21.0 - 62.0   21.0 - 50.0    20.0 - 69.0     20.0 - 69.0 
+#> Sex                                                                           
+#>   n                      134           134            132             400     
+#>   M                   55 (41%)     51 (38.1%)      60 (45.5%)     166 (41.5%) 
+#>   F                  77 (57.5%)     79 (59%)        66 (50%)      222 (55.5%) 
+#>   U                   2 (1.5%)      3 (2.2%)         4 (3%)         9 (2.2%)  
+#>   UNDIFFERENTIATED        0         1 (0.7%)        2 (1.5%)        3 (0.8%)
+

The tern package includes many functions similar to +analyze_vars(). These functions are called layout creating +functions and are used in combination with other rtables +layout functions just like in the examples above. Layout creating +functions are wrapping calls to rtables +analyze(), analyze_colvars() and +summarize_row_groups() and provide options for easy +formatting and analysis modifications.

+

To customize the display for the demographics table, we can do so via +the arguments in analyze_vars(). Most layout creating +functions in tern include the standard arguments +.stats, .formats, .labels and +.indent_mods which control which statistics are displayed +and how the numbers are formatted. Refer to the package help with +help("analyze_vars") or ?analyze_vars to see +the full set of options.

+

For this example we will change the default summary for numeric +variables to include the number of records, and the mean and standard +deviation (in a single statistic, i.e. within a single cell). For +categorical variables we modify the summary to include the number of +records and the counts of categories. We also modify the display format +for the mean and standard deviation to print two decimal places instead +of just one.

+
+# Select statistics and modify default formats.
+basic_table() %>%
+  split_cols_by(var = "ARM") %>%
+  add_overall_col("All Patients") %>%
+  add_colcounts() %>%
+  analyze_vars(
+    vars = vars,
+    var_labels = var_labels,
+    .stats = c("n", "mean_sd", "count"),
+    .formats = c(mean_sd = "xx.xx (xx.xx)")
+  ) %>%
+  build_table(adsl)
+#>                       B: Placebo     A: Drug X     C: Combination   All Patients
+#>                        (N=134)        (N=134)         (N=132)         (N=400)   
+#> ————————————————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                                        
+#>   n                      134            134             132             400     
+#>   Mean (SD)          35.43 (7.90)   33.77 (6.55)    35.43 (7.72)    34.88 (7.44)
+#> Sex                                                                             
+#>   n                      134            134             132             400     
+#>   M                       55             51              60             166     
+#>   F                       77             79              66             222     
+#>   U                       2              3               4               9      
+#>   UNDIFFERENTIATED        0              1               2               3
+

One feature of a layout is that it can be used with +different datasets to create different summaries. For example, here we +can easily create the same summary of demographics for the Brazil and +China subgroups, respectively:

+
+lyt <- basic_table() %>%
+  split_cols_by(var = "ARM") %>%
+  add_overall_col("All Patients") %>%
+  add_colcounts() %>%
+  analyze_vars(
+    vars = vars,
+    var_labels = var_labels
+  )
+
+build_table(lyt, df = adsl %>% dplyr::filter(COUNTRY == "BRA"))
+#>                      B: Placebo     A: Drug X    C: Combination   All Patients
+#>                         (N=7)        (N=13)          (N=10)          (N=30)   
+#> ——————————————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                                      
+#>   n                       7            13              10              30     
+#>   Mean (SD)          32.0 (6.1)    36.7 (6.4)     38.3 (10.6)      36.1 (8.1) 
+#>   Median                32.0          37.0            35.0            35.5    
+#>   Min - Max          25.0 - 42.0   24.0 - 47.0    25.0 - 64.0     24.0 - 64.0 
+#> Sex                                                                           
+#>   n                       7            13              10              30     
+#>   M                   4 (57.1%)     8 (61.5%)       5 (50%)        17 (56.7%) 
+#>   F                   3 (42.9%)     5 (38.5%)       5 (50%)        13 (43.3%) 
+#>   U                       0             0              0               0      
+#>   UNDIFFERENTIATED        0             0              0               0
+
+build_table(lyt, df = adsl %>% dplyr::filter(COUNTRY == "CHN"))
+#>                      B: Placebo     A: Drug X    C: Combination   All Patients
+#>                        (N=81)        (N=74)          (N=64)         (N=219)   
+#> ——————————————————————————————————————————————————————————————————————————————
+#> Age (yr)                                                                      
+#>   n                      81            74              64             219     
+#>   Mean (SD)          35.7 (7.3)    33.0 (6.4)      35.2 (6.4)      34.6 (6.8) 
+#>   Median                36.0          32.0            35.0            34.0    
+#>   Min - Max          21.0 - 58.0   23.0 - 48.0    21.0 - 49.0     21.0 - 58.0 
+#> Sex                                                                           
+#>   n                      81            74              64             219     
+#>   M                  35 (43.2%)    27 (36.5%)      30 (46.9%)       92 (42%)  
+#>   F                  45 (55.6%)    44 (59.5%)      29 (45.3%)     118 (53.9%) 
+#>   U                   1 (1.2%)      2 (2.7%)        3 (4.7%)        6 (2.7%)  
+#>   UNDIFFERENTIATED        0         1 (1.4%)        2 (3.1%)        3 (1.4%)
+
+
+

Adverse Event Table +

+

The standard table of adverse events is a summary by system organ +class and preferred term. For frequency counts by preferred term, if +there are multiple occurrences of the same AE in an +individual we count them only once.

+

To create this table we will need to use a combination of several +layout creating functions in a tabulation pipeline.

+

We start by creating the high-level summary. The layout creating +function in tern that can do this is +summarize_num_patients():

+
+basic_table() %>%
+  split_cols_by(var = "ACTARM") %>%
+  add_colcounts() %>%
+  add_overall_col(label = "All Patients") %>%
+  summarize_num_patients(
+    var = "USUBJID",
+    .stats = c("unique", "nonunique"),
+    .labels = c(
+      unique = "Total number of patients with at least one AE",
+      nonunique = "Overall total number of events"
+    )
+  ) %>%
+  build_table(
+    df = adae,
+    alt_counts_df = adsl
+  )
+#>                                                  A: Drug X    B: Placebo    C: Combination   All Patients
+#>                                                   (N=134)       (N=134)        (N=132)         (N=400)   
+#> —————————————————————————————————————————————————————————————————————————————————————————————————————————
+#> Total number of patients with at least one AE   122 (91.0%)   123 (91.8%)    120 (90.9%)     365 (91.2%) 
+#> Overall total number of events                      609           622            703             1934
+

Note that for this table, the denominator used for percentages and +shown in the header of the table (N = xx) is defined based +on the subject-level dataset adsl. This is done by using +the alt_df_counts argument in build_table(), +which provides an alternative data set for deriving the counts in the +header. This is often required when we work with data sets that include +multiple records per patient as df, such as +adae here.

+
+

Statistics Functions +

+

Before building out the rest of the AE table it is +helpful to introduce some more tern package design +conventions. Each layout creating function in tern is a +wrapper for a Statistics function. Statistics functions are the ones +that do the actual computation of numbers in a table. These functions +always return named lists whose elements are the statistics available to +include in a layout via the .stats argument at the layout +creating function level.

+

Statistics functions follow a naming convention to always begin with +s_* and for ease of use are documented on the same page as +their layout creating function counterpart. It is helpful to review a +Statistic function to understand the logic used to calculate the numbers +in a table and see what options may be available to modify the +analysis.

+

For example, the Statistics function calculating the numbers in +summarize_num_patients() is s_num_patients(). +The results of this Statistics function is a list with the elements +unique, nonunique and +unique_count:

+
+s_num_patients(x = adae$USUBJID, labelstr = "", .N_col = nrow(adae))
+#> $unique
+#> [1] 365.000000   0.188728
+#> attr(,"label")
+#> [1] ""
+#> 
+#> $nonunique
+#> [1] 1934
+#> attr(,"label")
+#> [1] ""
+#> 
+#> $unique_count
+#> [1] 365
+#> attr(,"label")
+#> [1] "(n)"
+

From these results you can see that the unique and +nonunique statistics are those displayed in the “All +Patients” column in the initial AE table output above. Also +you can see that these are raw numbers and are not formatted in any way. +All formatting functionality is handled at the layout creating function +level with the .formats argument.

+

Now that we know what types of statistics can be derived by +s_num_patients(), we can try modifying the default layout +returned by summarize_num_patients(). Instead of reporting +the unique and nonqunie statistics, we specify +that the analysis should include only the unique_count +statistic. The result will show only the counts of unique patients. Note +we make this update in both the .stats and +.labels argument of +summarize_num_patients().

+
+basic_table() %>%
+  split_cols_by(var = "ACTARM") %>%
+  add_colcounts() %>%
+  add_overall_col(label = "All Patients") %>%
+  summarize_num_patients(
+    var = "USUBJID",
+    .stats = "unique_count",
+    .labels = c(unique_count = "Total number of patients with at least one AE")
+  ) %>%
+  build_table(
+    df = adae,
+    alt_counts_df = adsl
+  )
+#>                                                 A: Drug X   B: Placebo   C: Combination   All Patients
+#>                                                  (N=134)     (N=134)        (N=132)         (N=400)   
+#> ——————————————————————————————————————————————————————————————————————————————————————————————————————
+#> Total number of patients with at least one AE      122         123            120             365
+

Let’s now continue building on the layout for the adverse event +table.

+

After we have the top-level summary, we can repeat the same summary +at each system organ class level. To do this we split the analysis data +with split_rows_by() before calling again +summarize_num_patients().

+
+basic_table() %>%
+  split_cols_by(var = "ACTARM") %>%
+  add_colcounts() %>%
+  add_overall_col(label = "All Patients") %>%
+  summarize_num_patients(
+    var = "USUBJID",
+    .stats = c("unique", "nonunique"),
+    .labels = c(
+      unique = "Total number of patients with at least one AE",
+      nonunique = "Overall total number of events"
+    )
+  ) %>%
+  split_rows_by(
+    "AEBODSYS",
+    child_labels = "visible",
+    nested = FALSE,
+    indent_mod = -1L,
+    split_fun = drop_split_levels
+  ) %>%
+  summarize_num_patients(
+    var = "USUBJID",
+    .stats = c("unique", "nonunique"),
+    .labels = c(
+      unique = "Total number of patients with at least one AE",
+      nonunique = "Overall total number of events"
+    )
+  ) %>%
+  build_table(
+    df = adae,
+    alt_counts_df = adsl
+  )
+#>                                                    A: Drug X    B: Placebo    C: Combination   All Patients
+#>                                                     (N=134)       (N=134)        (N=132)         (N=400)   
+#> ———————————————————————————————————————————————————————————————————————————————————————————————————————————
+#> Total number of patients with at least one AE     122 (91.0%)   123 (91.8%)    120 (90.9%)     365 (91.2%) 
+#> Overall total number of events                        609           622            703             1934    
+#> cl A.1                                                                                                     
+#>   Total number of patients with at least one AE   78 (58.2%)    75 (56.0%)      89 (67.4%)     242 (60.5%) 
+#>   Overall total number of events                      132           130            160             422     
+#> cl B.1                                                                                                     
+#>   Total number of patients with at least one AE   47 (35.1%)    49 (36.6%)      43 (32.6%)     139 (34.8%) 
+#>   Overall total number of events                      56            60              62             178     
+#> cl B.2                                                                                                     
+#>   Total number of patients with at least one AE   79 (59.0%)    74 (55.2%)      85 (64.4%)     238 (59.5%) 
+#>   Overall total number of events                      129           138            143             410     
+#> cl C.1                                                                                                     
+#>   Total number of patients with at least one AE   43 (32.1%)    46 (34.3%)      43 (32.6%)     132 (33.0%) 
+#>   Overall total number of events                      55            63              64             182     
+#> cl C.2                                                                                                     
+#>   Total number of patients with at least one AE   35 (26.1%)    48 (35.8%)      55 (41.7%)     138 (34.5%) 
+#>   Overall total number of events                      48            53              65             166     
+#> cl D.1                                                                                                     
+#>   Total number of patients with at least one AE   79 (59.0%)    67 (50.0%)      80 (60.6%)     226 (56.5%) 
+#>   Overall total number of events                      127           106            135             368     
+#> cl D.2                                                                                                     
+#>   Total number of patients with at least one AE   47 (35.1%)    58 (43.3%)      57 (43.2%)     162 (40.5%) 
+#>   Overall total number of events                      62            72              74             208
+

The table looks almost ready. For the final step, we need a layout +creating function that can produce a count table of event frequencies. +The layout creating function for this is +count_occurrences(). Let’s first try using this function in +a simpler layout without row splits:

+
+basic_table() %>%
+  split_cols_by(var = "ACTARM") %>%
+  add_colcounts() %>%
+  add_overall_col(label = "All Patients") %>%
+  count_occurrences(vars = "AEDECOD") %>%
+  build_table(
+    df = adae,
+    alt_counts_df = adsl
+  )
+#>                 A: Drug X    B: Placebo   C: Combination   All Patients
+#>                  (N=134)      (N=134)        (N=132)         (N=400)   
+#> ———————————————————————————————————————————————————————————————————————
+#> dcd A.1.1.1.1   50 (37.3%)   45 (33.6%)     63 (47.7%)     158 (39.5%) 
+#> dcd A.1.1.1.2   48 (35.8%)   48 (35.8%)     50 (37.9%)     146 (36.5%) 
+#> dcd B.1.1.1.1   47 (35.1%)   49 (36.6%)     43 (32.6%)     139 (34.8%) 
+#> dcd B.2.1.2.1   49 (36.6%)   44 (32.8%)     52 (39.4%)     145 (36.2%) 
+#> dcd B.2.2.3.1   48 (35.8%)   54 (40.3%)     51 (38.6%)     153 (38.2%) 
+#> dcd C.1.1.1.3   43 (32.1%)   46 (34.3%)     43 (32.6%)     132 (33.0%) 
+#> dcd C.2.1.2.1   35 (26.1%)   48 (35.8%)     55 (41.7%)     138 (34.5%) 
+#> dcd D.1.1.1.1   50 (37.3%)   42 (31.3%)     51 (38.6%)     143 (35.8%) 
+#> dcd D.1.1.4.2   48 (35.8%)   42 (31.3%)     50 (37.9%)     140 (35.0%) 
+#> dcd D.2.1.5.3   47 (35.1%)   58 (43.3%)     57 (43.2%)     162 (40.5%)
+

Putting everything together, the final AE table looks +like this:

+
+basic_table() %>%
+  split_cols_by(var = "ACTARM") %>%
+  add_colcounts() %>%
+  add_overall_col(label = "All Patients") %>%
+  summarize_num_patients(
+    var = "USUBJID",
+    .stats = c("unique", "nonunique"),
+    .labels = c(
+      unique = "Total number of patients with at least one AE",
+      nonunique = "Overall total number of events"
+    )
+  ) %>%
+  split_rows_by(
+    "AEBODSYS",
+    child_labels = "visible",
+    nested = FALSE,
+    indent_mod = -1L,
+    split_fun = drop_split_levels
+  ) %>%
+  summarize_num_patients(
+    var = "USUBJID",
+    .stats = c("unique", "nonunique"),
+    .labels = c(
+      unique = "Total number of patients with at least one AE",
+      nonunique = "Overall total number of events"
+    )
+  ) %>%
+  count_occurrences(vars = "AEDECOD") %>%
+  build_table(
+    df = adae,
+    alt_counts_df = adsl
+  )
+#>                                                    A: Drug X    B: Placebo    C: Combination   All Patients
+#>                                                     (N=134)       (N=134)        (N=132)         (N=400)   
+#> ———————————————————————————————————————————————————————————————————————————————————————————————————————————
+#> Total number of patients with at least one AE     122 (91.0%)   123 (91.8%)    120 (90.9%)     365 (91.2%) 
+#> Overall total number of events                        609           622            703             1934    
+#> cl A.1                                                                                                     
+#>   Total number of patients with at least one AE   78 (58.2%)    75 (56.0%)      89 (67.4%)     242 (60.5%) 
+#>   Overall total number of events                      132           130            160             422     
+#>     dcd A.1.1.1.1                                 50 (37.3%)    45 (33.6%)      63 (47.7%)     158 (39.5%) 
+#>     dcd A.1.1.1.2                                 48 (35.8%)    48 (35.8%)      50 (37.9%)     146 (36.5%) 
+#> cl B.1                                                                                                     
+#>   Total number of patients with at least one AE   47 (35.1%)    49 (36.6%)      43 (32.6%)     139 (34.8%) 
+#>   Overall total number of events                      56            60              62             178     
+#>     dcd B.1.1.1.1                                 47 (35.1%)    49 (36.6%)      43 (32.6%)     139 (34.8%) 
+#> cl B.2                                                                                                     
+#>   Total number of patients with at least one AE   79 (59.0%)    74 (55.2%)      85 (64.4%)     238 (59.5%) 
+#>   Overall total number of events                      129           138            143             410     
+#>     dcd B.2.1.2.1                                 49 (36.6%)    44 (32.8%)      52 (39.4%)     145 (36.2%) 
+#>     dcd B.2.2.3.1                                 48 (35.8%)    54 (40.3%)      51 (38.6%)     153 (38.2%) 
+#> cl C.1                                                                                                     
+#>   Total number of patients with at least one AE   43 (32.1%)    46 (34.3%)      43 (32.6%)     132 (33.0%) 
+#>   Overall total number of events                      55            63              64             182     
+#>     dcd C.1.1.1.3                                 43 (32.1%)    46 (34.3%)      43 (32.6%)     132 (33.0%) 
+#> cl C.2                                                                                                     
+#>   Total number of patients with at least one AE   35 (26.1%)    48 (35.8%)      55 (41.7%)     138 (34.5%) 
+#>   Overall total number of events                      48            53              65             166     
+#>     dcd C.2.1.2.1                                 35 (26.1%)    48 (35.8%)      55 (41.7%)     138 (34.5%) 
+#> cl D.1                                                                                                     
+#>   Total number of patients with at least one AE   79 (59.0%)    67 (50.0%)      80 (60.6%)     226 (56.5%) 
+#>   Overall total number of events                      127           106            135             368     
+#>     dcd D.1.1.1.1                                 50 (37.3%)    42 (31.3%)      51 (38.6%)     143 (35.8%) 
+#>     dcd D.1.1.4.2                                 48 (35.8%)    42 (31.3%)      50 (37.9%)     140 (35.0%) 
+#> cl D.2                                                                                                     
+#>   Total number of patients with at least one AE   47 (35.1%)    58 (43.3%)      57 (43.2%)     162 (40.5%) 
+#>   Overall total number of events                      62            72              74             208     
+#>     dcd D.2.1.5.3                                 47 (35.1%)    58 (43.3%)      57 (43.2%)     162 (40.5%)
+
+
+
+

Response Table +

+

A typical response table for a binary clinical trial endpoint may be +composed of several different analyses:

+
    +
  • Proportion of responders in each treatment group
  • +
  • Difference between proportion of responders in comparison groups +vs. control group
  • +
  • Chi-Square test for difference in response rates between comparison +groups vs. control group
  • +
+

We can build a table layout like this by following the same approach +we used for the AE table: each table section will be +produced using a different layout creating function from +tern.

+

First we start with some data preparation steps to set up the +analysis dataset. We select the endpoint to analyze from +PARAMCD and define the logical variable is_rsp +which indicates whether a patient is classified as a responder or +not.

+
+# Preprocessing to select an analysis endpoint.
+anl <- adrs %>%
+  dplyr::filter(PARAMCD == "BESRSPI") %>%
+  dplyr::mutate(is_rsp = AVALC %in% c("CR", "PR"))
+

To create a summary of the proportion of responders in each treatment +group, use the estimate_proportion() layout creating +function:

+
+basic_table() %>%
+  split_cols_by(var = "ARM") %>%
+  add_colcounts() %>%
+  estimate_proportion(
+    vars = "is_rsp",
+    table_names = "est_prop"
+  ) %>%
+  build_table(anl)
+#>                                   A: Drug X      B: Placebo    C: Combination
+#>                                    (N=134)        (N=134)         (N=132)    
+#> —————————————————————————————————————————————————————————————————————————————
+#> Responders                       114 (85.1%)     90 (67.2%)     120 (90.9%)  
+#> 95% CI (Wald, with correction)   (78.7, 91.5)   (58.8, 75.5)    (85.6, 96.2)
+

To specify which arm in the table should be used as the reference, +use the argument ref_group from +split_cols_by(). Below we change the reference arm to “B: +Placebo” and so this arm is displayed as the first column:

+
+basic_table() %>%
+  split_cols_by(var = "ARM", ref_group = "B: Placebo") %>%
+  add_colcounts() %>%
+  estimate_proportion(
+    vars = "is_rsp"
+  ) %>%
+  build_table(anl)
+#>                                   B: Placebo     A: Drug X     C: Combination
+#>                                    (N=134)        (N=134)         (N=132)    
+#> —————————————————————————————————————————————————————————————————————————————
+#> Responders                        90 (67.2%)    114 (85.1%)     120 (90.9%)  
+#> 95% CI (Wald, with correction)   (58.8, 75.5)   (78.7, 91.5)    (85.6, 96.2)
+

To further customize the analysis, we can use the method +and conf_level arguments to modify the type of confidence +interval that is calculated:

+
+basic_table() %>%
+  split_cols_by(var = "ARM", ref_group = "B: Placebo") %>%
+  add_colcounts() %>%
+  estimate_proportion(
+    vars = "is_rsp",
+    method = "clopper-pearson",
+    conf_level = 0.9
+  ) %>%
+  build_table(anl)
+#>                             B: Placebo     A: Drug X     C: Combination
+#>                              (N=134)        (N=134)         (N=132)    
+#> ———————————————————————————————————————————————————————————————————————
+#> Responders                  90 (67.2%)    114 (85.1%)     120 (90.9%)  
+#> 90% CI (Clopper-Pearson)   (59.9, 73.9)   (79.1, 89.9)    (85.7, 94.7)
+

The next table section needed should summarize the difference in +response rates between the reference arm each comparison arm. Use +estimate_proportion_diff() layout creating function for +this:

+
+basic_table() %>%
+  split_cols_by(var = "ARM", ref_group = "B: Placebo") %>%
+  add_colcounts() %>%
+  estimate_proportion_diff(
+    vars = "is_rsp",
+    show_labels = "visible",
+    var_labels = "Unstratified Analysis"
+  ) %>%
+  build_table(anl)
+#>                                      B: Placebo    A: Drug X    C: Combination
+#>                                       (N=134)       (N=134)        (N=132)    
+#> ——————————————————————————————————————————————————————————————————————————————
+#> Unstratified Analysis                                                         
+#>   Difference in Response rate (%)                    17.9            23.7     
+#>     95% CI (Wald, with correction)                (7.2, 28.6)    (13.7, 33.8)
+

The final section needed to complete the table includes a statistical +test for the difference in response rates. Use the +test_proportion_diff() layout creating function for +this:

+
+basic_table() %>%
+  split_cols_by(var = "ARM", ref_group = "B: Placebo") %>%
+  add_colcounts() %>%
+  test_proportion_diff(vars = "is_rsp") %>%
+  build_table(anl)
+#>                                B: Placebo   A: Drug X   C: Combination
+#>                                 (N=134)      (N=134)       (N=132)    
+#> ——————————————————————————————————————————————————————————————————————
+#>   p-value (Chi-Squared Test)                 0.0006        <0.0001
+

To customize the output, we use the method argument to +select a Chi-Squared test with Schouten correction.

+
+basic_table() %>%
+  split_cols_by(var = "ARM", ref_group = "B: Placebo") %>%
+  add_colcounts() %>%
+  test_proportion_diff(
+    vars = "is_rsp",
+    method = "schouten"
+  ) %>%
+  build_table(anl)
+#>                                                         B: Placebo   A: Drug X   C: Combination
+#>                                                          (N=134)      (N=134)       (N=132)    
+#> ———————————————————————————————————————————————————————————————————————————————————————————————
+#>   p-value (Chi-Squared Test with Schouten Correction)                 0.0008        <0.0001
+

Now we can put all the table sections together in one layout +pipeline. Note there is one more small change needed. Since the primary +analysis variable in all table sections is the same +(is_rsp), we need to give each sub-table a unique name. +This is done by adding the table_names argument and +providing unique names through that:

+
+basic_table() %>%
+  split_cols_by(var = "ARM", ref_group = "B: Placebo") %>%
+  add_colcounts() %>%
+  estimate_proportion(
+    vars = "is_rsp",
+    method = "clopper-pearson",
+    conf_level = 0.9,
+    table_names = "est_prop"
+  ) %>%
+  estimate_proportion_diff(
+    vars = "is_rsp",
+    show_labels = "visible",
+    var_labels = "Unstratified Analysis",
+    table_names = "est_prop_diff"
+  ) %>%
+  test_proportion_diff(
+    vars = "is_rsp",
+    method = "schouten",
+    table_names = "test_prop_diff"
+  ) %>%
+  build_table(anl)
+#>                                                          B: Placebo     A: Drug X     C: Combination
+#>                                                           (N=134)        (N=134)         (N=132)    
+#> ————————————————————————————————————————————————————————————————————————————————————————————————————
+#> Responders                                               90 (67.2%)    114 (85.1%)     120 (90.9%)  
+#> 90% CI (Clopper-Pearson)                                (59.9, 73.9)   (79.1, 89.9)    (85.7, 94.7) 
+#> Unstratified Analysis                                                                               
+#>   Difference in Response rate (%)                                          17.9            23.7     
+#>     95% CI (Wald, with correction)                                     (7.2, 28.6)     (13.7, 33.8) 
+#>   p-value (Chi-Squared Test with Schouten Correction)                     0.0008         <0.0001
+
+
+
+

Summary +

+

Tabulation with tern builds on top of the the layout +tabulation framework from rtables. Complex tables are built +step by step in a pipeline by combining layout creating functions that +perform a specific type of analysis.

+

The tern analyze functions introduced in this vignette +are:

+ +

Layout creating functions build a formatted layout by +controlling features such as labels, numerical display formats and +indentation. These functions are wrappers for the Statistics functions +which calculate the raw summaries of each analysis. You can easily spot +Statistics functions in the documentation because they always begin with +the prefix s_. It can be helpful to inspect and run +Statistics functions to understand ways an analysis can be +customized.

+
+
+
+ + + + +
+ + + + + + + diff --git a/v0.9.2-rc1/articles/tern.html b/v0.9.2-rc1/articles/tern.html new file mode 100644 index 0000000000..af25388e64 --- /dev/null +++ b/v0.9.2-rc1/articles/tern.html @@ -0,0 +1,330 @@ + + + + + + + + +Introduction to tern • tern + + + + + + + + + + + Skip to contents + + +
+ + + + +
+
+ + + +
+

Introduction to tern +

+
+

This vignette shows the general purpose and syntax of the +tern R package.
+The tern R package contains analytical functions for +creating tables and graphs useful for clinical trials and other +statistical analysis. The main focus is on the clinical trial reporting +tables but the graphs related to the clinical trials are also valuable. +The core functionality for tabulation is built on top of the more +general purpose rtables package.

+

It +is strongly recommended that you start by reading the “Introduction to +rtables” vignette to get familiar with the concept of +rtables.

+
+
+
+

Common Clinical Trials Analyses +

+

The package provides a large range of functionality to create tables +and graphs used for clinical trial and other statistical analysis.

+

rtables tabulation extended by clinical trials specific +functions:

+
    +
  • demographics
  • +
  • unique patients
  • +
  • exposure across patients
  • +
  • change from baseline for parameters
  • +
  • statistical model fits: MMRM, logistic regression, Cox +regression, …
  • +
  • +
+

rtables tabulation helper functions:

+
    +
  • pre-processing
  • +
  • conversions and transformations
  • +
  • +
+

data visualizations connected with clinical trials:

+
    +
  • Kaplan-Meier plots
  • +
  • forest plots
  • +
  • line plots
  • +
  • +
+

data visualizations helper functions:

+
    +
  • arrange/stack multiple graphs
  • +
  • embellishing graphs/tables with metadata and details, such as adding +titles, footnotes, page number, etc.
  • +
  • +
+

The reference of tern functions is available on the +tern website functions reference.

+
+
+
+

Analytical Functions for rtables +

+

Analytical functions are used in combination with other +rtables layout functions, in the pipeline which creates the +rtables table. They apply some statistical logic to the +layout of the rtables table. The table layout is +materialized with the rtables::build_table function and the +data.

+

The tern analytical functions are wrappers around the +rtables::analyze function; they offer various methods +useful from the perspective of clinical trials and other statistical +projects.

+

Examples of the tern analytical functions are +tern::count_occurrences, +tern::summarize_ancova and tern::analyze_vars. +As there is no one prefix to identify all tern analytical +functions it is recommended to use the reference subsection on the +tern website.

+

In the rtables code below we first describe the two +tables and assign the descriptions to the variables lyt and +lyt2. We then built the tables using the actual data with +rtables::build_table. The description of a table is called +a table layout. The analyze +instruction adds to the layout that the ARM +variable should be analyzed with the mean analysis function +and the result should be rounded to 1 decimal place. Hence, a +layout is “pre-data”; that is, it’s a description of +how to build a table once we get data.

+ +

Defining the table layout with a pure rtables code.

+
+# Create table layout pure rtables
+lyt <- rtables::basic_table() %>%
+  rtables::split_cols_by(var = "ARM") %>%
+  rtables::split_rows_by(var = "AVISIT") %>%
+  rtables::analyze(vars = "AVAL", mean, format = "xx.x")
+

Below the only tern function is +analyze_vars which replaces the +rtables::analyze function above.

+
+# Create table layout with tern analyze_vars analyze function
+lyt2 <- rtables::basic_table() %>%
+  rtables::split_cols_by(var = "ARM") %>%
+  rtables::split_rows_by(var = "AVISIT") %>%
+  tern::analyze_vars(vars = "AVAL", .formats = c("mean_sd" = "(xx.xx, xx.xx)"))
+
+# Apply table layout to data and produce `rtables` object
+
+adrs <- formatters::ex_adrs
+
+rtables::build_table(lyt, df = adrs)
+#>                    A: Drug X   B: Placebo   C: Combination
+#> ——————————————————————————————————————————————————————————
+#> SCREENING                                                 
+#>   mean                3.0         3.0            3.0      
+#> BASELINE                                                  
+#>   mean                2.5         2.8            2.5      
+#> END OF INDUCTION                                          
+#>   mean                1.7         2.1            1.6      
+#> FOLLOW UP                                                 
+#>   mean                2.2         2.9            2.0
+rtables::build_table(lyt2, df = adrs)
+#>                     A: Drug X      B: Placebo    C: Combination
+#> ———————————————————————————————————————————————————————————————
+#> SCREENING                                                      
+#>   n                    154            178             144      
+#>   Mean (SD)        (3.00, 0.00)   (3.00, 0.00)    (3.00, 0.00) 
+#>   Median               3.0            3.0             3.0      
+#>   Min - Max         3.0 - 3.0      3.0 - 3.0       3.0 - 3.0   
+#> BASELINE                                                       
+#>   n                    136            146             124      
+#>   Mean (SD)        (2.46, 0.88)   (2.77, 1.00)    (2.46, 1.08) 
+#>   Median               3.0            3.0             3.0      
+#>   Min - Max         1.0 - 4.0      1.0 - 5.0       1.0 - 5.0   
+#> END OF INDUCTION                                               
+#>   n                    218            205             217      
+#>   Mean (SD)        (1.75, 0.90)   (2.14, 1.28)    (1.65, 1.06) 
+#>   Median               2.0            2.0             1.0      
+#>   Min - Max         1.0 - 4.0      1.0 - 5.0       1.0 - 5.0   
+#> FOLLOW UP                                                      
+#>   n                    164            153             167      
+#>   Mean (SD)        (2.23, 1.26)   (2.89, 1.29)    (1.97, 1.01) 
+#>   Median               2.0            4.0             2.0      
+#>   Min - Max         1.0 - 4.0      1.0 - 4.0       1.0 - 4.0
+

We see that tern offers advanced analysis by extending +rtables function calls with only one additional function +call.

+

More examples with tabulation analyze functions are presented +in the Tabulation vignette.

+
+
+

Clinical Trials Visualizations +

+

Clinical trial related plots complement the rich palette of +tern tabulation analysis functions. Thus the +tern package delivers a full-featured tool for clinical +trial reporting. The tern plot functions return +ggplot2 or gTree objects, the latter is +returned when a table is attached to the plot.

+
+adsl <- formatters::ex_adsl
+adlb <- formatters::ex_adlb
+adlb <- dplyr::filter(adlb, PARAMCD == "ALT", AVISIT != "SCREENING")
+

The optional nestcolor package can be loaded in to apply +the standardized NEST color palette to all tern plots.

+ +

Line plot without a table generated by the +tern::g_lineplot function.

+
+# Mean with CI
+tern::g_lineplot(adlb, adsl, subtitle = "Laboratory Test:")
+

+

Line plot with a table generated by the tern::g_lineplot +function.

+
+# Mean with CI, table and customized confidence level
+tern::g_lineplot(
+  adlb,
+  adsl,
+  table = c("n", "mean", "mean_ci"),
+  title = "Plot of Mean and 80% Confidence Limits by Visit"
+)
+

+

The first plot is a ggplot2 object and the second plot +is a gTree object, as the latter contains the table. The +second plot has to be properly resized to get a clear and readable table +content.

+

The tern functions used for plot generation are mostly +g_ prefixed. All tern plot functions are +listed on the +tern website functions reference.

+
+
+

Interactive Apps +

+

Most of tern outputs could be easily accommodated into +shiny apps. We recommend applying tern outputs +into teal apps. The teal +package is a shiny-based interactive exploration framework for +analyzing data. teal shiny apps with tern +outputs are available in the teal.modules.clinical +package.

+
+
+

Summary +

+

In summary, tern contains many additional functions for +creating tables, listing and graphs used in clinical trials and other +statistical analyses. The design of the package gives users a lot of +flexibility to meet the analysis needs in a regulatory or exploratory +reporting context.

+

For more information please explore the tern +website.

+
+
+
+ + + + +
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