Risk Difference • Tplyr

Tplyr does not support, nor do we intend to support, a wide array of statistical methods. Our goal is rather to take your focus as an analyst off the mundane summaries so you can focus on the interesting analysis. That said, there are some things that are common enough that we feel that it’s reasonable for us to include. So let’s take a look at risk difference.

Tplyr Implementation

Our current implementation of risk difference is solely built on top of the base R function stats::prop.test(). For any and all questions about this method, please review the stats::prop.test() documentation within R.

Risk difference is built on top of count layers, as it’s a comparison of proportions. To add a risk difference calculation into a count layer, you simply use the function add_risk_diff(). We made a large effort to make this flow very naturally with the count layer construction, so let’s walk through it step by step.

t <- tplyr_table(tplyr_adae, TRTA) %>% 
  add_layer(
    group_count(AEDECOD) %>% 
      set_distinct_by(USUBJID) %>% 
      add_risk_diff(
        c('Xanomeline High Dose', 'Placebo'),
        c('Xanomeline Low Dose', 'Placebo')
      )
  )

suppressWarnings(build(t)) %>% 
  head() %>% 
  select(starts_with("rdiff"), everything()) %>% 
  kable()

rdiff_Xanomeline High Dose_Placebo	rdiff_Xanomeline Low Dose_Placebo	row_label1	var1_Placebo	var1_Xanomeline High Dose	var1_Xanomeline Low Dose	ord_layer_index	ord_layer_1
0.024 (-0.046, 0.094)	0.000 ( 0.000, 0.000)	ACTINIC KERATOSIS	0 ( 0.0%)	1 ( 2.4%)	0 ( 0.0%)	1	1
-0.048 (-0.174, 0.079)	-0.048 (-0.174, 0.079)	ALOPECIA	1 ( 4.8%)	0 ( 0.0%)	0 ( 0.0%)	1	2
0.024 (-0.046, 0.094)	0.119 (-0.015, 0.253)	BLISTER	0 ( 0.0%)	1 ( 2.4%)	5 ( 11.9%)	1	3
-0.048 (-0.174, 0.079)	-0.048 (-0.174, 0.079)	COLD SWEAT	1 ( 4.8%)	0 ( 0.0%)	0 ( 0.0%)	1	4
-0.048 (-0.174, 0.079)	-0.048 (-0.174, 0.079)	DERMATITIS ATOPIC	1 ( 4.8%)	0 ( 0.0%)	0 ( 0.0%)	1	5
0.000 ( 0.000, 0.000)	0.024 (-0.046, 0.094)	DERMATITIS CONTACT	0 ( 0.0%)	0 ( 0.0%)	1 ( 2.4%)	1	6

Comparisons are specified with two-element character vectors. These are simply your comparison group - the first element, and your reference group - the second. This coincides with how you might see risk difference specified in the header of your mock, where you’ll see something like T1-Placebo. You can provide as many comparisons as you want - the values specified in the comparison just need to be valid treatment groups within your data. This works with any treatment group built using add_treat_grps() or add_total_group() as well.

The risk difference calculations are displayed in the rdiff columns. There will be an rdiff column for every comparison that is made, following the convention rdiff_<comparison>_<reference>.

Note the use of base::suppressWarnings() - if the counts used in stats::prop.test() are too low, you’ll get a warning that says “Chi-squared approximation may be incorrect” for every time stats::prop.test() is run with counts that are too low… This could happen a lot, but the warning is perfectly valid.

Controlling Presentation

The default values presented within formatted strings in the built table will be:

The difference
95% confidence interval low
95% confidence interval high

You have a good bit of control over these values though, and this can be controlled in the same way you format the count summaries - using set_format_strings().

t <- tplyr_table(tplyr_adae, TRTA) %>% 
  add_layer(
    group_count(AEDECOD) %>% 
      set_distinct_by(USUBJID) %>% 
      add_risk_diff(
        c('Xanomeline High Dose', 'Placebo'),
        c('Xanomeline Low Dose', 'Placebo')
      ) %>% 
      set_format_strings(
        'n_counts' = f_str('xx (xx.x) [x]', distinct_n, distinct_pct, n),
        'riskdiff' = f_str('xx.xxx, xx.xxx, xx.xxx, xx.xxx, xx.xxx', comp, ref, dif, low, high)
      )
  )

suppressWarnings(build(t)) %>% 
  head() %>% 
  select(starts_with("rdiff"), everything()) %>% 
  kable()

rdiff_Xanomeline High Dose_Placebo	rdiff_Xanomeline Low Dose_Placebo	row_label1	var1_Placebo	var1_Xanomeline High Dose	var1_Xanomeline Low Dose	ord_layer_index	ord_layer_1
0.024, 0.000, 0.024, -0.046, 0.094	0.000, 0.000, 0.000, 0.000, 0.000	ACTINIC KERATOSIS	0 ( 0.0) [0]	1 ( 2.4) [1]	0 ( 0.0) [0]	1	1
0.000, 0.048, -0.048, -0.174, 0.079	0.000, 0.048, -0.048, -0.174, 0.079	ALOPECIA	1 ( 4.8) [1]	0 ( 0.0) [0]	0 ( 0.0) [0]	1	2
0.024, 0.000, 0.024, -0.046, 0.094	0.119, 0.000, 0.119, -0.015, 0.253	BLISTER	0 ( 0.0) [0]	1 ( 2.4) [2]	5 (11.9) [8]	1	3
0.000, 0.048, -0.048, -0.174, 0.079	0.000, 0.048, -0.048, -0.174, 0.079	COLD SWEAT	1 ( 4.8) [3]	0 ( 0.0) [0]	0 ( 0.0) [0]	1	4
0.000, 0.048, -0.048, -0.174, 0.079	0.000, 0.048, -0.048, -0.174, 0.079	DERMATITIS ATOPIC	1 ( 4.8) [1]	0 ( 0.0) [0]	0 ( 0.0) [0]	1	5
0.000, 0.000, 0.000, 0.000, 0.000	0.024, 0.000, 0.024, -0.046, 0.094	DERMATITIS CONTACT	0 ( 0.0) [0]	0 ( 0.0) [0]	1 ( 2.4) [2]	1	6

Take a look at the rdiff columns now - you’ll see they have 5 values. These are:

The comparison proportion (i.e. the estimate[1] output from a stats::prop.test() object)
The reference proportion (i.e. the estimate[2] output from a stats::prop.test() object)
The difference (i.e. estimate[1] - estimate[2])
The lower end of the confidence interval
The upper end of the confidence interval

You have the same control over the formatting of the display of these values here as you do with the count summaries. Taking things a step further, you can also pass forward arguments to stats::prop.test() using a named list and the args argument in add_risk_diff(). This wasn’t done using the ellipsis (i.e. ...) like typical R functions because it’s already used to capture a varying number of comparisons, but it’s not much more difficult to use:

t <- tplyr_table(tplyr_adae, TRTA) %>% 
  add_layer(
    group_count(AEDECOD) %>% 
      set_distinct_by(USUBJID) %>% 
      add_risk_diff(
        c('Xanomeline High Dose', 'Placebo'),
        c('Xanomeline Low Dose', 'Placebo'),
        args = list(conf.level=0.90, alternative='less', correct=FALSE)
      ) %>% 
      set_format_strings(
        'n_counts' = f_str('xx (xx.x) [x]', distinct_n, distinct_pct, n),
        'riskdiff' = f_str('xx.xxx, xx.xxx, xx.xxx, xx.xxx, xx.xxx', comp, ref, dif, low, high)
      )
  )

suppressWarnings(build(t)) %>% 
  head() %>%
  select(starts_with("rdiff"), everything()) %>%  
  kable()

rdiff_Xanomeline High Dose_Placebo	rdiff_Xanomeline Low Dose_Placebo	row_label1	var1_Placebo	var1_Xanomeline High Dose	var1_Xanomeline Low Dose	ord_layer_index	ord_layer_1
0.024, 0.000, 0.024, -1.000, 0.054	0.000, 0.000, 0.000, -1.000, 0.000	ACTINIC KERATOSIS	0 ( 0.0) [0]	1 ( 2.4) [1]	0 ( 0.0) [0]	1	1
0.000, 0.048, -0.048, -1.000, 0.012	0.000, 0.048, -0.048, -1.000, 0.012	ALOPECIA	1 ( 4.8) [1]	0 ( 0.0) [0]	0 ( 0.0) [0]	1	2
0.024, 0.000, 0.024, -1.000, 0.054	0.119, 0.000, 0.119, -1.000, 0.183	BLISTER	0 ( 0.0) [0]	1 ( 2.4) [2]	5 (11.9) [8]	1	3
0.000, 0.048, -0.048, -1.000, 0.012	0.000, 0.048, -0.048, -1.000, 0.012	COLD SWEAT	1 ( 4.8) [3]	0 ( 0.0) [0]	0 ( 0.0) [0]	1	4
0.000, 0.048, -0.048, -1.000, 0.012	0.000, 0.048, -0.048, -1.000, 0.012	DERMATITIS ATOPIC	1 ( 4.8) [1]	0 ( 0.0) [0]	0 ( 0.0) [0]	1	5
0.000, 0.000, 0.000, -1.000, 0.000	0.024, 0.000, 0.024, -1.000, 0.054	DERMATITIS CONTACT	0 ( 0.0) [0]	0 ( 0.0) [0]	1 ( 2.4) [2]	1	6

As seen above, using the args argument, we:

Changed the confidence interval level to 90% instead of the default 95%
Switched the alternative hypothesis of stats::prop.test() to “less” instead of the default “two.sided”
Turned off the Yates’ continuity correction

For more information on these parameters, see the documentation for stats::prop.test().

Other Notes

The default of add_risk_diff() works on the distinct counts available within the count summary.

t <- tplyr_table(tplyr_adae, TRTA, where= AEBODSYS == "SKIN AND SUBCUTANEOUS TISSUE DISORDERS") %>% 
  set_pop_data(tplyr_adsl) %>% 
  set_pop_treat_var(TRT01A) %>% 
  set_pop_where(TRUE) %>% 
  add_layer(
    group_count(vars(AEBODSYS, AEDECOD)) %>% 
      set_distinct_by(USUBJID) %>% 
      add_risk_diff(
        c('Xanomeline High Dose', 'Placebo'),
        c('Xanomeline Low Dose', 'Placebo')
      ) 
  )

suppressWarnings(build(t)) %>% 
  head() %>% 
  select(starts_with("rdiff"), everything()) %>%  
  kable()

rdiff_Xanomeline High Dose_Placebo	rdiff_Xanomeline Low Dose_Placebo	row_label1	row_label2	var1_Placebo	var1_Xanomeline High Dose	var1_Xanomeline Low Dose	ord_layer_index	ord_layer_1	ord_layer_2
0.256 ( 0.104, 0.408)	0.256 ( 0.104, 0.408)	SKIN AND SUBCUTANEOUS TISSUE DISORDERS	SKIN AND SUBCUTANEOUS TISSUE DISORDERS	21 ( 24.4%)	42 ( 50.0%)	42 ( 50.0%)	1	1	Inf
0.012 (-0.023, 0.047)	0.000 ( 0.000, 0.000)	SKIN AND SUBCUTANEOUS TISSUE DISORDERS	ACTINIC KERATOSIS	0 ( 0.0%)	1 ( 1.2%)	0 ( 0.0%)	1	1	1
-0.012 (-0.046, 0.023)	-0.012 (-0.046, 0.023)	SKIN AND SUBCUTANEOUS TISSUE DISORDERS	ALOPECIA	1 ( 1.2%)	0 ( 0.0%)	0 ( 0.0%)	1	1	2
0.012 (-0.023, 0.047)	0.060 (-0.003, 0.122)	SKIN AND SUBCUTANEOUS TISSUE DISORDERS	BLISTER	0 ( 0.0%)	1 ( 1.2%)	5 ( 6.0%)	1	1	3
-0.012 (-0.046, 0.023)	-0.012 (-0.046, 0.023)	SKIN AND SUBCUTANEOUS TISSUE DISORDERS	COLD SWEAT	1 ( 1.2%)	0 ( 0.0%)	0 ( 0.0%)	1	1	4
-0.012 (-0.046, 0.023)	-0.012 (-0.046, 0.023)	SKIN AND SUBCUTANEOUS TISSUE DISORDERS	DERMATITIS ATOPIC	1 ( 1.2%)	0 ( 0.0%)	0 ( 0.0%)	1	1	5

If for whatever reason you’d like to run risk difference on the non-distinct counts, switch the distinct argument to FALSE. add_risk_diff() also will function on multi-level summaries no different than single level, so no concerns there either.

t <- tplyr_table(tplyr_adae, TRTA, where= AEBODSYS == "SKIN AND SUBCUTANEOUS TISSUE DISORDERS") %>% 
  add_layer(
    group_count(AEDECOD) %>% 
      set_distinct_by(USUBJID) %>% 
      add_risk_diff(
        c('Xanomeline High Dose', 'Placebo'),
        c('Xanomeline Low Dose', 'Placebo'),
        distinct=FALSE
      ) 
  )

suppressWarnings(build(t)) %>% 
  head() %>% 
  select(starts_with("rdiff"), everything()) %>%  
  kable()

rdiff_Xanomeline High Dose_Placebo	rdiff_Xanomeline Low Dose_Placebo	row_label1	var1_Placebo	var1_Xanomeline High Dose	var1_Xanomeline Low Dose	ord_layer_index	ord_layer_1
0.009 (-0.018, 0.036)	0.000 ( 0.000, 0.000)	ACTINIC KERATOSIS	0 ( 0.0%)	1 ( 2.4%)	0 ( 0.0%)	1	1
-0.021 (-0.078, 0.035)	-0.021 (-0.077, 0.035)	ALOPECIA	1 ( 4.8%)	0 ( 0.0%)	0 ( 0.0%)	1	2
0.018 (-0.022, 0.058)	0.068 ( 0.008, 0.128)	BLISTER	0 ( 0.0%)	1 ( 2.4%)	5 ( 11.9%)	1	3
-0.064 (-0.149, 0.021)	-0.064 (-0.149, 0.021)	COLD SWEAT	1 ( 4.8%)	0 ( 0.0%)	0 ( 0.0%)	1	4
-0.021 (-0.078, 0.035)	-0.021 (-0.077, 0.035)	DERMATITIS ATOPIC	1 ( 4.8%)	0 ( 0.0%)	0 ( 0.0%)	1	5
0.000 ( 0.000, 0.000)	0.017 (-0.021, 0.055)	DERMATITIS CONTACT	0 ( 0.0%)	0 ( 0.0%)	1 ( 2.4%)	1	6

Risk difference also works with the cols argument, but it’s important to understand how the comparisons work in these situation. Here, it’s still the treatment groups that are compared - but the column argument is used as a “by” variable. For example:

t <- tplyr_table(tplyr_adae, TRTA, where= AEBODSYS == "SKIN AND SUBCUTANEOUS TISSUE DISORDERS", cols=SEX) %>% 
  add_layer(
    group_count(AEDECOD) %>% 
      set_distinct_by(USUBJID) %>% 
      add_risk_diff(
        c('Xanomeline High Dose', 'Placebo'),
        c('Xanomeline Low Dose', 'Placebo')
      ) 
  )

suppressWarnings(build(t)) %>% 
  head() %>% 
  select(starts_with("rdiff"), starts_with("row")) %>% 
  kable()

rdiff_Xanomeline High Dose_Placebo_F	rdiff_Xanomeline High Dose_Placebo_M	rdiff_Xanomeline Low Dose_Placebo_F	rdiff_Xanomeline Low Dose_Placebo_M	row_label1
0.000 ( 0.000, 0.000)	0.036 (-0.069, 0.140)	0.000 ( 0.000, 0.000)	0.000 ( 0.000, 0.000)	ACTINIC KERATOSIS
-0.077 (-0.296, 0.142)	0.000 ( 0.000, 0.000)	-0.077 (-0.281, 0.127)	0.000 ( 0.000, 0.000)	ALOPECIA
0.000 ( 0.000, 0.000)	0.036 (-0.069, 0.140)	0.083 (-0.087, 0.253)	0.167 (-0.096, 0.429)	BLISTER
0.000 ( 0.000, 0.000)	-0.125 (-0.435, 0.185)	0.000 ( 0.000, 0.000)	-0.125 (-0.444, 0.194)	COLD SWEAT
0.000 ( 0.000, 0.000)	-0.125 (-0.435, 0.185)	0.000 ( 0.000, 0.000)	-0.125 (-0.444, 0.194)	DERMATITIS ATOPIC
0.000 ( 0.000, 0.000)	0.000 ( 0.000, 0.000)	0.000 ( 0.000, 0.000)	0.056 (-0.106, 0.217)	DERMATITIS CONTACT

Getting Raw Numbers

Just like you can get the numeric data from a Tplyr layer with get_numeric_data(), we’ve also opened up the door to extract the raw numeric data from risk difference calculations as well. This is done using the function get_stats_data(). The function interface is almost identical to get_numeric_data(), except for the extra parameter of statistic. Although risk difference is the only statistic implemented in Tplyr at the moment (outside of descriptive statistics), we understand that there are multiple methods to calculate risk difference, so we’ve built risk difference in a way that it could be expanded to easily add new methods in the future. And therefore, get_stats_data() the statistic parameter to allow you to differentiate in the situation where there are multiple statistical methods applied to the layer.

The output of get_stats_data() depends on what parameters have been used:

If no specific layer has been entered in the layer parameter, then an element will be returned for each layer
If no statistic has been entered in the statistic parameter, an element will be returned for each statistic for each layer
If neither statistic nor layer are entered, a list of lists is returned, where the outer list is each layer and the inside list is the numeric statistic data for that layer.

This works best when layers are named, as it makes the output much clearer.

t <- tplyr_table(tplyr_adae, TRTA) %>% 
  add_layer(name="PreferredTerm",
    group_count(AEDECOD) %>% 
      set_distinct_by(USUBJID) %>% 
      add_risk_diff(
        c('Xanomeline High Dose', 'Placebo'),
        c('Xanomeline Low Dose', 'Placebo')
      ) 
  ) %>% 
  add_layer(name="BodySystem",
    group_count(AEBODSYS) %>% 
      set_distinct_by(USUBJID) %>% 
      add_risk_diff(
        c('Xanomeline High Dose', 'Placebo'),
        c('Xanomeline Low Dose', 'Placebo')
      ) 
  )

suppressWarnings(
  get_stats_data(t)
  )
#> $PreferredTerm
#> $PreferredTerm$riskdiff
#> # A tibble: 105 × 4
#>    summary_var       measure Xanomeline High Dose_Place…¹ Xanomeline Low Dose_…²
#>    <chr>             <chr>                          <dbl>                  <dbl>
#>  1 ACTINIC KERATOSIS comp                          0.0238                 0     
#>  2 ACTINIC KERATOSIS ref                           0                      0     
#>  3 ACTINIC KERATOSIS dif                           0.0238                 0     
#>  4 ACTINIC KERATOSIS low                          -0.0461                 0     
#>  5 ACTINIC KERATOSIS high                          0.0937                 0     
#>  6 ALOPECIA          comp                          0                      0     
#>  7 ALOPECIA          ref                           0.0476                 0.0476
#>  8 ALOPECIA          dif                          -0.0476                -0.0476
#>  9 ALOPECIA          low                          -0.174                 -0.174 
#> 10 ALOPECIA          high                          0.0792                 0.0792
#> # ℹ 95 more rows
#> # ℹ abbreviated names: ¹`Xanomeline High Dose_Placebo`,
#> #   ²`Xanomeline Low Dose_Placebo`
#> 
#> 
#> $BodySystem
#> $BodySystem$riskdiff
#> # A tibble: 5 × 4
#>   summary_var              measure Xanomeline High Dose…¹ Xanomeline Low Dose_…²
#>   <chr>                    <chr>                    <dbl>                  <dbl>
#> 1 SKIN AND SUBCUTANEOUS T… comp                         1                      1
#> 2 SKIN AND SUBCUTANEOUS T… ref                          1                      1
#> 3 SKIN AND SUBCUTANEOUS T… dif                          0                      0
#> 4 SKIN AND SUBCUTANEOUS T… low                          0                      0
#> 5 SKIN AND SUBCUTANEOUS T… high                         0                      0
#> # ℹ abbreviated names: ¹`Xanomeline High Dose_Placebo`,
#> #   ²`Xanomeline Low Dose_Placebo`

Instead of playing around with lists, get_stats_data() is most advantageous if you’d like to extract out some data specifically. Let’s say that you’d like to see just the difference values from the Preferred Term layer in the table above.


suppressWarnings(
  get_stats_data(t, layer='PreferredTerm', statistic='riskdiff', where= measure == "dif")
  ) %>% 
  head() %>% 
  kable()

summary_var	measure	Xanomeline High Dose_Placebo	Xanomeline Low Dose_Placebo
ACTINIC KERATOSIS	dif	0.0238095	0.0000000
ALOPECIA	dif	-0.0476190	-0.0476190
BLISTER	dif	0.0238095	0.1190476
COLD SWEAT	dif	-0.0476190	-0.0476190
DERMATITIS ATOPIC	dif	-0.0476190	-0.0476190
DERMATITIS CONTACT	dif	0.0000000	0.0238095

Using this data frame, you have access to the un-formatted numeric values before any rounding or formatting. This gives you flexibility to use these calculations in other contexts, make more precise comparisons in a double programming scenario, or take a deeper look into the calculations that were made if any values in the result warrant further investigation.