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Risk Difference

riskdiff.Rmd

Introduction

In clinical trials, adverse event tables typically display the frequency of events by treatment group. While these counts are informative on their own, regulatory reviewers and study teams often want to see a direct statistical comparison between groups – specifically, the difference in proportions and a confidence interval around that difference. This quantity is the risk difference.

The risk difference answers a straightforward question: how much more (or less) likely is an event in one group compared to another? A risk difference of 10% with a 95% confidence interval of (2%, 18%) tells you the event rate was 10 percentage points higher in the treatment group, and you can be reasonably confident the true difference falls between 2 and 18 percentage points.

tplyr2 computes risk differences using stats::prop.test() with no continuity correction, producing an asymptotic Wald-type confidence interval. This is configured entirely through the risk_diff parameter in layer_settings(), and the results appear as additional columns in the output alongside the standard count summaries.

Basic Risk Difference

To add a risk difference to a count layer, pass a risk_diff list inside layer_settings(). At minimum, you need to specify which two treatment levels to compare via the comparisons parameter.

spec <- tplyr_spec(
  cols = "TRTA",
  layers = tplyr_layers(
    group_count("AEDECOD",
      settings = layer_settings(
        distinct_by = "USUBJID",
        format_strings = list(
          n_counts = f_str("xxx (xx.x%)", "distinct_n", "distinct_pct")
        ),
        risk_diff = list(
          comparisons = list(c("Xanomeline High Dose", "Placebo"))
        )
      )
    )
  )
)

result <- tplyr_build(spec, tplyr_adae)
kable(head(result[, c("rowlabel1", "res1", "res2", "res3", "rdiff1")], 10))
rowlabel1 res1 res2 res3 rdiff1
ABDOMINAL PAIN 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0)
AGITATION 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0)
ANXIETY 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0)
APPLICATION SITE DERMATITIS 1 ( 3.1%) 3 ( 7.0%) 2 ( 4.0%) 1.8 (-4.2, 7.7)
APPLICATION SITE ERYTHEMA 0 ( 0.0%) 3 ( 7.0%) 4 ( 8.0%) 3.9 (-0.4, 8.2)
APPLICATION SITE IRRITATION 1 ( 3.1%) 3 ( 7.0%) 2 ( 4.0%) 3.1 (-3.4, 9.5)
APPLICATION SITE PAIN 0 ( 0.0%) 1 ( 2.3%) 0 ( 0.0%) 1.3 (-1.2, 3.8)
APPLICATION SITE PRURITUS 4 (12.5%) 6 (14.0%) 5 (10.0%) 0.6 (-9.7, 10.8)
APPLICATION SITE REACTION 1 ( 3.1%) 1 ( 2.3%) 0 ( 0.0%) -0.8 (-5.7, 4.0)
APPLICATION SITE URTICARIA 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0)

The risk difference appears in the rdiff1 column. Each comparison pair you specify produces one rdiff column, numbered sequentially. The column carries a label attribute indicating which groups were compared.

attr(result$rdiff1, "label")
#> [1] "Xanomeline High Dose vs Placebo"

Note the order of the comparison pair matters: the first element is the treatment group and the second is the reference. The risk difference is computed as the treatment proportion minus the reference proportion, expressed as a percentage.

Configuring Comparisons

You are not limited to a single comparison. When your study has multiple active dose groups, you often want to compare each one against placebo. Pass multiple pairs in the comparisons list.

spec <- tplyr_spec(
  cols = "TRTA",
  layers = tplyr_layers(
    group_count("AEDECOD",
      settings = layer_settings(
        distinct_by = "USUBJID",
        format_strings = list(
          n_counts = f_str("xxx (xx.x%)", "distinct_n", "distinct_pct")
        ),
        risk_diff = list(
          comparisons = list(
            c("Xanomeline High Dose", "Placebo"),
            c("Xanomeline Low Dose", "Placebo")
          ),
          format = f_str("xx.x (xx.x, xx.x)", "rdiff", "lower", "upper")
        )
      )
    )
  )
)

result <- tplyr_build(spec, tplyr_adae)
kable(head(result[, c("rowlabel1", "res1", "res2", "res3", "rdiff1", "rdiff2")], 8))
rowlabel1 res1 res2 res3 rdiff1 rdiff2
ABDOMINAL PAIN 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0) 1.3 (-1.2, 3.9)
AGITATION 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0) 1.3 (-1.2, 3.9)
ANXIETY 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0) 1.3 (-1.2, 3.9)
APPLICATION SITE DERMATITIS 1 ( 3.1%) 3 ( 7.0%) 2 ( 4.0%) 1.8 (-4.2, 7.7) 0.5 (-5.0, 6.0)
APPLICATION SITE ERYTHEMA 0 ( 0.0%) 3 ( 7.0%) 4 ( 8.0%) 3.9 (-0.4, 8.2) 5.3 ( 0.2, 10.3)
APPLICATION SITE IRRITATION 1 ( 3.1%) 3 ( 7.0%) 2 ( 4.0%) 3.1 (-3.4, 9.5) 0.5 (-5.0, 6.0)
APPLICATION SITE PAIN 0 ( 0.0%) 1 ( 2.3%) 0 ( 0.0%) 1.3 (-1.2, 3.8) 0.0 ( 0.0, 0.0)
APPLICATION SITE PRURITUS 4 (12.5%) 6 (14.0%) 5 (10.0%) 0.6 (-9.7, 10.8) -1.9 (-11.7, 7.8)

The first comparison (Xanomeline High Dose vs Placebo) goes into rdiff1, and the second (Xanomeline Low Dose vs Placebo) goes into rdiff2. Each column gets its own label.

attr(result$rdiff1, "label")
#> [1] "Xanomeline High Dose vs Placebo"
attr(result$rdiff2, "label")
#> [1] "Xanomeline Low Dose vs Placebo"

Formatting Output

The risk difference format is controlled through the format parameter, which takes an f_str() object just like the count format strings. Four variables are available for use in the format:

  • rdiff – the risk difference as a percentage
  • lower – the lower bound of the confidence interval
  • upper – the upper bound of the confidence interval
  • p_value – the p-value from prop.test()

When no format is specified, tplyr2 uses the default: f_str("xx.x (xx.x, xx.x)", "rdiff", "lower", "upper").

You can include the p-value in the formatted string if your table requires it.

spec <- tplyr_spec(
  cols = "TRTA",
  layers = tplyr_layers(
    group_count("AEDECOD",
      settings = layer_settings(
        distinct_by = "USUBJID",
        format_strings = list(
          n_counts = f_str("xxx (xx.x%)", "distinct_n", "distinct_pct")
        ),
        risk_diff = list(
          comparisons = list(c("Xanomeline High Dose", "Placebo")),
          format = f_str("xx.x (xx.x, xx.x) [x.xxxx]", "rdiff", "lower", "upper", "p_value")
        )
      )
    )
  )
)

result <- tplyr_build(spec, tplyr_adae)
kable(head(result[, c("rowlabel1", "res1", "res2", "res3", "rdiff1")], 8))
rowlabel1 res1 res2 res3 rdiff1
ABDOMINAL PAIN 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0) [ ]
AGITATION 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0) [ ]
ANXIETY 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0) [ ]
APPLICATION SITE DERMATITIS 1 ( 3.1%) 3 ( 7.0%) 2 ( 4.0%) 1.8 (-4.2, 7.7) [0.5887]
APPLICATION SITE ERYTHEMA 0 ( 0.0%) 3 ( 7.0%) 4 ( 8.0%) 3.9 (-0.4, 8.2) [0.1707]
APPLICATION SITE IRRITATION 1 ( 3.1%) 3 ( 7.0%) 2 ( 4.0%) 3.1 (-3.4, 9.5) [0.3996]
APPLICATION SITE PAIN 0 ( 0.0%) 1 ( 2.3%) 0 ( 0.0%) 1.3 (-1.2, 3.8) [0.4328]
APPLICATION SITE PRURITUS 4 (12.5%) 6 (14.0%) 5 (10.0%) 0.6 (-9.7, 10.8) [0.9122]

The x characters in the format string control field width, just as they do for count format strings. Each x reserves one character position, so xx.x gives one decimal place with room for a two-digit integer part. You can adjust the precision to match your table shell requirements.

Confidence Interval Level

By default, tplyr2 computes a 95% confidence interval. You can change this with the ci parameter.

spec <- tplyr_spec(
  cols = "TRTA",
  layers = tplyr_layers(
    group_count("AEDECOD",
      settings = layer_settings(
        distinct_by = "USUBJID",
        format_strings = list(
          n_counts = f_str("xxx (xx.x%)", "distinct_n", "distinct_pct")
        ),
        risk_diff = list(
          comparisons = list(c("Xanomeline High Dose", "Placebo")),
          ci = 0.90,
          format = f_str("xx.x (xx.x, xx.x)", "rdiff", "lower", "upper")
        )
      )
    )
  )
)

result <- tplyr_build(spec, tplyr_adae)
kable(head(result[, c("rowlabel1", "rdiff1")], 8))
rowlabel1 rdiff1
ABDOMINAL PAIN 0.0 ( 0.0, 0.0)
AGITATION 0.0 ( 0.0, 0.0)
ANXIETY 0.0 ( 0.0, 0.0)
APPLICATION SITE DERMATITIS 1.8 (-3.2, 6.8)
APPLICATION SITE ERYTHEMA 3.9 ( 0.3, 7.5)
APPLICATION SITE IRRITATION 3.1 (-2.3, 8.5)
APPLICATION SITE PAIN 1.3 (-0.8, 3.4)
APPLICATION SITE PRURITUS 0.6 (-8.0, 9.2)

A 90% interval is narrower than a 95% interval for the same data. The confidence level you choose should match your study’s statistical analysis plan.

Risk Difference with Distinct Counts

Risk difference calculations naturally work with the distinct_by setting. When distinct_by is specified, the proportions used for the risk difference are based on distinct subject counts rather than event counts. This is almost always what you want for adverse event tables, where a single subject can contribute multiple events.

spec <- tplyr_spec(
  cols = "TRTA",
  layers = tplyr_layers(
    group_count("AEDECOD",
      settings = layer_settings(
        distinct_by = "USUBJID",
        format_strings = list(
          n_counts = f_str("xxx (xx.x%) [xxx]", "distinct_n", "distinct_pct", "n")
        ),
        risk_diff = list(
          comparisons = list(c("Xanomeline High Dose", "Placebo")),
          format = f_str("xx.x (xx.x, xx.x)", "rdiff", "lower", "upper")
        )
      )
    )
  )
)

result <- tplyr_build(spec, tplyr_adae)
kable(head(result[, c("rowlabel1", "res1", "res2", "res3", "rdiff1")], 8))
rowlabel1 res1 res2 res3 rdiff1
ABDOMINAL PAIN 0 ( 0.0%) [ 0] 0 ( 0.0%) [ 0] 1 ( 2.0%) [ 1] 0.0 ( 0.0, 0.0)
AGITATION 0 ( 0.0%) [ 0] 0 ( 0.0%) [ 0] 1 ( 2.0%) [ 1] 0.0 ( 0.0, 0.0)
ANXIETY 0 ( 0.0%) [ 0] 0 ( 0.0%) [ 0] 1 ( 2.0%) [ 1] 0.0 ( 0.0, 0.0)
APPLICATION SITE DERMATITIS 1 ( 3.1%) [ 1] 3 ( 7.0%) [ 3] 2 ( 4.0%) [ 2] 1.8 (-4.2, 7.7)
APPLICATION SITE ERYTHEMA 0 ( 0.0%) [ 0] 3 ( 7.0%) [ 3] 4 ( 8.0%) [ 4] 3.9 (-0.4, 8.2)
APPLICATION SITE IRRITATION 1 ( 3.1%) [ 1] 3 ( 7.0%) [ 4] 2 ( 4.0%) [ 2] 3.1 (-3.4, 9.5)
APPLICATION SITE PAIN 0 ( 0.0%) [ 0] 1 ( 2.3%) [ 1] 0 ( 0.0%) [ 0] 1.3 (-1.2, 3.8)
APPLICATION SITE PRURITUS 4 (12.5%) [ 4] 6 (14.0%) [ 7] 5 (10.0%) [ 5] 0.6 (-9.7, 10.8)

In this output, the count columns show distinct subjects, their percentage, and the total event count in brackets. The risk difference is computed from the distinct subject proportions, which is the clinically meaningful comparison.

Interaction with Special Rows

An important detail: risk differences are computed before special rows (total rows and missing rows) are appended. This means total and missing rows will have empty risk difference values, which is the expected behavior – a risk difference on a total row is not meaningful.

spec <- tplyr_spec(
  cols = "TRTA",
  layers = tplyr_layers(
    group_count("AEDECOD",
      settings = layer_settings(
        distinct_by = "USUBJID",
        format_strings = list(
          n_counts = f_str("xxx (xx.x%)", "distinct_n", "distinct_pct")
        ),
        total_row = TRUE,
        total_row_label = "Any adverse event",
        risk_diff = list(
          comparisons = list(c("Xanomeline High Dose", "Placebo")),
          format = f_str("xx.x (xx.x, xx.x)", "rdiff", "lower", "upper")
        )
      )
    )
  )
)

result <- tplyr_build(spec, tplyr_adae)
# Show the last few rows including the total row
tail_rows <- tail(result[, c("rowlabel1", "res1", "res2", "res3", "rdiff1")], 5)
kable(tail_rows)
rowlabel1 res1 res2 res3 rdiff1
85 URTICARIA 0 ( 0.0%) 1 ( 2.3%) 1 ( 2.0%) 2.6 (-1.0, 6.2)
86 VENTRICULAR EXTRASYSTOLES 0 ( 0.0%) 1 ( 2.3%) 0 ( 0.0%) 1.3 (-1.2, 3.8)
87 VENTRICULAR SEPTAL DEFECT 0 ( 0.0%) 1 ( 2.3%) 0 ( 0.0%) 1.3 (-1.2, 3.8)
88 VOMITING 0 ( 0.0%) 2 ( 4.7%) 0 ( 0.0%) 2.6 (-1.0, 6.2)
89 WOUND 0 ( 0.0%) 0 ( 0.0%) 1 ( 2.0%) 0.0 ( 0.0, 0.0)

The “Any adverse event” row has an empty rdiff1 value because it is a total row added after the risk difference computation.

Extracting Raw Numbers

The formatted risk difference strings are useful for display, but sometimes you need the underlying numeric values for further analysis or custom formatting. The tplyr_numeric_data() function gives you access to the raw counts that were used to compute the risk differences.

spec <- tplyr_spec(
  cols = "TRTA",
  layers = tplyr_layers(
    group_count("AEDECOD",
      settings = layer_settings(
        distinct_by = "USUBJID",
        format_strings = list(
          n_counts = f_str("xxx (xx.x%)", "distinct_n", "distinct_pct")
        ),
        risk_diff = list(
          comparisons = list(c("Xanomeline High Dose", "Placebo")),
          format = f_str("xx.x (xx.x, xx.x)", "rdiff", "lower", "upper")
        )
      )
    )
  )
)

result <- tplyr_build(spec, tplyr_adae)
nd <- tplyr_numeric_data(result, layer = 1)
kable(head(nd, 10))
TRTA AEDECOD n distinct_n pct distinct_pct total distinct_total
Placebo ABDOMINAL PAIN 0 0 0.000000 0.000 47 32
Placebo AGITATION 0 0 0.000000 0.000 47 32
Placebo ANXIETY 0 0 0.000000 0.000 47 32
Placebo APPLICATION SITE DERMATITIS 1 1 2.127660 3.125 47 32
Placebo APPLICATION SITE ERYTHEMA 0 0 0.000000 0.000 47 32
Placebo APPLICATION SITE IRRITATION 1 1 2.127660 3.125 47 32
Placebo APPLICATION SITE PAIN 0 0 0.000000 0.000 47 32
Placebo APPLICATION SITE PRURITUS 4 4 8.510638 12.500 47 32
Placebo APPLICATION SITE REACTION 1 1 2.127660 3.125 47 32
Placebo APPLICATION SITE URTICARIA 0 0 0.000000 0.000 47 32

This data.frame contains the raw counts, percentages, and denominators per treatment group and preferred term. These are the values that feed into the prop.test() calls.

You can also extract numeric values directly from the formatted risk difference strings using str_extract_num(). This function pulls the nth number from a formatted string.

# Extract the risk difference value (1st number)
result$rdiff_value <- str_extract_num(result$rdiff1, 1)

# Extract the lower CI bound (2nd number)
result$rdiff_lower <- str_extract_num(result$rdiff1, 2)

# Extract the upper CI bound (3rd number)
result$rdiff_upper <- str_extract_num(result$rdiff1, 3)

kable(head(result[, c("rowlabel1", "rdiff1", "rdiff_value", "rdiff_lower", "rdiff_upper")], 8))
rowlabel1 rdiff1 rdiff_value rdiff_lower rdiff_upper
ABDOMINAL PAIN 0.0 ( 0.0, 0.0) 0.0 0.0 0.0
AGITATION 0.0 ( 0.0, 0.0) 0.0 0.0 0.0
ANXIETY 0.0 ( 0.0, 0.0) 0.0 0.0 0.0
APPLICATION SITE DERMATITIS 1.8 (-4.2, 7.7) 1.8 -4.2 7.7
APPLICATION SITE ERYTHEMA 3.9 (-0.4, 8.2) 3.9 -0.4 8.2
APPLICATION SITE IRRITATION 3.1 (-3.4, 9.5) 3.1 -3.4 9.5
APPLICATION SITE PAIN 1.3 (-1.2, 3.8) 1.3 -1.2 3.8
APPLICATION SITE PRURITUS 0.6 (-9.7, 10.8) 0.6 -9.7 10.8

This approach is useful when you need numeric risk difference values for downstream tasks like sorting, filtering, or creating forest plots.

Summary

Risk difference in tplyr2 is configured entirely through the risk_diff parameter in layer_settings(). The key points to remember:

  • Comparisons are specified as pairs of treatment levels, with the first element as the treatment and the second as the reference.
  • Multiple comparisons each produce a separate rdiff column (rdiff1, rdiff2, etc.).
  • Formatting uses f_str() with the variables rdiff, lower, upper, and p_value.
  • Confidence level defaults to 0.95 and is adjustable via the ci parameter.
  • Risk differences are computed before special rows (total, missing), so those rows have empty risk difference values.
  • Raw count data is accessible through tplyr_numeric_data(), and formatted values can be parsed with str_extract_num().