Model-based risk ratios and risk differences

rift_risk_ratio() and rift_risk_difference() estimate the ratio and the difference of the risk of a binary outcome between the levels of an exposure, each level against the first, optionally adjusted for covariates, with a confidence interval. They are the estimators behind the "rr" and "rd" rows of tbl_rift(), exported so they can be called on their own, passed to add_difference() as a custom method, or wrapped in a stat_fns function of tbl_custom_summary().

Four approaches are available, all computed in base R:

"margstd_delta" (the default): marginal standardization after logistic regression. The model outcome ~ by + adj.vars is fit with glm(family = binomial()), every observation's risk is predicted with the exposure set to each level in turn, the predictions are averaged per level, and the ratio or difference of the averages is reported with a delta-method standard error (Localio, Margolis and Berlin, 2007). Without covariates this is the crude risk ratio with its log-scale interval and the crude risk difference with its Wald interval.
"glm": a binomial model with a log link (ratio) or an identity link (difference) (Wacholder, 1986). These models often fail to converge.
"glm_startp": the same binomial model started at the coefficients of the Poisson model with the same link (Spiegelman and Hertzmark, 2005).
"robpoisson": a Poisson model with a log link (ratio) or an identity link (difference) with the HC0 sandwich variance (Zou, 2004).

The limits are large-sample (Wald) limits at conf.level, on the log scale for ratios. The names of the approaches are those of the risks package, which computes the same estimates.

Usage

rift_risk_ratio(
  data,
  variable,
  by,
  adj.vars = NULL,
  value = NULL,
  approach = c("margstd_delta", "glm", "glm_startp", "robpoisson"),
  conf.level = 0.95,
  test.args = list(),
  ...
)

rift_risk_difference(
  data,
  variable,
  by,
  adj.vars = NULL,
  value = NULL,
  approach = c("margstd_delta", "glm", "glm_startp", "robpoisson"),
  conf.level = 0.95,
  test.args = list(),
  ...
)

Arguments

data: (data.frame)
A data frame.
variable: (string)
The outcome column: 0/1, logical, or a column whose event value is given in value.
by: (string)
The exposure column, a factor, character or logical. Its first level is the reference.
adj.vars: (character)
Covariates added to the model. Default is NULL.
value: The value of variable that counts as the event. Default is NULL, which uses 1 for a 0/1 variable, TRUE for a logical, and the yes of a yes/no variable.
approach: (string)
One of "margstd_delta", "glm", "glm_startp" and "robpoisson", described above.
conf.level: (scalar numeric)
Confidence level. Default is 0.95.
test.args: (named list)
An approach given here wins over the argument, so add_difference(test.args = ~ list(approach = "robpoisson")) reaches the function. Default is an empty list.
...: Not used. Accepted so that the functions can be passed to add_difference(), which calls them with more arguments.

Value

A data frame with one row per level of by other than the first: level, reference (the first level), estimate, std.error (on the log scale for a ratio), statistic, p.value, conf.low, conf.high and method. With a two-level by the frame has one row, the shape add_difference() expects from a custom method.

In add_difference()

add_difference(test = ~ "rift_risk_ratio") compares the second level of by with the first, the direction of a regression coefficient and the opposite of "prop.test", which subtracts the second from the first. add_difference() formats a dichotomous variable's estimate as a percentage by default, so pass estimate_fun = ~ label_style_ratio() for a ratio, and rename the header with modify_header().

References

Localio AR, Margolis DJ, Berlin JA. Relative risks and confidence intervals were easily computed indirectly from multivariable logistic regression. J Clin Epidemiol 2007;60:874-82.

Wacholder S. Binomial regression in GLIM: estimating risk ratios and risk differences. Am J Epidemiol 1986;123:174-84.

Spiegelman D, Hertzmark E. Easy SAS calculations for risk or prevalence ratios and differences. Am J Epidemiol 2005;162:199-200.

Zou G. A modified Poisson regression approach to prospective studies with binary data. Am J Epidemiol 2004;159:702-6.

Stopsack KH. risks: Estimate risk ratios and risk differences using regression. R package, https://stopsack.github.io/risks/.

Examples

# Example 1 ----------------------------------
# the crude risk ratio and risk difference of response by treatment
rift_risk_ratio(trial, variable = "response", by = "trt")
#>    level reference estimate std.error  statistic   p.value  conf.low conf.high
#> 1 Drug B    Drug A 1.014545 0.2576207 0.05605406 0.9552987 0.6123284  1.680965
#>                                                method
#> 1 Risk ratio (marginal standardization, delta method)
rift_risk_difference(trial, variable = "response", by = "trt")
#>    level reference   estimate  std.error  statistic   p.value   conf.low
#> 1 Drug B    Drug A 0.00344086 0.06136707 0.05607014 0.9552859 -0.1168364
#>   conf.high                                                   method
#> 1 0.1237181 Risk difference (marginal standardization, delta method)

# Example 2 ----------------------------------
# adjusted for grade, with a Poisson model and robust variance
rift_risk_ratio(trial, "response", "trt", adj.vars = "grade", approach = "robpoisson")
#>    level reference estimate std.error statistic   p.value  conf.low conf.high
#> 1 Drug B    Drug A 1.078426 0.2542111 0.2970079 0.7664605 0.6552478  1.774906
#>                                        method
#> 1 Risk ratio (Poisson model, robust variance)

# Example 3 ----------------------------------
# as a custom method of add_difference()
trial |>
  tbl_summary(by = trt, include = response, missing = "no") |>
  add_difference(test = ~ "rift_risk_ratio", estimate_fun = ~ label_style_ratio()) |>
  modify_header(estimate = "**Risk Ratio**")