Analysis of Covariance

Performs an analysis of covariance between two groups returning the estimated "treatment effect" (i.e. the contrast between the two treatment groups) and the least square means estimates in each group.

Usage

ancova(
  data,
  vars,
  visits = NULL,
  weights = c("counterfactual", "equal", "proportional_em", "proportional")
)

Arguments

data: A data.frame containing the data to be used in the model.
vars: A vars object as generated by set_vars(). Only the group, visit, outcome and covariates elements are required. See details.
visits: An optional character vector specifying which visits to fit the ancova model at. If NULL, a separate ancova model will be fit to the outcomes for each visit (as determined by unique(data[[vars$visit]])). See details.
weights: Character, either "counterfactual" (default), "equal", "proportional_em" or "proportional". Specifies the weighting strategy to be used when calculating the lsmeans. See the weighting section for more details.

Details

The function works as follows:

Select the first value from visits.
Subset the data to only the observations that occurred on this visit.
Fit a linear model as vars$outcome ~ vars$group + vars$covariates.
Extract the "treatment effect" & least square means for each treatment group.
Repeat points 2-3 for all other values in visits.

If no value for visits is provided then it will be set to unique(data[[vars$visit]]).

In order to meet the formatting standards set by analyse() the results will be collapsed into a single list suffixed by the visit name, e.g.:

list(
   trt_visit_1 = list(est = ...),
   lsm_ref_visit_1 = list(est = ...),
   lsm_alt_visit_1 = list(est = ...),
   trt_visit_2 = list(est = ...),
   lsm_ref_visit_2 = list(est = ...),
   lsm_alt_visit_2 = list(est = ...),
   ...
)

Please note that "ref" refers to the first factor level of vars$group which does not necessarily coincide with the control arm. Analogously, "alt" refers to the second factor level of vars$group. "trt" refers to the model contrast translating the mean difference between the second level and first level.

If you want to include interaction terms in your model this can be done by providing them to the covariates argument of set_vars() e.g. set_vars(covariates = c("sex*age")).

Weighting

Counterfactual

For weights = "counterfactual" (the default) the lsmeans are obtained by taking the average of the predicted values for each patient after assigning all patients to each arm in turn. This approach is equivalent to standardization or g-computation. In comparison to emmeans this approach is equivalent to:

emmeans::emmeans(model, specs = "<treatment>", counterfactual = "<treatment>")

Note that to ensure backwards compatibility with previous versions of rbmi weights = "proportional" is an alias for weights = "counterfactual". To get results consistent with emmeans's weights = "proportional" please use weights = "proportional_em".

Equal

For weights = "equal" the lsmeans are obtained by taking the model fitted value of a hypothetical patient whose covariates are defined as follows:

Continuous covariates are set to mean(X)
Dummy categorical variables are set to 1/N where N is the number of levels
Continuous * continuous interactions are set to mean(X) * mean(Y)
Continuous * categorical interactions are set to mean(X) * 1/N
Dummy categorical * categorical interactions are set to 1/N * 1/M

In comparison to emmeans this approach is equivalent to:

emmeans::emmeans(model, specs = "<treatment>", weights = "equal")

Proportional

For weights = "proportional_em" the lsmeans are obtained as per weights = "equal" except instead of weighting each observation equally they are weighted by the proportion in which the given combination of categorical values occurred in the data. In comparison to emmeans this approach is equivalent to:

emmeans::emmeans(model, specs = "<treatment>", weights = "proportional")

Note that this is not to be confused with weights = "proportional" which is an alias for weights = "counterfactual".