Fitting Trimmed Mean Linear Models:

tm performs a trimmed means analysis for data with a continuous outcome/response and a binary treatment/exposure variable. Outcomes are sorted and trimmed per treatment group, and a linear regression is fitted using lm.

Usage

tm(
  formula,
  GR,
  trF = NULL,
  side = c("LOW", "HIGH"),
  n_perm = 1000,
  adj_est = FALSE,
  data
)

Arguments

formula: an object of class formula, specifying the model, of the form outcome ~ terms, where terms must include the binary treatment variable, with additional variables optional.
GR: a string denoting the name of the binary treatment variable. This function assumes the lowest value to be the comparator/reference group
trF: a number between 0 and 1, specifying the trimming fraction: the proportion of the data that is trimmed away for each treatment group. trF should be equal to or greater than the largest observed dropout proportion. If left unspecified, a default trimming fraction of 0.5 is assumed.
side: specifies if higher value trimming ("HIGH") or lower value trimming ("LOW") should be performed.
n_perm: the number of permutations performed to obtain the p-value and 95% confidence intervals for the estimates. Default is 1000.
adj_est: logical. If TRUE the adjusted trimmed means estimate is computed. The default is FALSE.
data: a data frame containing the variables in the model. data should contain at least the following: a numeric outcome variable and a binary treatment variable (numeric, character or factor).

Value

tm returns an object of class tm. The function summary is used to obtain a summary of the results. The generic accessor function coefficients extracts the regression coefficients with corresponding p-values and 95% confidence intervals.

An object of class "tm" is a list containing the following components:

call: the matched call
n: the number of observations per treatment group
dropout: the proportion of dropout per treatment group
trimfrac: the proportion of data that was trimmed away per treatment group
trimside: specifies if lower or higher value trimming was performed
n_after_trimming: the number of observations per treatment group after trimming
coefficients: an array of coefficients with corresponding p-values and 95% confidence intervals
Analysis_details: reiterates trimming fraction and side, and, for adjest=TRUE specifies if the adjustment was performed on the comparator or treatment group.
SD_outcome: an array of the standard deviation per treatment group, for the observed outcomes and for the trimmed outcomes

Details

The trimmed means estimate is subject to two assumptions: the strong MNAR assumption requires that all dropouts (unobserved outcome values) are located in the fraction of the distribution that is trimmed away; the location shift assumption requires the group variances of the full sample to be equal. The adjusted trimmed means estimator relaxes the latter, but assumes normally distributed outcomes. The adjustment is performed on the group with the smallest dropout proportion.

The p-value and 95% confidence intervals for the trimmed means estimate and the adjusted trimmed means estimate are obtained in a permutation approach.

Examples

set.seed(123456)
test_dat <- as.data.frame(cbind(c(rep(0, 500), rep(1, 500)),
                          c(sort(rnorm(500, 0, 1)), sort(rnorm(500, 1, 1.5))),
                          rbinom(1000, 2, 0.4), rnorm(1000, 0, 1)))
colnames(test_dat) <- c("TR", "Y", "U", "U2")
test_dat$Y[1:200] <- NA
# Note that we usually recommend setting n_perm to a larger value, e.g., 1000
tm_obj <- tm(formula= Y ~ TR + U + U2,
             GR = "TR", trF = 0.5, side = "LOW",
             n_perm = 100, adj_est = TRUE, data = test_dat)
print(tm_obj)
#> 
#> Call:
#> tm(formula = Y ~ TR + U + U2, GR = "TR", trF = 0.5, side = "LOW", 
#>     n_perm = 100, adj_est = TRUE, data = test_dat)
#> 
#> Coefficients:
#>        Estimate      Pval 95% CI LO 95% CI HI
#> TR     1.354308  0.000000  1.166162     1.542
#> U     -0.071352  0.960000 -0.163494     0.021
#> U2     0.055791  0.050000 -0.009835     0.121
#> TRadj  0.969812  0.000000  0.850012     1.090
#> 
summary(tm_obj)
#> 
#> Call:
#> tm(formula = Y ~ TR + U + U2, GR = "TR", trF = 0.5, side = "LOW", 
#>     n_perm = 100, adj_est = TRUE, data = test_dat)
#> 
#> 
#> Analysis details:
#> Treatment (1) group rescaled for adjusted TM estimate
#> 
#> Coefficients:
#>        Estimate      Pval 95% CI LO 95% CI HI
#> TR     1.354308  0.000000  1.166162     1.542
#> U     -0.071352  0.960000 -0.163494     0.021
#> U2     0.055791  0.050000 -0.009835     0.121
#> TRadj  0.969812  0.000000  0.850012     1.090
#> 
#> 
#> Dropout:
#> 40%
#> 
#> Sample size after trimming:
#> 250
#> 
#> Trimming fraction: 
#> 50% lower value trimming
#>