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Continuous outcomes

Source: vignettes/estimators_continuous.Rmd
estimators_continuous.Rmd

Example

The example uses the cancer data from the survival package. To compare patient age by ECOG performance status, recode the variable ph.ecog to be categorical (a factor) and exclude patients with rare elevated ecog.ps:

library(dplyr)
library(rifttable)
data(cancer, package = "survival")
cancer <- cancer %>%
  filter(ph.ecog < 3) %>%
  mutate(ph.ecog = factor(ph.ecog))
attr(cancer$ph.ecog, which = "label") <- "ECOG performance status"

tribble(
  ~label,                                       ~type,
  "**Absolute estimates**",                     "",
  "Observations",                               "total",
  "Range",                                      "range",
  "Mean",                                       "", 
  "  Mean (i.e., arithmetic mean)",             "mean",
  "  Mean (95% CI)",                            "mean (ci)",
  "  Mean (standard deviation)",                "mean (sd)",
  "  Geometric mean",                           "geomean",
  "Median",                                     "median",
  "Median (interquartile range)",               "median (iqr)",
  "",                                           "",
  "**Comparative estimates**",                  "",
  "Mean difference (95% CI)",                   "diff",
  "Median difference (95% CI)",                 "quantreg",
  "Mean ratio",                                 "",
  "  of arithmetic means",                      "fold",
  "  of arithmetic means, empirical SE",        "irrrob",
  "  of geometric means",                       "foldlog") %>%
  mutate(
    exposure = "ph.ecog",
    outcome = "age") %>%
  rifttable(
    data = cancer, 
    diff_digits = 1,  # Suppress unnecessary precision in most estimates
    # Show extraneous digits to highlight (minor) differences in ratio  models:
    ratio_digits = 3,
    overall = TRUE) %>%  
  rt_gt()  # obtain formatted output
Summary Overall 0 1 2

Absolute estimates

Observations

 226 63 113 50

Range

 39.0, 82.0 39.0, 82.0 40.0, 80.0 48.0, 77.0

Mean

Mean (i.e., arithmetic mean)

 62.4 61.2 61.5 66.2

Mean (95% CI)

 62.4 (61.2, 63.6) 61.2 (58.8, 63.5) 61.5 (59.8, 63.1) 66.2 (64.0, 68.5)

Mean (standard deviation)

 62.4 (9.1) 61.2 (9.6) 61.5 (8.9) 66.2 (8.1)

Geometric mean

 61.7 60.4 60.8 65.7

Median

 63.0 61.0 63.0 68.0

Median (interquartile range)

 63.0 (56.0, 69.0) 61.0 (56.5, 68.0) 63.0 (55.0, 68.0) 68.0 (60.2, 73.0)

Comparative estimates

Mean difference (95% CI)

 0 (reference) 0.3 (-2.5, 3.1) 5.1 (1.7, 8.4)

Median difference (95% CI)

 0 (reference) 2.0 (-4.8, 8.8) 7.0 (1.3, 12.2)

Mean ratio

of arithmetic means

 1 (reference) 1.005 (0.961, 1.051) 1.083 (1.028, 1.140)

of arithmetic means, empirical SE

 1 (reference) 1.005 (0.959, 1.053) 1.083 (1.029, 1.139)

of geometric means

 1 (reference) 1.007 (0.961, 1.055) 1.088 (1.029, 1.151)

Absolute estimates per exposure category

type Description Options (arguments =)
"range" Range: Minimum to maximum value.
"mean" Mean (arithmetic mean).
"mean (ci)" Mean and CI (default: 95%).
"mean (sd)" Mean and standard deviation.
"geomean" Geometric mean.
"median" Median.
"median (iqr)" Median and interquartile range.

Comparative estimates with confidence intervals

type Description Options (arguments =)
"diff" Mean difference from linear model.
"fold" Fold change from generalized linear model with log link (i.e., ratio of arithmetic means).
"foldlog" Fold change from linear model after log transformation of the outcome (i.e., ratio of geometric means).
"irrrob" Fold change from generalized linear model with Poisson distribution and log link and robust (sandwich) standard errors
"quantreg" Quantile difference from quantile regression using quantreg::rq() with method = "fn". By default, this is the difference in medians. list(tau = 0.75) to change the quantile to, e.g., the 75th percentile.

More on ratios of continuous outcomes

Three types of ratios for continuous outcomes are implemented in rifttable():

type = Ratio of … Model Use
"fold" Arithmetic means Generalized linear model with Gaussian distribution and log link: glm(y ~ x, family = gaussian(link = "log")) Tolerates 0 in the outcome variable. May be informative if outcome is normally distributed without transformation.
"irrrob" Arithmetic means Generalized linear model with Poisson distribution and log link: glm(y ~ x, family = poisson()), with robust (sandwich) standard errors Tolerates 0 in the outcome variable. May be informative if outcome is normally distributed without transformation.
"foldlog" Geometric means Linear model with log-transformed outcome: lm(log(y) ~ x) Does not tolerate 0 in the outcome variable, as log(0) is undefined (R returns -Inf). May be informative if outcome is normally distributed after log transformation.

In all models, after exponentiation, beta coefficients can be interpreted as ratios. rifttable automatically does all necessary transformations.

In the cancer data, ratios of usual (arithmetic) means of age could be considered informative, given that hist(cancer$age) etc. does not show a major skew in this outcome.