Cox Proportional Hazards Regression

Fits a Cox regression model and estimates hazard ratio to describe the effect size in a survival analysis.

Usage

s_coxreg(model_df, .stats, .which_vars = "all", .var_nms = NULL)

a_coxreg(
  df,
  labelstr,
  eff = FALSE,
  var_main = FALSE,
  multivar = FALSE,
  variables,
  at = list(),
  control = control_coxreg(),
  .spl_context,
  .stats,
  .formats,
  .indent_mods = NULL,
  na_level = lifecycle::deprecated(),
  na_str = "",
  cache_env = NULL
)

summarize_coxreg(
  lyt,
  variables,
  control = control_coxreg(),
  at = list(),
  multivar = FALSE,
  common_var = "STUDYID",
  .stats = c("n", "hr", "ci", "pval", "pval_inter"),
  .formats = c(n = "xx", hr = "xx.xx", ci = "(xx.xx, xx.xx)", pval =
    "x.xxxx | (<0.0001)", pval_inter = "x.xxxx | (<0.0001)"),
  varlabels = NULL,
  .indent_mods = NULL,
  na_level = lifecycle::deprecated(),
  na_str = "",
  .section_div = NA_character_
)

Arguments

model_df

(data.frame)
contains the resulting model fit from a fit_coxreg function with tidying applied via broom::tidy().

.stats

(character)
the name of statistics to be reported among:

• n: number of observations (univariate only)

• hr: hazard ratio

• ci: confidence interval

• pval: p-value of the treatment effect

• pval_inter: p-value of the interaction effect between the treatment and the covariate (univariate only)

.which_vars

(character)
which rows should statistics be returned for from the given model. Defaults to "all". Other options include "var_main" for main effects, "inter" for interaction effects, and "multi_lvl" for multivariate model covariate level rows. When .which_vars is "all" specific variables can be selected by specifying .var_nms.

.var_nms

(character)
the term value of rows in df for which .stats should be returned. Typically this is the name of a variable. If using variable labels, var should be a vector of both the desired variable name and the variable label in that order to see all .stats related to that variable. When .which_vars is "var_main" .var_nms should be only the variable name.

df

(data.frame)
data set containing all analysis variables.

labelstr

(character)
label of the level of the parent split currently being summarized (must be present as second argument in Content Row Functions). See rtables::summarize_row_groups() for more information.

eff

(flag)
whether treatment effect should be calculated. Defaults to FALSE.

var_main

(flag)
whether main effects should be calculated. Defaults to FALSE.

multivar

(flag)
Defaults to FALSE. If TRUE multivariate Cox regression will run, otherwise univariate Cox regression will run.

variables

(named list of string)
list of additional analysis variables.

at

(list of numeric)
when the candidate covariate is a numeric, use at to specify the value of the covariate at which the effect should be estimated.

control

(list)
a list of parameters as returned by the helper function control_coxreg().

.spl_context

(data.frame)
gives information about ancestor split states that is passed by rtables.

.formats

(named character or list)
formats for the statistics. See Details in analyze_vars for more information on the "auto" setting.

.indent_mods

(named integer)
indent modifiers for the labels. Defaults to 0, which corresponds to the unmodified default behavior. Can be negative.

na_level

Please use the na_str argument instead.

na_str

(string)
custom string to replace all NA values with. Defaults to "".

cache_env

(environment)
an environment object used to cache the regression model in order to avoid repeatedly fitting the same model for every row in the table. Defaults to NULL (no caching).

lyt

(layout)
input layout where analyses will be added to.

common_var

(character)
the name of a factor variable in the dataset which takes the same value for all rows. This should be created during pre-processing if no such variable currently exists.

varlabels

(list)
a named list corresponds to the names of variables found in data, passed as a named list and corresponding to time, event, arm, strata, and covariates terms. If arm is missing from variables, then only Cox model(s) including the covariates will be fitted and the corresponding effect estimates will be tabulated later.

.section_div

(character)
string which should be repeated as a section divider between sections. Defaults to NA for no section divider. If a vector of two strings are given, the first will be used between treatment and covariate sections and the second between different covariates.

Value

• s_coxreg() returns the selected statistic for from the Cox regression model for the selected variable(s).

• a_coxreg() returns formatted rtables::CellValue().

• summarize_coxreg() returns a layout object suitable for passing to further layouting functions, or to rtables::build_table(). Adding this function to an rtable layout will add a Cox regression table containing the chosen statistics to the table layout.

Details

Cox models are the most commonly used methods to estimate the magnitude of the effect in survival analysis. It assumes proportional hazards: the ratio of the hazards between groups (e.g., two arms) is constant over time. This ratio is referred to as the "hazard ratio" (HR) and is one of the most commonly reported metrics to describe the effect size in survival analysis (NEST Team, 2020).

Functions

• s_coxreg(): Statistics function that transforms results tabulated from fit_coxreg_univar() or fit_coxreg_multivar() into a list.

• a_coxreg(): Analysis function which is used as afun in rtables::analyze() and cfun in rtables::summarize_row_groups() within summarize_coxreg().

• summarize_coxreg(): Layout-creating function which creates a Cox regression summary table layout. This function is a wrapper for several rtables layouting functions. This function is a wrapper for rtables::analyze_colvars() and rtables::summarize_row_groups().

See also

fit_coxreg for relevant fitting functions, h_cox_regression for relevant helper functions, and tidy_coxreg for custom tidy methods.

fit_coxreg_univar() and fit_coxreg_multivar() which also take the variables, data, at (univariate only), and control arguments but return unformatted univariate and multivariate Cox regression models, respectively.

Examples

library(survival)

# Testing dataset [survival::bladder].
set.seed(1, kind = "Mersenne-Twister")
dta_bladder <- with(
  data = bladder[bladder$enum < 5, ],
  tibble::tibble(
    TIME = stop,
    STATUS = event,
    ARM = as.factor(rx),
    COVAR1 = as.factor(enum) %>% formatters::with_label("A Covariate Label"),
    COVAR2 = factor(
      sample(as.factor(enum)),
      levels = 1:4, labels = c("F", "F", "M", "M")
    ) %>% formatters::with_label("Sex (F/M)")
  )
)
dta_bladder$AGE <- sample(20:60, size = nrow(dta_bladder), replace = TRUE)
dta_bladder$STUDYID <- factor("X")

plot(
  survfit(Surv(TIME, STATUS) ~ ARM + COVAR1, data = dta_bladder),
  lty = 2:4,
  xlab = "Months",
  col = c("blue1", "blue2", "blue3", "blue4", "red1", "red2", "red3", "red4")
)


# s_coxreg

# Univariate
u1_variables <- list(
  time = "TIME", event = "STATUS", arm = "ARM", covariates = c("COVAR1", "COVAR2")
)
univar_model <- fit_coxreg_univar(variables = u1_variables, data = dta_bladder)
df1 <- broom::tidy(univar_model)
s_coxreg(model_df = df1, .stats = "hr")
#> $hr
#> $hr$`2 vs control (1)`
#> [1] 0.6386426
#> 
#> 
#> $hr
#> $hr$`A Covariate Label`
#> [1] 0.607037
#> 
#> 
#> $hr
#> $hr$`Sex (F/M)`
#> [1] 0.6242738
#> 
#> 

# Univariate with interactions
univar_model_inter <- fit_coxreg_univar(
  variables = u1_variables, control = control_coxreg(interaction = TRUE), data = dta_bladder
)
df1_inter <- broom::tidy(univar_model_inter)
s_coxreg(model_df = df1_inter, .stats = "hr", .which_vars = "inter", .var_nms = "COVAR1")
#> $hr
#> $hr$`  1`
#> [1] 0.6284569
#> 
#> $hr$`  2`
#> [1] 0.5806499
#> 
#> $hr$`  3`
#> [1] 0.5486103
#> 
#> $hr$`  4`
#> [1] 0.6910725
#> 
#> 

# Univariate without treatment arm - only "COVAR2" covariate effects
u2_variables <- list(time = "TIME", event = "STATUS", covariates = c("COVAR1", "COVAR2"))
univar_covs_model <- fit_coxreg_univar(variables = u2_variables, data = dta_bladder)
df1_covs <- broom::tidy(univar_covs_model)
s_coxreg(model_df = df1_covs, .stats = "hr", .var_nms = c("COVAR2", "Sex (F/M)"))
#> $hr
#> $hr$`Sex (F/M) (reference = F)`
#> numeric(0)
#> 
#> 
#> $hr
#> $hr$M
#> [1] 1.3271
#> 
#> 

# Multivariate.
m1_variables <- list(
  time = "TIME", event = "STATUS", arm = "ARM", covariates = c("COVAR1", "COVAR2")
)
multivar_model <- fit_coxreg_multivar(variables = m1_variables, data = dta_bladder)
df2 <- broom::tidy(multivar_model)
s_coxreg(model_df = df2, .stats = "pval", .which_vars = "var_main", .var_nms = "COVAR1")
#> $pval
#> $pval$`A Covariate Label (reference = 1)`
#> [1] 7.209956e-09
#> 
#> 
s_coxreg(
  model_df = df2, .stats = "pval", .which_vars = "multi_lvl",
  .var_nms = c("COVAR1", "A Covariate Label")
)
#> $pval
#> $pval$`2`
#> [1] 0.001120332
#> 
#> $pval$`3`
#> [1] 6.293725e-06
#> 
#> $pval$`4`
#> [1] 3.013875e-08
#> 
#> 

# Multivariate without treatment arm - only "COVAR1" main effect
m2_variables <- list(time = "TIME", event = "STATUS", covariates = c("COVAR1", "COVAR2"))
multivar_covs_model <- fit_coxreg_multivar(variables = m2_variables, data = dta_bladder)
df2_covs <- broom::tidy(multivar_covs_model)
s_coxreg(model_df = df2_covs, .stats = "hr")
#> $hr
#> $hr$`2`
#> [1] 0.4600728
#> 
#> $hr$`3`
#> [1] 0.3100455
#> 
#> $hr$`4`
#> [1] 0.1854177
#> 
#> 
#> $hr
#> $hr$`A Covariate Label (reference = 1)`
#> numeric(0)
#> 
#> 
#> $hr
#> $hr$`Sex (F/M) (reference = F)`
#> numeric(0)
#> 
#> 
#> $hr
#> $hr$M
#> [1] 1.285406
#> 
#> 

a_coxreg(
  df = dta_bladder,
  labelstr = "Label 1",
  variables = u1_variables,
  .spl_context = list(value = "COVAR1"),
  .stats = "n",
  .formats = "xx"
)
#> RowsVerticalSection (in_rows) object print method:
#> ----------------------------
#>   row_name formatted_cell indent_mod row_label
#> 1  Label 1            340          0   Label 1

a_coxreg(
  df = dta_bladder,
  labelstr = "",
  variables = u1_variables,
  .spl_context = list(value = "COVAR2"),
  .stats = "pval",
  .formats = "xx.xxxx"
)
#> RowsVerticalSection (in_rows) object print method:
#> ----------------------------
#>    row_name formatted_cell indent_mod row_label
#> 1 Sex (F/M)         0.0182          0 Sex (F/M)

# summarize_coxreg

result_univar <- basic_table() %>%
  summarize_coxreg(variables = u1_variables) %>%
  build_table(dta_bladder)
result_univar
#>                        n    Hazard Ratio      95% CI      p-value
#> —————————————————————————————————————————————————————————————————
#> Treatment:                                                       
#>   2 vs control (1)    340       0.64       (0.43, 0.94)   0.0242 
#> Covariate:                                                       
#>   A Covariate Label   340       0.61       (0.41, 0.90)   0.0126 
#>   Sex (F/M)           340       0.62       (0.42, 0.92)   0.0182 

result_multivar <- basic_table() %>%
  summarize_coxreg(
    variables = m1_variables,
    multivar = TRUE,
  ) %>%
  build_table(dta_bladder)
result_multivar
#>                                       Hazard Ratio      95% CI      p-value
#> ———————————————————————————————————————————————————————————————————————————
#> Treatment:                                                                 
#>   ARM (reference = 1)                                                      
#>     2                                     0.61       (0.41, 0.90)   0.0123 
#> Covariate:                                                                 
#>   A Covariate Label (reference = 1)                                 <0.0001
#>     2                                     0.46       (0.28, 0.73)   0.0011 
#>     3                                     0.31       (0.18, 0.51)   <0.0001
#>     4                                     0.18       (0.10, 0.33)   <0.0001
#>   Sex (F/M) (reference = F)                                                
#>     M                                     1.29       (0.88, 1.89)   0.1911 

result_univar_covs <- basic_table() %>%
  summarize_coxreg(
    variables = u2_variables,
  ) %>%
  build_table(dta_bladder)
result_univar_covs
#>                                       Hazard Ratio      95% CI      p-value
#> ———————————————————————————————————————————————————————————————————————————
#> Covariate:                                                                 
#>   A Covariate Label (reference = 1)                                 <0.0001
#>     2                                     0.45       (0.28, 0.71)   0.0007 
#>     3                                     0.31       (0.19, 0.52)   <0.0001
#>     4                                     0.18       (0.10, 0.33)   <0.0001
#>   Sex (F/M) (reference = F)                                                
#>     M                                     1.33       (0.91, 1.94)   0.1414 

result_multivar_covs <- basic_table() %>%
  summarize_coxreg(
    variables = m2_variables,
    multivar = TRUE,
    varlabels = c("Covariate 1", "Covariate 2") # custom labels
  ) %>%
  build_table(dta_bladder)
result_multivar_covs
#>                                 Hazard Ratio      95% CI      p-value
#> —————————————————————————————————————————————————————————————————————
#> Covariate:                                                           
#>   Covariate 1 (reference = 1)                                 <0.0001
#>     2                               0.46       (0.29, 0.74)   0.0012 
#>     3                               0.31       (0.19, 0.52)   <0.0001
#>     4                               0.19       (0.10, 0.34)   <0.0001
#>   Covariate 2 (reference = F)                                        
#>     M                               1.29       (0.88, 1.88)   0.1958