Cox Proportional Hazards Regression — cox

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

Usage

h_coxreg_univar_formulas(variables, interaction = FALSE)

h_coxreg_multivar_formula(variables)

fit_coxreg_univar(variables, data, at = list(), control = control_coxreg())

# S3 method for summary.coxph
tidy(x, ...)

h_coxreg_univar_extract(effect, covar, data, mod, control = control_coxreg())

# S3 method for coxreg.univar
tidy(x, ...)

fit_coxreg_multivar(variables, data, control = control_coxreg())

h_coxreg_multivar_extract(var, data, mod, control = control_coxreg())

# S3 method for coxreg.multivar
tidy(x, ...)

s_coxreg(df, .var)

summarize_coxreg(
  lyt,
  conf_level,
  multivar = FALSE,
  vars = c("n", "hr", "ci", "pval")
)

Arguments

variables: (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.
interaction: (flag)
if TRUE, the model includes the interaction between the studied treatment and candidate covariate. Note that for univariate models without treatment arm, and multivariate models, no interaction can be used so that this needs to be FALSE.
data: (data frame)
the dataset containing the variables to fit the models.
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().
x: (list)
Result of the Cox regression model fitted by fit_coxreg_multivar().
...: additional arguments for the lower level functions.
effect: (string)
the treatment variable.
covar: (string)
the name of the covariate in the model.
mod: (coxph)
Cox regression model fitted by survival::coxph().
df: (data frame)
data set containing all analysis variables.
.var, var: (string)
single variable name that is passed by rtables when requested by a statistics function.
lyt: (layout)
input layout where analyses will be added to.
conf_level: (proportion)
confidence level of the interval.
multivar: (flag)
if TRUE, the multi-variable Cox regression will run and no interaction will be considered between the studied treatment and c candidate covariate. Default is FALSE for univariate Cox regression including an arm variable. When no arm variable is included in the univariate Cox regression, then also TRUE should be used to tabulate the covariate effect estimates instead of the treatment arm effect estimate across models.
vars: (character)
the name of statistics to be reported among n (number of observation), hr (Hazard Ratio), ci (confidence interval), pval (p.value of the treatment effect) and pval_inter (the p.value of the interaction effect between the treatment and the covariate).

Value

The function h_coxreg_univar_formulas returns a character vector coercible into formulas (e.g stats::as.formula()).

The function fit_coxreg_univar returns a coxreg.univar class object which is a named list with 5 elements:

mod: Cox regression models fitted by survival::coxph().
data: The original data frame input.
control: The original control input.
vars: The variables used in the model.
at: Value of the covariate at which the effect should be estimated.

The function fit_coxreg_multivar returns a coxreg.multivar class object which is a named list with 4 elements:

mod: Cox regression model fitted by survival::coxph().
data: The original data frame input.
control: The original control input.
vars: The variables used in the model.

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

h_coxreg_univar_formulas(): Helper for Cox Regression Formula

Creates a list of formulas. It is used internally by fit_coxreg_univar() for the comparison of univariate Cox regression models.
h_coxreg_multivar_formula(): Helper for Multi-variable Cox Regression Formula

Creates a formulas string. It is used internally by fit_coxreg_multivar() for the comparison of multi-variable Cox regression models. Interactions will not be included in multi-variable Cox regression model.
fit_coxreg_univar(): Fit a series of univariate Cox regression models given the inputs.
tidy(summary.coxph): Custom tidy method for survival::coxph() summary results.

Tidy the survival::coxph() results into a data.frame to extract model results.
h_coxreg_univar_extract(): Utility function to help tabulate the result of a univariate Cox regression model.
tidy(coxreg.univar): Custom tidy method for a Univariate Cox Regression

Tidy up the result of a Cox regression model fitted by fit_coxreg_univar().
fit_coxreg_multivar(): Fit a multi-variable Cox regression model.
h_coxreg_multivar_extract(): Tabulation of Multi-variable Cox Regressions

Utility function to help tabulate the result of a multi-variable Cox regression model for a treatment/covariate variable.
tidy(coxreg.multivar): Custom tidy method for a Multi-variable Cox Regression

Tidy up the result of a Cox regression model fitted by fit_coxreg_multivar().
s_coxreg(): transforms the tabulated results from fit_coxreg_univar() and fit_coxreg_multivar() into a list. Not much calculation is done here, it rather prepares the data to be used by the layout creating function.
summarize_coxreg(): layout creating function.

Note

The usual formatting arguments for the layout creating function summarize_coxreg are not yet accepted (.stats, .indent_mod, .formats, .labels).

When using fit_coxreg_univar there should be two study arms.

Examples

# Testing dataset [survival::bladder].

library(survival)
library(rtables)
set.seed(1, kind = "Mersenne-Twister")
dta_bladder <- with(
  data = bladder[bladder$enum < 5, ],
  data.frame(
    time = stop,
    status = event,
    armcd = as.factor(rx),
    covar1 = as.factor(enum),
    covar2 = factor(
      sample(as.factor(enum)),
      levels = 1:4, labels = c("F", "F", "M", "M")
    )
  )
)
labels <- c("armcd" = "ARM", "covar1" = "A Covariate Label", "covar2" = "Sex (F/M)")
formatters::var_labels(dta_bladder)[names(labels)] <- labels
dta_bladder$age <- sample(20:60, size = nrow(dta_bladder), replace = TRUE)

plot(
  survfit(Surv(time, status) ~ armcd + covar1, data = dta_bladder),
  lty = 2:4,
  xlab = "Months",
  col = c("blue1", "blue2", "blue3", "blue4", "red1", "red2", "red3", "red4")
)

# `h_coxreg_univar_formulas`

## Simple formulas.
h_coxreg_univar_formulas(
  variables = list(
    time = "time", event = "status", arm = "armcd", covariates = c("X", "y")
  )
)
#>                                        ref 
#>     "survival::Surv(time, status) ~ armcd" 
#>                                          X 
#> "survival::Surv(time, status) ~ armcd + X" 
#>                                          y 
#> "survival::Surv(time, status) ~ armcd + y" 

## Addition of an optional strata.
h_coxreg_univar_formulas(
  variables = list(
    time = "time", event = "status", arm = "armcd", covariates = c("X", "y"),
    strata = "SITE"
  )
)
#>                                                       ref 
#>     "survival::Surv(time, status) ~ armcd + strata(SITE)" 
#>                                                         X 
#> "survival::Surv(time, status) ~ armcd + X + strata(SITE)" 
#>                                                         y 
#> "survival::Surv(time, status) ~ armcd + y + strata(SITE)" 

## Inclusion of the interaction term.
h_coxreg_univar_formulas(
  variables = list(
    time = "time", event = "status", arm = "armcd", covariates = c("X", "y"),
    strata = "SITE"
  ),
  interaction = TRUE
)
#>                                                       ref 
#>     "survival::Surv(time, status) ~ armcd + strata(SITE)" 
#>                                                         X 
#> "survival::Surv(time, status) ~ armcd * X + strata(SITE)" 
#>                                                         y 
#> "survival::Surv(time, status) ~ armcd * y + strata(SITE)" 

## Only covariates fitted in separate models.
h_coxreg_univar_formulas(
  variables = list(
    time = "time", event = "status", covariates = c("X", "y")
  )
)
#>                                      X                                      y 
#> "survival::Surv(time, status) ~ 1 + X" "survival::Surv(time, status) ~ 1 + y" 

# `h_coxreg_multivar_formula`

h_coxreg_multivar_formula(
  variables = list(
    time = "AVAL", event = "event", arm = "ARMCD", covariates = c("RACE", "AGE")
  )
)
#> [1] "survival::Surv(AVAL, event) ~ ARMCD + RACE + AGE"

# Addition of an optional strata.
h_coxreg_multivar_formula(
  variables = list(
    time = "AVAL", event = "event", arm = "ARMCD", covariates = c("RACE", "AGE"),
    strata = "SITE"
  )
)
#> [1] "survival::Surv(AVAL, event) ~ ARMCD + RACE + AGE + strata(SITE)"

# Example without treatment arm.
h_coxreg_multivar_formula(
  variables = list(
    time = "AVAL", event = "event", covariates = c("RACE", "AGE"),
    strata = "SITE"
  )
)
#> [1] "survival::Surv(AVAL, event) ~ 1 + RACE + AGE + strata(SITE)"
# fit_coxreg_univar

## Cox regression: arm + 1 covariate.
mod1 <- fit_coxreg_univar(
  variables = list(
    time = "time", event = "status", arm = "armcd",
    covariates = "covar1"
  ),
  data = dta_bladder,
  control = control_coxreg(conf_level = 0.91)
)

## Cox regression: arm + 1 covariate + interaction, 2 candidate covariates.
mod2 <- fit_coxreg_univar(
  variables = list(
    time = "time", event = "status", arm = "armcd",
    covariates = c("covar1", "covar2")
  ),
  data = dta_bladder,
  control = control_coxreg(conf_level = 0.91, interaction = TRUE)
)

## Cox regression: arm + 1 covariate, stratified analysis.
mod3 <- fit_coxreg_univar(
  variables = list(
    time = "time", event = "status", arm = "armcd", strata = "covar2",
    covariates = c("covar1")
  ),
  data = dta_bladder,
  control = control_coxreg(conf_level = 0.91)
)

## Cox regression: no arm, only covariates.
mod4 <- fit_coxreg_univar(
  variables = list(
    time = "time", event = "status",
    covariates = c("covar1", "covar2")
  ),
  data = dta_bladder
)
library(survival)
library(broom)
library(rtables)

set.seed(1, kind = "Mersenne-Twister")

dta_bladder <- with(
  data = bladder[bladder$enum < 5, ],
  data.frame(
    time = stop,
    status = event,
    armcd = as.factor(rx),
    covar1 = as.factor(enum),
    covar2 = factor(
      sample(as.factor(enum)),
      levels = 1:4, labels = c("F", "F", "M", "M")
    )
  )
)
labels <- c("armcd" = "ARM", "covar1" = "A Covariate Label", "covar2" = "Sex (F/M)")
formatters::var_labels(dta_bladder)[names(labels)] <- labels
dta_bladder$age <- sample(20:60, size = nrow(dta_bladder), replace = TRUE)

formula <- "survival::Surv(time, status) ~ armcd + covar1"
msum <- summary(coxph(stats::as.formula(formula), data = dta_bladder))
tidy(msum)
#>       Pr(>|z|) exp(coef) exp(-coef)  lower .95 upper .95   level   n
#> 1 1.287954e-02 0.6110123   1.636628 0.41442417 0.9008549  armcd2 340
#> 2 6.407916e-04 0.4460731   2.241785 0.28061816 0.7090818 covar12 340
#> 3 5.272933e-06 0.3075864   3.251119 0.18517346 0.5109230 covar13 340
#> 4 2.125359e-08 0.1808795   5.528541 0.09943722 0.3290258 covar14 340
library(survival)

dta_simple <- data.frame(
  time = c(5, 5, 10, 10, 5, 5, 10, 10),
  status = c(0, 0, 1, 0, 0, 1, 1, 1),
  armcd = factor(LETTERS[c(1, 1, 1, 1, 2, 2, 2, 2)], levels = c("A", "B")),
  var1 = c(45, 55, 65, 75, 55, 65, 85, 75),
  var2 = c("F", "M", "F", "M", "F", "M", "F", "U")
)
mod <- coxph(Surv(time, status) ~ armcd + var1, data = dta_simple)
result <- h_coxreg_univar_extract(
  effect = "armcd", covar = "armcd", mod = mod, data = dta_simple
)
result
#>       effect  term       term_label level n       hr       lcl      ucl
#> 1 Treatment: armcd B vs control (A)     B 8 6.551448 0.4606904 93.16769
#>       pval
#> 1 0.165209

library(broom)
tidy(mod1)
#>            effect   term        term_label level   n        hr       lcl
#> ref    Treatment:  armcd  2 vs control (1)     2 340 0.6386426 0.4557586
#> covar1 Covariate: covar1 A Covariate Label     2 340  0.607037 0.4324571
#>              ucl       pval                   ci
#> ref    0.8949131 0.02423805 0.4557586, 0.8949131
#> covar1 0.8520935 0.01257339 0.4324571, 0.8520935
tidy(mod2)
#>                           effect   term        term_label level   n        hr
#> ref                   Treatment:  armcd  2 vs control (1)     2 340 0.6386426
#> covar1.1              Covariate: covar1 A Covariate Label       340          
#> covar1.armcd2/covar11 Covariate: covar1                 1     1     0.6284569
#> covar1.armcd2/covar12 Covariate: covar1                 2     2     0.5806499
#> covar1.armcd2/covar13 Covariate: covar1                 3     3     0.5486103
#> covar1.armcd2/covar14 Covariate: covar1                 4     4     0.6910725
#> covar2.1              Covariate: covar2         Sex (F/M)       340          
#> covar2.armcd2/covar2F Covariate: covar2                 F     F     0.6678243
#> covar2.armcd2/covar2M Covariate: covar2                 M     M     0.5954021
#>                             lcl       ucl       pval pval_inter
#> ref                   0.4557586 0.8949131 0.02423805           
#> covar1.1                     NA        NA             0.9883021
#> covar1.armcd2/covar11 0.3450471 1.1446499                      
#> covar1.armcd2/covar12 0.2684726 1.2558239                      
#> covar1.armcd2/covar13 0.2226814 1.3515868                      
#> covar1.armcd2/covar14 0.2308006 2.0692373                      
#> covar2.1                     NA        NA             0.7759013
#> covar2.armcd2/covar2F 0.3649842 1.2219413                      
#> covar2.armcd2/covar2M 0.3572772 0.9922368                      
#>                                         ci
#> ref                   0.4557586, 0.8949131
#> covar1.1                                  
#> covar1.armcd2/covar11 0.3450471, 1.1446499
#> covar1.armcd2/covar12 0.2684726, 1.2558239
#> covar1.armcd2/covar13 0.2226814, 1.3515868
#> covar1.armcd2/covar14 0.2308006, 2.0692373
#> covar2.1                                  
#> covar2.armcd2/covar2F 0.3649842, 1.2219413
#> covar2.armcd2/covar2M 0.3572772, 0.9922368
# fit_coxreg_multivar

## Cox regression: multivariate Cox regression.
multivar_model <- fit_coxreg_multivar(
  variables = list(
    time = "time", event = "status", arm = "armcd",
    covariates = c("covar1", "covar2")
  ),
  data = dta_bladder
)

# Example without treatment arm.
multivar_covs_model <- fit_coxreg_multivar(
  variables = list(
    time = "time", event = "status",
    covariates = c("covar1", "covar2")
  ),
  data = dta_bladder
)
library(survival)

mod <- coxph(Surv(time, status) ~ armcd + var1, data = dta_simple)
result <- h_coxreg_multivar_extract(
  var = "var1", mod = mod, data = dta_simple
)
result
#>        pval        hr      lcl      ucl level n term term_label
#> 2 0.4456195 0.9423284 0.808931 1.097724  var1 8 var1       var1
library(broom)
broom::tidy(multivar_model)
#>                       term         pval                        term_label
#> armcd.1              armcd                            ARM (reference = 1)
#> armcd.2                ARM   0.01232761                                 2
#> covar1.1            covar1 7.209956e-09 A Covariate Label (reference = 1)
#> covar1.2 A Covariate Label  0.001120332                                 2
#> covar1.3 A Covariate Label 6.293725e-06                                 3
#> covar1.4 A Covariate Label 3.013875e-08                                 4
#> covar2.1            covar2                      Sex (F/M) (reference = F)
#> covar2.2         Sex (F/M)    0.1910521                                 M
#>                 hr        lcl       ucl level                     ci
#> armcd.1                    NA        NA  <NA>                       
#> armcd.2  0.6062777 0.40970194 0.8971710     2   0.4097019, 0.8971710
#> covar1.1                   NA        NA  <NA>                       
#> covar1.2 0.4564763 0.28481052 0.7316115     2   0.2848105, 0.7316115
#> covar1.3 0.3069612 0.18386073 0.5124813     3   0.1838607, 0.5124813
#> covar1.4 0.1817017 0.09939435 0.3321668     4 0.09939435, 0.33216684
#> covar2.1                   NA        NA  <NA>                       
#> covar2.2  1.289373 0.88087820 1.8873019     M   0.8808782, 1.8873019
# s_coxreg

univar_model <- fit_coxreg_univar(
  variables = list(
    time = "time", event = "status", arm = "armcd",
    covariates = c("covar1", "covar2")
  ),
  data = dta_bladder
)
df1 <- broom::tidy(univar_model)
s_coxreg(df = df1, .var = "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
#> 
#> 

# Only covariates.
univar_covs_model <- fit_coxreg_univar(
  variables = list(
    time = "time", event = "status",
    covariates = c("covar1", "covar2")
  ),
  data = dta_bladder
)
df1_covs <- broom::tidy(univar_covs_model)
s_coxreg(df = df1_covs, .var = "hr")
#> $hr
#> $hr$`2`
#> [1] 0.446633
#> 
#> $hr$`3`
#> [1] 0.3098658
#> 
#> $hr$`4`
#> [1] 0.1828626
#> 
#> 
#> $hr
#> $hr$M
#> [1] 1.3271
#> 
#> 
#> $hr
#> $hr$`A Covariate Label (reference = 1)`
#> numeric(0)
#> 
#> 
#> $hr
#> $hr$`Sex (F/M) (reference = F)`
#> numeric(0)
#> 
#> 

# Multivariate.
multivar_model <- fit_coxreg_multivar(
  variables = list(
    time = "time", event = "status", arm = "armcd",
    covariates = c("covar1", "covar2")
  ),
  data = dta_bladder
)
df2 <- broom::tidy(multivar_model)
s_coxreg(df = df2, .var = "hr")
#> $hr
#> $hr$`2`
#> [1] 0.4564763
#> 
#> $hr$`3`
#> [1] 0.3069612
#> 
#> $hr$`4`
#> [1] 0.1817017
#> 
#> 
#> $hr
#> $hr$`2`
#> [1] 0.6062777
#> 
#> 
#> $hr
#> $hr$M
#> [1] 1.289373
#> 
#> 
#> $hr
#> $hr$`ARM (reference = 1)`
#> numeric(0)
#> 
#> 
#> $hr
#> $hr$`A Covariate Label (reference = 1)`
#> numeric(0)
#> 
#> 
#> $hr
#> $hr$`Sex (F/M) (reference = F)`
#> numeric(0)
#> 
#> 

# Multivariate without treatment arm.
multivar_covs_model <- fit_coxreg_multivar(
  variables = list(
    time = "time", event = "status",
    covariates = c("covar1", "covar2")
  ),
  data = dta_bladder
)
df2_covs <- broom::tidy(multivar_covs_model)
s_coxreg(df = df2_covs, .var = "hr")
#> $hr
#> $hr$`2`
#> [1] 0.4600728
#> 
#> $hr$`3`
#> [1] 0.3100455
#> 
#> $hr$`4`
#> [1] 0.1854177
#> 
#> 
#> $hr
#> $hr$M
#> [1] 1.285406
#> 
#> 
#> $hr
#> $hr$`A Covariate Label (reference = 1)`
#> numeric(0)
#> 
#> 
#> $hr
#> $hr$`Sex (F/M) (reference = F)`
#> numeric(0)
#> 
#> 
# summarize_coxreg
result_univar <- basic_table() %>%
  split_rows_by("effect") %>%
  split_rows_by("term", child_labels = "hidden") %>%
  summarize_coxreg(conf_level = 0.95) %>%
  build_table(df1)
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() %>%
  split_rows_by("term", child_labels = "hidden") %>%
  summarize_coxreg(multivar = TRUE, conf_level = .95) %>%
  build_table(df2)
result_multivar
#>                                     Hazard Ratio      95% CI      p-value
#> —————————————————————————————————————————————————————————————————————————
#> ARM (reference = 1)                                                      
#> 2                                       0.61       (0.41, 0.90)   0.0123 
#> 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 

# When tabulating univariate models with only covariates, also `multivar = TRUE`
# is used.
result_univar_covs <- basic_table() %>%
  split_rows_by("term", child_labels = "hidden") %>%
  summarize_coxreg(multivar = TRUE, conf_level = 0.95) %>%
  build_table(df1_covs)
result_univar_covs
#>                                     Hazard Ratio      95% CI      p-value
#> —————————————————————————————————————————————————————————————————————————
#> 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 

# No change for the multivariate tabulation when no treatment arm is included.
result_multivar_covs <- basic_table() %>%
  split_rows_by("term", child_labels = "hidden") %>%
  summarize_coxreg(multivar = TRUE, conf_level = .95) %>%
  build_table(df2_covs)
result_multivar_covs
#>                                     Hazard Ratio      95% CI      p-value
#> —————————————————————————————————————————————————————————————————————————
#> A Covariate Label (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
#> Sex (F/M) (reference = F)                                                
#> M                                       1.29       (0.88, 1.88)   0.1958