rpriori

The goal of rpriori is to provide a framework that simplifies apriori hypothesis testing. In particular, rpriori focuses on building sets of models that examine one primary hypothesis under several sets of potential confounding variables.

Installation

You can install the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("bcjaeger/rpriori")

Example

Let’s use the titanic data to show how the pieces of rpriori fit together. The first thing we need is to load some packages:

library(rpriori)
library(magrittr)
library(glue)
library(tidyverse)
library(knitr)
library(kableExtra)
library(geepack)

The next thing we need is a question that we can engage with using a-priori model specifications. Let’s investigate whether survival on the titanic was associated with ticket class. We’ll start by initiating an empty model.

# Make an unadjusted model
m0  <- mspec_empty("Model 0")

# mspec_describe(mspec) is the same as print(mspec)
mspec_describe(m0)
#> [1] "Model 0 is unadjusted."

Now we can make Model 1, a descendant of the unadjusted model.

# Model 1 includes adjustment for sex and age
m1  <- mspec_add(m0, name = "Model 1", sex, age)

m1
#> [1] "Model 1 includes adjustment for sex and age."

# model 0 is automatically set as the parent since m0
# was supplied to mspec_add.
m1$parent$name
#> [1] "Model 0"

# relation is automatically set by the mspec_add function
m1$relation
#> [1] "add"

And now we can make descendants of model 1.

# Model 2a = model 1 + no. of siblings/spouses
m2a <- mspec_add(m1, sibsp, name = 'Model 2a')

# Model 2b = model 1 + no. of parents/children
m2b <- mspec_add(m1, parch, name = 'Model 2b')

# Model 3 = model 1, swapping out age for ticket fare
m3 <- mspec_sub(m1, age = fare, name = 'Model 3')

What comes next? Our specifications are set, but they are separate. They also haven’t been embedded into the main question of interest, i.e. survival ~ pclass. We can pull these specifications together into an object that encapsulates our main hypothesis with mspec_embed

ttnc <- drop_na(titanic) %>% 
  mutate(survived = as.numeric(survived) - 1)

main_hypothesis <- hypothesize_that(survived ~ pclass)

apri <- main_hypothesis %>% embed_mspecs(m0, m1, m2a, m2b, m3)

# Model descriptions are embedded as an attribute
cat(paste(attr(apri, 'model_description'), collapse = '\n'))
#> Model 0 is unadjusted.
#> Model 1 includes adjustment for sex and age.
#> Model 2a = Model 1 plus sibsp.
#> Model 2b = Model 1 plus parch.
#> Model 3 = Model 1 with fare replacing age.

# Print the apriori analysis plan
apri
#> # A tibble: 5 x 4
#>   name     outcome  exposure formula  
#>   <chr>    <chr>    <chr>    <list>   
#> 1 Model 0  survived pclass   <formula>
#> 2 Model 1  survived pclass   <formula>
#> 3 Model 2a survived pclass   <formula>
#> 4 Model 2b survived pclass   <formula>
#> 5 Model 3  survived pclass   <formula>

Now that we have organized an analysis plan, we can bring data into the mix. The embed_data() function fits into an a priori analysis workflow as the penultimate step. A dataset (or list of datasets if multiple imputation is used) is supplied as the first argument to embed_data(). Following this argument, key-value pairs can be supplied to set labels for variables in the analysis (see code below). For continuous variables, a label and unit can be specified by supplying a character vector, i.e., c("label here", "units here").

apri %<>% embed_data(
  data = ttnc,
  pclass = 'Ticket class',
  sex = 'Sex',
  age = c('Passenger age', 'years'), 
  sibsp = 'No. of siblings/spouses',
  parch = 'No. of parents/children',
  fare = c('Price of ticket','dollars') # (maybe pounds?)
)

# Note that embed_data transforms apri into a list
names(apri)
#> [1] "analysis" "var_data" "fit_data"

# But it still prints like a tibble
apri
#> A priori model specifications for assessing survived ~ pclass: 
#>   Model 0 is unadjusted.
#>   Model 1 includes adjustment for sex and age.
#>   Model 2a = Model 1 plus sibsp.
#>   Model 2b = Model 1 plus parch.
#>   Model 3 = Model 1 with fare replacing age.
#> 
#>  Analysis object 
#> # A tibble: 5 x 4
#>   name     outcome  exposure formula  
#>   <chr>    <chr>    <chr>    <list>   
#> 1 Model 0  survived pclass   <formula>
#> 2 Model 1  survived pclass   <formula>
#> 3 Model 2a survived pclass   <formula>
#> 4 Model 2b survived pclass   <formula>
#> 5 Model 3  survived pclass   <formula>

The next step is to fit models defined by the specifications in analysis. Here, we use the fit_apri() function, which spans multiple different modeling frameworks, including

linear and generalized linear models (engine = 'lm' and engine = 'glm', respectively),
generalized linear models fit with generalized estimating equations (engine = 'gee'), and
Cox proportional hazards models (engine = 'cph').

Here we will use the glm engine to make a set of logistic regression models.

apri_heavy <- apri %>% 
  embed_fits(
    engine = 'glm', 
    family = binomial(link = 'logit'),
    keep_models = TRUE
  )

# It's nice to check the original models, whether you 
# want to do diagnostics or just make sure they are
# specified the way you expect them to be specified.
# Keep em with keep_models = TRUE

mdls <- apri_heavy %>% 
  pull_analysis() %>% 
  pluck("fit") %>% 
  map("model")

summary(mdls[[1]])
#> 
#> Call:
#> survived ~ pclass
#> 
#> Deviance Residuals: 
#>     Min       1Q   Median       3Q      Max  
#> -1.4607  -0.7399  -0.7399   0.9184   1.6908  
#> 
#> Coefficients:
#>              Estimate Std. Error z value Pr(>|z|)    
#> (Intercept)    0.6451     0.1543   4.180 2.92e-05 ***
#> pclassSecond  -0.7261     0.2168  -3.350 0.000808 ***
#> pclassThird   -1.8009     0.1982  -9.086  < 2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for binomial family taken to be 1)
#> 
#>     Null deviance: 964.52  on 713  degrees of freedom
#> Residual deviance: 869.81  on 711  degrees of freedom
#> AIC: 875.81
#> 
#> Number of Fisher Scoring iterations: 4

# But sometimes you may prefer to manage your 
# memory, and model objects tend to eat that up.
# Dump em with keep_models = FALSE.

apri_light <- apri %>% 
  embed_fits(
    engine = 'glm', 
    family = binomial(link = 'logit'),
    keep_models = FALSE
  )

# Note that you can keep the original models 
# if you want, but usually all you need is
# the output from embed_fits(). Here, the 
# heavy apri object requires 35 times as
# much memory as the light version

object.size(apri_heavy) / object.size(apri_light)
#> 35 bytes

# we'll use the light apri object for the
# rest of this tutorial.

rm(apri_heavy)

apri <- apri_light

Now we can dig a little deeper into these models. How about we start by peeking at the effects of our main exposure? To hoist these effects out of the model objects, we use the hoist_effect() function. The main input to this function is a data frame containing a list (or lists) of model fits. If we want to get the effect of pclass from each model, we just specify effect = pclass.

apri %>% 
  hoist_effect(pclass)
#> A priori model specifications for assessing survived ~ pclass: 
#>   Model 0 is unadjusted.
#>   Model 1 includes adjustment for sex and age.
#>   Model 2a = Model 1 plus sibsp.
#>   Model 2b = Model 1 plus parch.
#>   Model 3 = Model 1 with fare replacing age.
#> 
#>  Analysis object 
#> # A tibble: 5 x 8
#>   name     outcome  exposure formula   fit        First Second Third
#>   <chr>    <chr>    <chr>    <list>    <list>     <dbl>  <dbl> <dbl>
#> 1 Model 0  survived pclass   <formula> <apri_fit>     0 -0.726 -1.80
#> 2 Model 1  survived pclass   <formula> <apri_fit>     0 -1.31  -2.58
#> 3 Model 2a survived pclass   <formula> <apri_fit>     0 -1.41  -2.65
#> 4 Model 2b survived pclass   <formula> <apri_fit>     0 -1.33  -2.58
#> 5 Model 3  survived pclass   <formula> <apri_fit>     0 -0.800 -1.83

Neat, but maybe not as easy to read as it could be. hoist_effect has a few aesthetic helper inputs to make model output a little easier to interpret. For example, instead of looking at estimates on the log-scale, we can exponentiate them:

apri %>% 
  hoist_effect(effect = pclass, transform = exp)
#> A priori model specifications for assessing survived ~ pclass: 
#>   Model 0 is unadjusted.
#>   Model 1 includes adjustment for sex and age.
#>   Model 2a = Model 1 plus sibsp.
#>   Model 2b = Model 1 plus parch.
#>   Model 3 = Model 1 with fare replacing age.
#> 
#>  Analysis object 
#> # A tibble: 5 x 8
#>   name     outcome  exposure formula   fit        First Second  Third
#>   <chr>    <chr>    <chr>    <list>    <list>     <dbl>  <dbl>  <dbl>
#> 1 Model 0  survived pclass   <formula> <apri_fit>     1  0.484 0.165 
#> 2 Model 1  survived pclass   <formula> <apri_fit>     1  0.270 0.0757
#> 3 Model 2a survived pclass   <formula> <apri_fit>     1  0.243 0.0705
#> 4 Model 2b survived pclass   <formula> <apri_fit>     1  0.265 0.0757
#> 5 Model 3  survived pclass   <formula> <apri_fit>     1  0.449 0.160

Now we have odds-ratios instead of regression coefficients. According to the apriori models, ticket class has a strong effect on survival. A natural follow-up question is how much uncertainty we have regarding those point estimates, and a natural follow-up answer is to use the ci input argument of hoist_effect like so:

apri %>% 
  hoist_effect(effect = pclass, ci = 0.95, transform = exp)
#> A priori model specifications for assessing survived ~ pclass: 
#>   Model 0 is unadjusted.
#>   Model 1 includes adjustment for sex and age.
#>   Model 2a = Model 1 plus sibsp.
#>   Model 2b = Model 1 plus parch.
#>   Model 3 = Model 1 with fare replacing age.
#> 
#>  Analysis object 
#> # A tibble: 5 x 8
#>   name    outcome  exposure formula  fit     First    Second     Third     
#>   <chr>   <chr>    <chr>    <list>   <list>  <chr>    <chr>      <chr>     
#> 1 Model 0 survived pclass   <formul~ <apri_~ 1 (refe~ 0.48 (0.3~ 0.17 (0.1~
#> 2 Model 1 survived pclass   <formul~ <apri_~ 1 (refe~ 0.27 (0.1~ 0.08 (0.0~
#> 3 Model ~ survived pclass   <formul~ <apri_~ 1 (refe~ 0.24 (0.1~ 0.07 (0.0~
#> 4 Model ~ survived pclass   <formul~ <apri_~ 1 (refe~ 0.27 (0.1~ 0.08 (0.0~
#> 5 Model 3 survived pclass   <formul~ <apri_~ 1 (refe~ 0.45 (0.2~ 0.16 (0.0~

This type of output can be passed right into your favorite table function.

lbl <- map(apri$fit_data, attr, 'label') %>% 
  purrr::discard(is.null)

footer <- map_chr(
  .x = list(m0, m1, m2a, m2b, m3),
  .f = ~{
    .x$control <- enframe(.x$control) %>% 
      mutate(value = tolower(recode(value, !!!lbl))) %>% 
      pull(value)
    mspec_describe(.x, verbose = TRUE)
  }
)

apri %>% 
  hoist_effect(pclass, ci = 0.95, transform = exp) %>% 
  pull_analysis(name, First, Second, Third) %>% 
  kable(
    col.names = c(glue("Model{footnote_marker_symbol(1)}"), names(.)[-1]), 
    align = 'lccc', 
    format = 'html',
    escape = FALSE,
    caption = glue("Odds ratios (95% confidence limits) \\
      for survival on the titanic, stratified by ticket class")
  ) %>% 
  kable_styling(full_width = FALSE, bootstrap_options = c('striped')) %>% 
  add_header_above(header = c(" " = 1, "Ticket Class" = 3)) %>% 
  footnote(symbol = glue_collapse(footer, sep = ' '))

Summarizing `rpriori` models

Many a-priori analyses aim to present a tabular summary of all the variables used for analyses, i.e., not just the main exposure. For example, a summary should show the relationship between age (a control variable in m1) and survival as well as the relationship between sibsp (is a control variable in m2a) and survival, for all of the given model fits.

In order to obtain a regression coefficient for age in all of the models for this analysis, we need to re-fit Model 0 (the unadjusted model) as survived ~ age instead of survived ~ pclass.
In order to obtain a regression coefficient for sibsp in all of the models for this analysis, we need to re-fit Model 0 (the unadjusted model) as survived ~ sibsp instead of survived ~ pclass, but that’s not all! We also need to re-fit Model 1 as survived ~ sibsp + sex + age instead of survived ~ pclass + sex + age.

This approach is standard for population science papers and it can also create very informative tables, but making those tables can get very tedious very quickly. rpriori is designed to help generate and tabulate these tables without having to fit dozens of models by hand. All we need to do is apply the summary function to an apri_fit model to get regression coefficients estimated by the recursive substitution process outlined above:

# Summary of unadjusted relationships between survival
# and each of the variables used in this analysis, separately.
summary(apri$analysis$fit[[1]])
#> # A tibble: 9 x 8
#>   variable term         level  ref   estimate std.error   pv_term   pv_ovrl
#>   <fct>    <fct>        <fct>  <lgl>    <dbl>     <dbl>     <dbl>     <dbl>
#> 1 pclass   pclassFirst  First  TRUE   NA        0       NA        NA       
#> 2 pclass   pclassSecond Second FALSE  -0.726    0.217    8.08e- 4  2.72e-21
#> 3 pclass   pclassThird  Third  FALSE  -1.80     0.198    1.03e-19  2.72e-21
#> 4 age      age          years  FALSE  -0.0110   0.00533  3.97e- 2  3.97e- 2
#> 5 sibsp    sibsp        <NA>   FALSE  -0.0384   0.0828   6.43e- 1  6.43e- 1
#> 6 parch    parch        <NA>   FALSE   0.220    0.0898   1.42e- 2  1.42e- 2
#> 7 fare     fare         dolla~ FALSE   0.0160   0.00250  1.61e-10  1.61e-10
#> 8 sex      sexMale      Male   TRUE    0        0       NA        NA       
#> 9 sex      sexFemale    Female FALSE   2.48     0.185    6.70e-41  6.70e-41

These summaries are meant to be fairly easy to manipulate using dplyr and other tools in the tidyverse. For example, the code below creates a summary for all models used in the analysis, then applies tidyverse functions to create a table with estimated odds ratios (95% confidence intervals) for each variable in each of the five models we specified apriori.

lbl <- map(apri$fit_data, attr, 'label') %>% 
  purrr::discard(is.null)

apri_tbl <- apri %>%
  pull_analysis() %>% 
  mutate(mdl_smry = map(fit, summary)) %>% 
  select(name, mdl_smry) %>% 
  unnest() %>% 
  mutate(
    variable = recode(variable, !!!lbl),
    tbl_value = fmt_effect(
      effect = estimate,
      std.error = std.error,
      transform = exp,
      conf_level = 0.95,
      reference_index = which(ref),
      reference_label = '1 (reference)'
    )
  ) %>% 
  select(name, variable, level, tbl_value) %>% 
  spread(name, tbl_value) 

apri_tbl
#> # A tibble: 9 x 7
#>   variable   level  `Model 0`   `Model 1`  `Model 2a` `Model 2b` `Model 3` 
#>   <fct>      <fct>  <chr>       <chr>      <chr>      <chr>      <chr>     
#> 1 Ticket cl~ First  1 (referen~ 1 (refere~ 1 (refere~ 1 (refere~ 1 (refere~
#> 2 Ticket cl~ Second 0.48 (0.32~ 0.27 (0.1~ 0.24 (0.1~ 0.27 (0.1~ 0.45 (0.2~
#> 3 Ticket cl~ Third  0.17 (0.11~ 0.08 (0.0~ 0.07 (0.0~ 0.08 (0.0~ 0.16 (0.0~
#> 4 Passenger~ years  0.99 (0.98~ 0.99 (0.9~ 0.99 (0.9~ 0.99 (0.9~ 0.99 (0.9~
#> 5 No. of si~ <NA>   0.96 (0.82~ 0.74 (0.6~ 0.74 (0.6~ 0.76 (0.6~ 0.69 (0.5~
#> 6 No. of pa~ <NA>   1.25 (1.05~ 0.86 (0.6~ 0.94 (0.7~ 0.86 (0.6~ 0.75 (0.6~
#> 7 Price of ~ dolla~ 1.02 (1.01~ 1.01 (1.0~ 1.02 (1.0~ 1.02 (1.0~ 1.01 (1.0~
#> 8 Sex        Male   1 (referen~ 1 (refere~ 1 (refere~ 1 (refere~ 1 (refere~
#> 9 Sex        Female 11.9 (8.29~ 11.8 (8.1~ 12.8 (8.7~ 12.7 (8.6~ 10.8 (7.4~

With a little tomfoolery, this can be presented in a clean table suitable for a journal article. (This code will someday be formalized into a more intuitive function).

kable_data <- apri_tbl %>% 
  group_by(variable) %>% 
  mutate(n = n()) %>% 
  ungroup() %>% 
  arrange(n, variable) %>% 
  mutate_if(is.factor, as.character) %>% 
  mutate(
    level = if_else(
      n == 1,
      paste(variable, level, sep = ', '), 
      level
    )
  )

grp_index <- table(kable_data$variable)
names(grp_index)[grp_index==1] <- " "

control <- list(m0, m1, m2a, m2b, m3)
footer <- map_chr(control, mspec_describe)

model_recoder <- control %>% 
  map_chr('name') %>% 
  paste0(footnote_marker_symbol(1:length(.)))

footnote_symbols <- kableExtra::footnote_marker_symbol(1:5)

kable_data %>% 
  select(-variable, -n) %>% 
  kable(
    align = c('l',rep('c',ncol(.)-1)),
    col.names = c("Characteristic", model_recoder),
    escape = FALSE
  ) %>% 
  kable_styling() %>% 
  pack_rows(index = grp_index) %>% 
  footnote(symbol = footer)

Name		Name	Last commit message	Last commit date
Latest commit History 6 Commits
R		R
data-raw		data-raw
data		data
fig		fig
inst		inst
man		man
tests		tests
.Rbuildignore		.Rbuildignore
.gitignore		.gitignore
.travis.yml		.travis.yml
DESCRIPTION		DESCRIPTION
LICENSE		LICENSE
LICENSE.md		LICENSE.md
NAMESPACE		NAMESPACE
NEWS.md		NEWS.md
README.Rmd		README.Rmd
README.md		README.md
appveyor.yml		appveyor.yml
kable_example2.png		kable_example2.png
rpriori.Rproj		rpriori.Rproj

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