Many of our projects involve getting doctors, nurses, and medical students to collect data on the patients they are looking after. We want to involve many of them in data analysis, without the requirement for coding experience or access to statistical software. To achieve this we have built Shinyfit, a shiny app for linear, logistic, and Cox PH regression.
Aim: allow access to model fitting without requirement for statistical software or coding experience.
Audience: Those sharing datasets in context of collaborative research or teaching.
Hosting requirements: Basic R coding skills including tidyverse to prepare dataset (5-10 minutes).
Linear, logistic or CPH regression tables Coefficient, odds ratio or hazard ratio plotsCrosstabsInspect dataset with ff_glimpse
Use your data
To use your own data, clone or download app from github.
Edit 0_prep.R to create a shinyfit_data object.
Test the app, usually within RStudio.
Deploy to your shiny hosting platform of choice.
Ensure you have permission to share the data
Editing 0_prep.R is straightforward and takes about 5 mins. The main purpose is to create human-readable menu items and allows sorting of variables into any categories, such as outcome and explanatory.
Errors in shinyfit are usually related to the underlying dataset, e.g.
Variables not appropriately specified as numerics or factors.
A particular factor level is empty, thus regression function (lm, glm, coxph etc.) gives error.
A variable with >2 factor levels is used as an outcome/dependent. This is not supported.
Use Glimpse tabs to check data when any error occurs.
It is fully mobile compliant, including datatables.
With over 11,000 patients now entered into REDCap and more being entered every day we thought it would be a good time to reflect on some of the ways in which GlobalSurg 3 has been set up to help collaborators from around the world enter accurate and high-quality data.
With so many important things to know about each patient undergoing cancer surgery, the GlobalSurg team of nearly 3000 collaborators has been busy entering data into our secure database at redcap.globalsurg.org (REDCap is an amazing database software developed by Vanderbilt University). With over 750,000 values entered, it isn’t surprising that from time to time a mistake occurs whilst entering the data. This might be because the data entered onto a paper form was incorrect to begin with or it might be due to accidentally clicking on the wrong options when entering the data to REDCap. In some cases, the incorrect data might even appear in the notes if the surgeon or the anaesthetist has forgotten how to decide on the most appropriate ASA grade.
To try to help our collaborators identify cases when these mistakes may have happened we have taught our REDCap some basic anatomy, cancer classifications and some common sense so that it can alert collaborators to mistake mistakes as soon as they occur. The automatic alerts appear when a collaborator tries to save a page with incorrect data meaning that they can change it immediately when they still have access to the patient notes.
Our REDCap now knows 58 things about cancer surgery that it is using to help collaborators enter accurate data.
Figure 1. Examples of our (a) paper data collection form, (b) REDCap interface, and (c) a data quality pop-up warning.
All 58 rules are given at the bottom of this post, but here are some examples:
Our REDCap knows some basic anaesthesiology:
As a collaborator if you have tried to enter a patient with diabetes mellitus and stated that they have an ASA grade of 1 Our REDCap should have informed you that diabetic patients should really have an ASA grade of 2 or more
Our REDCap knows the basics of anatomy:
It knows that if a patient had a total colectomy that they don’t have a colostomy
Our REDCap knows about TNM staging:
It knows that patients with an M score of M1 should also have an Essential TNM score of M+
Our REDCap also knows some common sense:
It knows that patients can’t have more involved lymph nodes in a specimen that the total number of lymph nodes in a specimen
It knows that a patient couldn’t have their operation before being admitted to the hospital
Our REDCap has been working tirelessly for several months to generate these alerts and help collaborators ensure their data is accurate. We hope that training REDCap to detect problems with the data will make the GlobalSurg 3 analysis more efficient and contribute to the accuracy of the data.
The final data entry deadline is 17th December so remember to upload all of your data before then. Our REDCap is ready and waiting to store and check the data.
Now this is very good already with hardly any overlapping labels and the world is pretty recognisable. And really, you can make this plot with just 2 lines of code:
So what these two lines make is already very amazing.
But I feel like Europe is a little bit misshapen and that the Caribbean and Africa are too close together. So I divided the world into regions (in this case same as continents except Russia is it’s own region – it’s just so big). Then wrote two functions that asked ggrepel to plot each region separately and use patchwork to patch each region together:
As a journal editor, I often receive studies in which the investigators fail to describe, analyse, or even acknowledge missing data. This is frustrating, as it is often of the utmost importance. Conclusions may (and do) change when missing data is accounted for. A few seem to not even appreciate that in conventional regression, only rows with complete data are included.
These are the five steps to ensuring missing data are correctly identified and appropriately dealt with:
Ensure your data are coded correctly.
Identify missing values within each variable.
Look for patterns of missingness.
Check for associations between missing and observed data.
Decide how to handle missing data.
Finalfit includes a number of functions to help with this.
Some confusing terminology
But first there are some terms which easy to mix up. These are important as they describe the mechanism of missingness and this determines how you can handle the missing data.
Missing completely at random (MCAR)
As it says, values are randomly missing from your dataset. Missing data values do not relate to any other data in the dataset and there is no pattern to the actual values of the missing data themselves.
For instance, when smoking status is not recorded in a random subset of patients.
This is easy to handle, but unfortunately, data are almost never missing completely at random.
Missing at random (MAR)
This is confusing and would be better stated as missing conditionally at random. Here, missing data do have a relationship with other variables in the dataset. However, the actual values that are missing are random.
For example, smoking status is not documented in female patients because the doctor was too shy to ask. Yes ok, not that realistic!
Missing not at random (MNAR)
The pattern of missingness is related to other variables in the dataset, but in addition, the values of the missing data are not random.
For example, when smoking status is not recorded in patients admitted as an emergency, who are also more likely to have worse outcomes from surgery.
Missing not at random data are important, can alter your conclusions, and are the most difficult to diagnose and handle. They can only be detected by collecting and examining some of the missing data. This is often difficult or impossible to do.
How you deal with missing data is dependent on the type of missingness. Once you know this, then you can sort it.
More on this below.
1. Ensure your data are coded correctly: ff_glimpse
While clearly obvious, this step is often ignored in the rush to get results. The first step in any analysis is robust data cleaning and coding. Lots of packages have a glimpse function and finalfit is no different. This function has three specific goals:
Ensure all factors and numerics are correctly assigned. That is the commonest reason to get an error with a finalfit function. You think you’re using a factor variable, but in fact it is incorrectly coded as a continuous numeric.
Ensure you know which variables have missing data. This presumes missing values are correctly assigned NA. See here for more details if you are unsure.
Ensure factor levels and variable labels are assigned correctly.
Example scenario
Using the colon cancer dataset that comes with finalfit, we are interested in exploring the association between a cancer obstructing the bowel and 5-year survival, accounting for other patient and disease characteristics.
For demonstration purposes, we will create random MCAR and MAR smoking variables to the dataset.
# Make sure finalfit is up-to-date
install.packages("finalfit")
library(finalfit)
# Create some extra missing data
## Smoking missing completely at random
set.seed(1)
colon_s$smoking_mcar =
sample(c("Smoker", "Non-smoker", NA),
dim(colon_s)[1], replace=TRUE,
prob = c(0.2, 0.7, 0.1)) %>%
factor()
Hmisc::label(colon_s$smoking_mcar) = "Smoking (MCAR)"
## Smoking missing conditional on patient sex
colon_s$smoking_mar[colon_s$sex.factor == "Female"] =
sample(c("Smoker", "Non-smoker", NA),
sum(colon_s$sex.factor == "Female"),
replace = TRUE,
prob = c(0.1, 0.5, 0.4))
colon_s$smoking_mar[colon_s$sex.factor == "Male"] =
sample(c("Smoker", "Non-smoker", NA),
sum(colon_s$sex.factor == "Male"),
replace=TRUE, prob = c(0.15, 0.75, 0.1))
colon_s$smoking_mar = factor(colon_s$smoking_mar)
Hmisc::label(colon_s$smoking_mar) = "Smoking (MAR)"
The function summarises a data frame or tibble by numeric (continuous) variables and factor (discrete) variables. The dependent and explanatory are for convenience. Pass either or neither e.g. to summarise data frame or tibble:
colon %>%
ff_glimpse()
It doesn’t present well if you have factors with lots of levels, so you may want to remove these.
Use this to check that the variables are all assigned and behaving as expected. The proportion of missing data can be seen, e.g. smoking_mar has 23% missing data.
2. Identify missing values in each variable: missing_plot
In detecting patterns of missingness, this plot is useful. Row number is on the x-axis and all included variables are on the y-axis. Associations between missingness and observations can be easily seen, as can relationships of missingness between variables.
colon_s %>%
missing_plot()
Click to enlarge.
It was only when writing this post that I discovered the amazing package, naniar. This package is recommended and provides lots of great visualisations for missing data.
3. Look for patterns of missingness: missing_pattern
missing_pattern simply wraps mice::md.pattern using finalfit grammar. This produces a table and a plot showing the pattern of missingness between variables.
This allows us to look for patterns of missingness between variables. There are 14 patterns in this data. The number and pattern of missingness help us to determine the likelihood of it being random rather than systematic.
Make sure you include missing data in demographics tables
Table 1 in a healthcare study is often a demographics table of an “explanatory variable of interest” against other explanatory variables/confounders. Do not silently drop missing values in this table. It is easy to do this correctly with summary_factorlist. This function provides a useful summary of a dependent variable against explanatory variables. Despite its name, continuous variables are handled nicely.
na_include=TRUE ensures missing data from the explanatory variables (but not dependent) are included. Note that any p-values are generated across missing groups as well, so run a second time with na_include=FALSE if you wish a hypothesis test only over observed data.
4. Check for associations between missing and observed data: missing_pairs | missing_compare
In deciding whether data is MCAR or MAR, one approach is to explore patterns of missingness between levels of included variables. This is particularly important (I would say absolutely required) for a primary outcome measure / dependent variable.
Take for example “death”. When that outcome is missing it is often for a particular reason. For example, perhaps patients undergoing emergency surgery were less likely to have complete records compared with those undergoing planned surgery. And of course, death is more likely after emergency surgery.
missing_pairs uses functions from the excellent GGally package. It produces pairs plots to show relationships between missing values and observed values in all variables.
For continuous variables (age and nodes), the distributions of observed and missing data can be visually compared. Is there a difference between age and mortality above?
For discrete, data, counts are presented by default. It is often easier to compare proportions:
colon_s %>%
missing_pairs(dependent, explanatory, position = "fill", )
It should be obvious that missingness in Smoking (MCAR) does not relate to sex (row 6, column 3). But missingness in Smoking (MAR) does differ by sex (last row, column 3) as was designed above when the missing data were created.
We can confirm this using missing_compare.
explanatory = c("age", "sex.factor",
"nodes", "obstruct.factor")
dependent = "smoking_mcar"
colon_s %>%
missing_compare(dependent, explanatory)
Missing data analysis: Smoking (MCAR) Not missing Missing p
Age (years) Mean (SD) 59.7 (11.9) 59.9 (12.6) 0.867
Sex Female 399 (89.7) 46 (10.3) 0.616
Male 429 (88.6) 55 (11.4)
nodes Mean (SD) 3.6 (3.4) 4 (4.5) 0.990
Obstruction No 654 (89.3) 78 (10.7) 0.786
Yes 156 (88.6) 20 (11.4)
dependent = "smoking_mar"
colon_s %>%
missing_compare(dependent, explanatory)
Missing data analysis: Smoking (MAR) Not missing Missing p
Age (years) Mean (SD) 59.6 (11.9) 60.1 (12) 0.709
Sex Female 288 (64.7) 157 (35.3)
It takes “dependent” and “explanatory” variables, but in this context “dependent” just refers to the variable being tested for missingness against the “explanatory” variables.
Comparisons for continuous data use a Kruskal Wallis and for discrete data a chi-squared test.
As expected, a relationship is seen between Sex and Smoking (MAR) but not Smoking (MCAR).
For those who like an omnibus test
If you are work predominately with numeric rather than discrete data (categorical/factors), you may find these tests from the MissMech package useful. The package and output is well documented, and provides two tests which can be used to determine whether data are MCAR.
These pages from Karen Grace-Martin are great for this.
Prior to a standard regression analysis, we can either:
Delete the variable with the missing data
Delete the cases with the missing data
Impute (fill in) the missing data
Model the missing data
MCAR, MAR, or MNAR
MCAR vs MAR
Using the examples, we identify that Smoking (MCAR) is missing completely at random.
We know nothing about the missing values themselves, but we know of no plausible reason that the values of the missing data, for say, people who died should be different to the values of the missing data for those who survived. The pattern of missingness is therefore not felt to be MNAR.
Common solution
Depending on the number of data points that are missing, we may have sufficient power with complete cases to examine the relationships of interest.
We therefore elect to simply omit the patients in whom smoking is missing. This is known as list-wise deletion and will be performed by default in standard regression analyses including finalfit.
explanatory = c("age", "sex.factor",
"nodes", "obstruct.factor",
"smoking_mcar")
dependent = "mort_5yr"
colon_s %>%
finalfit(dependent, explanatory, metrics=TRUE)
Dependent: Mortality 5 year Alive Died OR (univariable) OR (multivariable)
Age (years) Mean (SD) 59.8 (11.4) 59.9 (12.5) 1.00 (0.99-1.01, p=0.986) 1.01 (1.00-1.02, p=0.200)
Sex Female 243 (47.6) 194 (48.0) - -
Male 268 (52.4) 210 (52.0) 0.98 (0.76-1.27, p=0.889) 1.02 (0.76-1.38, p=0.872)
nodes Mean (SD) 2.7 (2.4) 4.9 (4.4) 1.24 (1.18-1.30, p
Other considerations
Sensitivity analysis
Omit the variable
Imputation
Model the missing data
If the variable in question is thought to be particularly important, you may wish to perform a sensitivity analysis. A sensitivity analysis in this context aims to capture the effect of uncertainty on the conclusions drawn from the model. Thus, you may choose to re-label all missing smoking values as “smoker”, and see if that changes the conclusions of your analysis. The same procedure can be performed labeling with “non-smoker”.
If smoking is not associated with the explanatory variable of interest (bowel obstruction) or the outcome, it may be considered not to be a confounder and so could be omitted. That neatly deals with the missing data issue, but of course may not be appropriate.
Imputation and modelling are considered below.
MCAR vs MAR
But life is rarely that simple.
Consider that the smoking variable is more likely to be missing if the patient is female (missing_compareshows a relationship). But, say, that the missing values are not different from the observed values. Missingness is then MAR.
If we simply drop all the cases (patients) in which smoking is missing (list-wise deletion), then proportionality we drop more females than men. This may have consequences for our conclusions if sex is associated with our explanatory variable of interest or outcome.
Common solution
mice is our go to package for multiple imputation. That’s the process of filling in missing data using a best-estimate from all the other data that exists. When first encountered, this doesn’t sounds like a good idea.
However, taking our simple example, if missingness in smoking is predicted strongly by sex, and the values of the missing data are random, then we can impute (best-guess) the missing smoking values using sex and other variables in the dataset.
Imputation is not usually appropriate for the explanatory variable of interest or the outcome variable. With both of these, the hypothesis is that there is an meaningful association with other variables in the dataset, therefore it doesn’t make sense to use these variables to impute them.
Here is some code to run mice. The package is well documented, and there are a number of checks and considerations that should be made to inform the imputation process. Read the documentation carefully prior to doing this yourself.
# Multivariate Imputation by Chained Equations (mice)
library(finalfit)
library(dplyr)
library(mice)
explanatory = c("age", "sex.factor",
"nodes", "obstruct.factor", "smoking_mar")
dependent = "mort_5yr"
colon_s %>%
select(dependent, explanatory) %>%
# Exclude outcome and explanatory variable of interest from imputation
dplyr::filter(!is.na(mort_5yr), !is.na(obstruct.factor)) %>%
# Run imputation with 10 imputed sets
mice(m = 10) %>%
# Run logistic regression on each imputed set
with(glm(formula(ff_formula(dependent, explanatory)),
family="binomial")) %>%
# Pool and summarise results
pool() %>%
summary(conf.int = TRUE, exponentiate = TRUE) %>%
# Jiggle into finalfit format
mutate(explanatory_name = rownames(.)) %>%
select(explanatory_name, estimate, `2.5 %`, `97.5 %`, p.value) %>%
condense_fit(estimate_suffix = " (multiple imputation)") %>%
remove_intercept() -> fit_imputed
# Use finalfit merge methods to create and compare results
colon_s %>%
summary_factorlist(dependent, explanatory, fit_id = TRUE) -> summary1
colon_s %>%
glmuni(dependent, explanatory) %>%
fit2df(estimate_suffix = " (univariable)") -> fit_uni
colon_s %>%
glmmulti(dependent, explanatory) %>%
fit2df(estimate_suffix = " (multivariable inc. smoking)") -> fit_multi
explanatory = c("age", "sex.factor",
"nodes", "obstruct.factor")
colon_s %>%
glmmulti(dependent, explanatory) %>%
fit2df(estimate_suffix = " (multivariable)") -> fit_multi_r
# Combine to final table
summary1 %>%
ff_merge(fit_uni) %>%
ff_merge(fit_multi_r) %>%
ff_merge(fit_multi) %>%
ff_merge(fit_imputed) %>%
select(-fit_id, -index)
label levels Alive Died OR (univariable) OR (multivariable) OR (multivariable inc. smoking) OR (multiple imputation)
Age (years) Mean (SD) 59.8 (11.4) 59.9 (12.5) 1.00 (0.99-1.01, p=0.986) 1.01 (1.00-1.02, p=0.122) 1.02 (1.00-1.03, p=0.010) 1.01 (1.00-1.02, p=0.116)
Sex Female 243 (55.6) 194 (44.4) - - - -
Male 268 (56.1) 210 (43.9) 0.98 (0.76-1.27, p=0.889) 0.98 (0.74-1.30, p=0.890) 0.88 (0.64-1.23, p=0.461) 0.99 (0.75-1.31, p=0.957)
nodes Mean (SD) 2.7 (2.4) 4.9 (4.4) 1.24 (1.18-1.30, p
The final table can easily be exported to Word or as a PDF as described else where.
By examining the coefficients, the effect of the imputation compared with the complete case analysis can be clearly seen.
Other considerations
Omit the variable
Imputing factors with new level for missing data
Model the missing data
As above, if the variable does not appear to be important, it may be omitted from the analysis. A sensitivity analysis in this context is another form of imputation. But rather than using all other available information to best-guess the missing data, we simply assign the value as above. Imputation is therefore likely to be more appropriate.
There is an alternative method to model the missing data for the categorical in this setting – just consider the missing data as a factor level. This has the advantage of simplicity, with the disadvantage of increasing the number of terms in the model. Multiple imputation is generally preferred.
library(dplyr)
colon_s %>%
mutate(
smoking_mar = forcats::fct_explicit_na(smoking_mar)
) %>%
finalfit(dependent, explanatory)
Dependent: Mortality 5 year Alive Died OR (univariable) OR (multivariable)
Age (years) Mean (SD) 59.8 (11.4) 59.9 (12.5) 1.00 (0.99-1.01, p=0.986) 1.01 (1.00-1.02, p=0.119)
Sex Female 243 (47.6) 194 (48.0) - -
Male 268 (52.4) 210 (52.0) 0.98 (0.76-1.27, p=0.889) 0.96 (0.72-1.30, p=0.809)
nodes Mean (SD) 2.7 (2.4) 4.9 (4.4) 1.24 (1.18-1.30, p
MNAR vs MAR
Missing not at random data is tough in healthcare. To determine if data are MNAR for definite, we need to know their value in a subset of observations (patients).
Using our example above. Say smoking status is poorly recorded in patients admitted to hospital as an emergency with an obstructing cancer. Obstructing bowel cancers may be larger or their position may make the prognosis worse. Smoking may relate to the aggressiveness of the cancer and may be an independent predictor of prognosis. The missing values for smoking may therefore not random. Smoking may be more common in the emergency patients and may be more common in those that die.
There is no easy way to handle this. If at all possible, try to get the missing data. Otherwise, take care when drawing conclusions from analyses where data are thought to be missing not at random.
Where to next
We are now doing more in Stan. Missing data can be imputed directly within a Stan model which feels neat. Stan doesn’t yet have the equivalent of NA which makes passing the data block into Stan a bit of a faff.
Alternatively, the missing data can be directly modelled in Stan. Examples are provided in the manual. Again, I haven’t found this that easy to do, but there are a number of Stan developments that will hopefully make this more straightforward in the future.
As a journal editor, I often receive studies in which the investigators fail to describe, analyse, or even acknowledge missing data. This is frustrating, as it is often of the utmost importance. Conclusions may (and do) change when missing data is accounted for. A few seem to not even appreciate that in conventional regression, only rows with complete data are included.
These are the five steps to ensuring missing data are correctly identified and appropriately dealt with:
Ensure your data are coded correctly.
Identify missing values within each variable.
Look for patterns of missingness.
Check for associations between missing and observed data.
Decide how to handle missing data.
Finalfit includes a number of functions to help with this.
Some confusing terminology
But first there are some terms which easy to mix up. These are important as they describe the mechanism of missingness and this determines how you can handle the missing data.
Missing completely at random (MCAR)
As it says, values are randomly missing from your dataset. Missing data values do not relate to any other data in the dataset and there is no pattern to the actual values of the missing data themselves.
For instance, when smoking status is not recorded in a random subset of patients.
This is easy to handle, but unfortunately, data are almost never missing completely at random.
Missing at random (MAR)
This is confusing and would be better stated as missing conditionally at random. Here, missing data do have a relationship with other variables in the dataset. However, the actual values that are missing are random.
For example, smoking status is not documented in female patients because the doctor was too shy to ask. Yes ok, not that realistic!
Missing not at random (MNAR)
The pattern of missingness is related to other variables in the dataset, but in addition, the values of the missing data are not random.
For example, when smoking status is not recorded in patients admitted as an emergency, who are also more likely to have worse outcomes from surgery.
Missing not at random data are important, can alter your conclusions, and are the most difficult to diagnose and handle. They can only be detected by collecting and examining some of the missing data. This is often difficult or impossible to do.
How you deal with missing data is dependent on the type of missingness. Once you know this, then you can sort it.
More on this below.
1. Ensure your data are coded correctly: ff_glimpse
While clearly obvious, this step is often ignored in the rush to get results. The first step in any analysis is robust data cleaning and coding. Lots of packages have a glimpse function and finalfit is no different. This function has three specific goals:
Ensure all factors and numerics are correctly assigned. That is the commonest reason to get an error with a finalfit function. You think you’re using a factor variable, but in fact it is incorrectly coded as a continuous numeric.
Ensure you know which variables have missing data. This presumes missing values are correctly assigned NA. See here for more details if you are unsure.
Ensure factor levels and variable labels are assigned correctly.
Example scenario
Using the colon cancer dataset that comes with finalfit, we are interested in exploring the association between a cancer obstructing the bowel and 5-year survival, accounting for other patient and disease characteristics.
For demonstration purposes, we will create random MCAR and MAR smoking variables to the dataset.
The function summarises a data frame or tibble by numeric (continuous) variables and factor (discrete) variables. The dependent and explanatory are for convenience. Pass either or neither e.g. to summarise data frame or tibble:
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colon%>%
ff_glimpse()
It doesn’t present well if you have factors with lots of levels, so you may want to remove these.
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library(dplyr)
colon_s%>%
select(-hospital)%>%
ff_glimpse()
Use this to check that the variables are all assigned and behaving as expected. The proportion of missing data can be seen, e.g. smoking_mar has 23% missing data.
2. Identify missing values in each variable: missing_plot
In detecting patterns of missingness, this plot is useful. Row number is on the x-axis and all included variables are on the y-axis. Associations between missingness and observations can be easily seen, as can relationships of missingness between variables.
R
1
2
colon_s%>%
missing_plot()
Click to enlarge.
It was only when writing this post that I discovered the amazing package, naniar. This package is recommended and provides lots of great visualisations for missing data.
3. Look for patterns of missingness: missing_pattern
missing_pattern simply wraps mice::md.pattern using finalfit grammar. This produces a table and a plot showing the pattern of missingness between variables.
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explanatory=c("age","sex.factor",
"nodes","obstruct.factor",
"smoking_mcar","smoking_mar")
dependent="mort_5yr"
colon_s%>%
missing_pattern(dependent,explanatory)
This allows us to look for patterns of missingness between variables. There are 14 patterns in this data. The number and pattern of missingness help us to determine the likelihood of it being random rather than systematic.
Make sure you include missing data in demographics tables
Table 1 in a healthcare study is often a demographics table of an “explanatory variable of interest” against other explanatory variables/confounders. Do not silently drop missing values in this table. It is easy to do this correctly with summary_factorlist. This function provides a useful summary of a dependent variable against explanatory variables. Despite its name, continuous variables are handled nicely.
na_include=TRUE ensures missing data from the explanatory variables (but not dependent) are included. Note that any p-values are generated across missing groups as well, so run a second time with na_include=FALSE if you wish a hypothesis test only over observed data.
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library(finalfit)
# Explanatory or confounding variables
explanatory=c("age","sex.factor",
"nodes",
"smoking_mcar","smoking_mar")
# Explanatory variable of interest
dependent="obstruct.factor"# Bowel obstruction
colon_s%>%
summary_factorlist(dependent,explanatory,
na_include=TRUE,p=TRUE)
label levels No Yesp
Age(years)Mean(SD)60.2(11.5)57.3(13.3)0.014
Sex Female346(79.2)91(20.8)0.290
Male386(82.0)85(18.0)
nodes Mean(SD)3.7(3.7)3.5(3.2)0.774
Smoking(MCAR)Non-smoker500(79.4)130(20.6)0.173
Smoker154(85.6)26(14.4)
Missing78(79.6)20(20.4)
Smoking(MAR)Non-smoker467(80.9)110(19.1)0.056
Smoker91(73.4)33(26.6)
Missing174(84.1)33(15.9)
4. Check for associations between missing and observed data: missing_pairs | missing_compare
In deciding whether data is MCAR or MAR, one approach is to explore patterns of missingness between levels of included variables. This is particularly important (I would say absolutely required) for a primary outcome measure / dependent variable.
Take for example “death”. When that outcome is missing it is often for a particular reason. For example, perhaps patients undergoing emergency surgery were less likely to have complete records compared with those undergoing planned surgery. And of course, death is more likely after emergency surgery.
missing_pairs uses functions from the excellent GGally package. It produces pairs plots to show relationships between missing values and observed values in all variables.
R
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2
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explanatory=c("age","sex.factor",
"nodes","obstruct.factor",
"smoking_mcar","smoking_mar")
dependent="mort_5yr"
colon_s%>%
missing_pairs(dependent,explanatory)
For continuous variables (age and nodes), the distributions of observed and missing data can be visually compared. Is there a difference between age and mortality above?
For discrete, data, counts are presented by default. It is often easier to compare proportions:
It should be obvious that missingness in Smoking (MCAR) does not relate to sex (row 6, column 3). But missingness in Smoking (MAR) does differ by sex (last row, column 3) as was designed above when the missing data were created.
We can confirm this using missing_compare.
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explanatory=c("age","sex.factor",
"nodes","obstruct.factor")
dependent="smoking_mcar"
colon_s%>%
missing_compare(dependent,explanatory)
Missing data analysis:Smoking(MCAR)Notmissing Missingp
Age(years)Mean(SD)59.7(11.9)59.9(12.6)0.867
Sex Female399(89.7)46(10.3)0.616
Male429(88.6)55(11.4)
nodes Mean(SD)3.6(3.4)4(4.5)0.990
Obstruction No654(89.3)78(10.7)0.786
Yes156(88.6)20(11.4)
dependent="smoking_mar"
colon_s%>%
missing_compare(dependent,explanatory)
Missing data analysis:Smoking(MAR)Notmissing Missingp
Age(years)Mean(SD)59.6(11.9)60.1(12)0.709
Sex Female288(64.7)157(35.3)
It takes “dependent” and “explanatory” variables, but in this context “dependent” just refers to the variable being tested for missingness against the “explanatory” variables.
Comparisons for continuous data use a Kruskal Wallis and for discrete data a chi-squared test.
As expected, a relationship is seen between Sex and Smoking (MAR) but not Smoking (MCAR).
For those who like an omnibus test
If you are work predominately with numeric rather than discrete data (categorical/factors), you may find these tests from the MissMech package useful. The package and output is well documented, and provides two tests which can be used to determine whether data are MCAR.
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library(finalfit)
library(dplyr)
library(MissMech)
explanatory=c("age","nodes")
dependent="mort_5yr"
colon_s%>%
select(explanatory)%>%
MissMech::TestMCARNormality()
5. Decide how to handle missing data
These pages from Karen Grace-Martin are great for this.
Prior to a standard regression analysis, we can either:
Delete the variable with the missing data
Delete the cases with the missing data
Impute (fill in) the missing data
Model the missing data
MCAR, MAR, or MNAR
MCAR vs MAR
Using the examples, we identify that Smoking (MCAR) is missing completely at random.
We know nothing about the missing values themselves, but we know of no plausible reason that the values of the missing data, for say, people who died should be different to the values of the missing data for those who survived. The pattern of missingness is therefore not felt to be MNAR.
Common solution
Depending on the number of data points that are missing, we may have sufficient power with complete cases to examine the relationships of interest.
We therefore elect to simply omit the patients in whom smoking is missing. This is known as list-wise deletion and will be performed by default in standard regression analyses including finalfit.
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explanatory=c("age","sex.factor",
"nodes","obstruct.factor",
"smoking_mcar")
dependent="mort_5yr"
colon_s%>%
finalfit(dependent,explanatory,metrics=TRUE)
Dependent:Mortality5year Alive Died OR(univariable)OR(multivariable)
If the variable in question is thought to be particularly important, you may wish to perform a sensitivity analysis. A sensitivity analysis in this context aims to capture the effect of uncertainty on the conclusions drawn from the model. Thus, you may choose to re-label all missing smoking values as “smoker”, and see if that changes the conclusions of your analysis. The same procedure can be performed labeling with “non-smoker”.
If smoking is not associated with the explanatory variable of interest (bowel obstruction) or the outcome, it may be considered not to be a confounder and so could be omitted. That neatly deals with the missing data issue, but of course may not be appropriate.
Imputation and modelling are considered below.
MCAR vs MAR
But life is rarely that simple.
Consider that the smoking variable is more likely to be missing if the patient is female (missing_compareshows a relationship). But, say, that the missing values are not different from the observed values. Missingness is then MAR.
If we simply drop all the cases (patients) in which smoking is missing (list-wise deletion), then proportionality we drop more females than men. This may have consequences for our conclusions if sex is associated with our explanatory variable of interest or outcome.
Common solution
mice is our go to package for multiple imputation. That’s the process of filling in missing data using a best-estimate from all the other data that exists. When first encountered, this doesn’t sounds like a good idea.
However, taking our simple example, if missingness in smoking is predicted strongly by sex, and the values of the missing data are random, then we can impute (best-guess) the missing smoking values using sex and other variables in the dataset.
Imputation is not usually appropriate for the explanatory variable of interest or the outcome variable. With both of these, the hypothesis is that there is an meaningful association with other variables in the dataset, therefore it doesn’t make sense to use these variables to impute them.
Here is some code to run mice. The package is well documented, and there are a number of checks and considerations that should be made to inform the imputation process. Read the documentation carefully prior to doing this yourself.
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# Multivariate Imputation by Chained Equations (mice)
library(finalfit)
library(dplyr)
library(mice)
explanatory=c("age","sex.factor",
"nodes","obstruct.factor","smoking_mar")
dependent="mort_5yr"
colon_s%>%
select(dependent,explanatory)%>%
# Exclude outcome and explanatory variable of interest from imputation
The final table can easily be exported to Word or as a PDF as described else where.
By examining the coefficients, the effect of the imputation compared with the complete case analysis can be clearly seen.
Other considerations
Omit the variable
Imputing factors with new level for missing data
Model the missing data
As above, if the variable does not appear to be important, it may be omitted from the analysis. A sensitivity analysis in this context is another form of imputation. But rather than using all other available information to best-guess the missing data, we simply assign the value as above. Imputation is therefore likely to be more appropriate.
There is an alternative method to model the missing data for the categorical in this setting – just consider the missing data as a factor level. This has the advantage of simplicity, with the disadvantage of increasing the number of terms in the model. Multiple imputation is generally preferred.
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library(dplyr)
colon_s%>%
mutate(
smoking_mar=forcats::fct_explicit_na(smoking_mar)
)%>%
finalfit(dependent,explanatory)
Dependent:Mortality5year Alive Died OR(univariable)OR(multivariable)
Missing not at random data is tough in healthcare. To determine if data are MNAR for definite, we need to know their value in a subset of observations (patients).
Using our example above. Say smoking status is poorly recorded in patients admitted to hospital as an emergency with an obstructing cancer. Obstructing bowel cancers may be larger or their position may make the prognosis worse. Smoking may relate to the aggressiveness of the cancer and may be an independent predictor of prognosis. The missing values for smoking may therefore not random. Smoking may be more common in the emergency patients and may be more common in those that die.
There is no easy way to handle this. If at all possible, try to get the missing data. Otherwise, take care when drawing conclusions from analyses where data are thought to be missing not at random.
Where to next
We are now doing more in Stan. Missing data can be imputed directly within a Stan model which feels neat. Stan doesn’t yet have the equivalent of NA which makes passing the data block into Stan a bit of a faff.
Alternatively, the missing data can be directly modelled in Stan. Examples are provided in the manual. Again, I haven’t found this that easy to do, but there are a number of Stan developments that will hopefully make this more straightforward in the future.
I’ve been doing data science for over 10 years now. Although most of this time I didn’t realise I was doing data science. I thought I was just doing normal science but focusing on simulations and data analysis, rather than field or lab work. I’ve switched fields a few times now- physics BSc, Chemistry PhD, now working in medical research. Therefore, instead of this lenghty introduction:
“I’m a physicist by background with substantial interdisciplinary expertise in simulations, data analysis, programming…”
I just go with:
I’m a data scientist.
Anyway, here’s how my toolbox and technical skills have evolved over the years:
If your new to modelling in R and don’t know what this title means, you definitely want to look into doing it.
I’ve always been a fan of converting model outputs to real-life quantities of interest. For example, I like to supplement a logistic regression model table with predicted probabilities for a given set of explanatory variable levels. This can be more intuitive than odds ratios, particularly for a lay audience.
For example, say I have run a logistic regression model for predicted 5 year survival after colon cancer. What is the actual probability of death for a patient under 40 with a small cancer that has not perforated? How does that probability differ for a patient over 40?
I’ve tried this various ways. I used Zelig for a while including here, but it started trying to do too much and was always broken (I updated it the other day in the hope that things were better, but was met with a string of errors again).
I also used rms, including here (checkout the nice plots!). I like it and respect the package. But I don’t use it as standard and so need to convert all the models first, e.g. to lrm. Again, for my needs it tries to do too much and I find datadist awkward.
Thirdly, I love Stan for this, e.g. used in this paper. The generated quantities block allows great flexibility to simulate whatever you wish from the posterior. I’m a Bayesian at heart will always come back to this. But for some applications it’s a bit much, and takes some time to get running as I want.
I often simply want to predicty-hat from lm and glm with bootstrapped intervals and ideally a comparison of explanatory levels sets. Just like sim does in Zelig. But I want it in a format I can immediately use in a publication.
Well now I can with finalfit.
You need to use the github version of the package until CRAN is updated
devtools::install_github("ewenharrison/finalfit")
There’s two main functions with some new internals to help expand to other models in the future.
Create new dataframe of explanatory variable levels
finalfit_newdata is used to generate a new dataframe. I usually want to set 4 or 5 combinations of x levels and often find it difficult to get this formatted for predict. Pass the original dataset, the names of explanatory variables used in the model, and a list of levels for these. For the latter, they can be included as rows or columns. If the data type is incorrect or you try to pass factor levels that don’t exist, it will fail with a useful warning.
boot_predict takes standard lm and glm model objects, together with finalfitlmlist and glmlist objects from fitters, e.g. lmmulti and glmmulti. In addition, it requires a newdata object generated from finalfit_newdata. If you’re new to this, don’t be put off by all those model acronyms, it is straightforward.
colon_s %>%
glmmulti(dependent, explanatory) %>%
boot_predict(newdata,
estimate_name = "Predicted probability of death",
R=100, boot_compare = FALSE,
digits = c(2,3))
Age Extent of spread Perforation Predicted probability of death
1 <40 years Submucosa No 0.28 (0.00 to 0.52)
2 <40 years Submucosa Yes 0.29 (0.00 to 0.61)
3 <40 years Adjacent structures No 0.71 (0.50 to 0.86)
4 <40 years Adjacent structures Yes 0.72 (0.45 to 0.89)
Note that the number of simulations (R) here is low for demonstration purposes. You should expect to use 1000 to 10000 to ensure you have stable estimates.
Output to Word, PDF, and html via RMarkdown
Simulations are produced using bootstrapping and everything is tidily outputted in a table/dataframe, which can be passed to knitr::kable.
# Within an .Rmd file
```{r}
knitr::kable(table, row.names = FALSE, align = c("l", "l", "l", "r"))
```
Make comparisons
Better still, by including boot_compare==TRUE, comparisons are made between the first row of newdata and each subsequent row. These can be first differences (e.g. absolute risk differences) or ratios (e.g. relative risk ratios). The comparisons are done on the individual bootstrap predictions and the distribution summarised as a mean with percentile confidence intervals (95% CI as default, e.g. 2.5 and 97.5 percentiles). A p-value is generated on the proportion of values on the other side of the null from the mean, e.g. for a ratio greater than 1.0, p is the number of bootstrapped predictions under 1.0. Multiplied by two so it is two-sided. (Sorry about including a p-value).
Scroll right here:
colon_s %>%
glmmulti(dependent, explanatory) %>%
boot_predict(newdata,
estimate_name = "Predicted probability of death",
compare_name = "Absolute risk difference",
R=100, digits = c(2,3))
Age Extent of spread Perforation Predicted probability of death Absolute risk difference
1 <40 years Submucosa No 0.28 (0.00 to 0.52) -
2 <40 years Submucosa Yes 0.29 (0.00 to 0.62) 0.01 (-0.15 to 0.20, p=0.920)
3 <40 years Adjacent structures No 0.71 (0.56 to 0.89) 0.43 (0.19 to 0.68, p<0.001)
4 <40 years Adjacent structures Yes 0.72 (0.45 to 0.91) 0.43 (0.11 to 0.73, p<0.001)
What is not included?
It doesn’t yet include our other common models, such as coxph which I may add in. It doesn’t do lmer or glmer either. bootMer works well mixed-effects models which take a bit more care and thought, e.g. how are random effects to be handled in the simulations. So I don’t have immediate plans to add that in, better to do directly.
Plotting
Finally, as with all finalfit functions, results can be produced as individual variables using condense == FALSE. This is particularly useful for plotting
If your new to modelling in R and don’t know what this title means, you definitely want to look into doing it.
I’ve always been a fan of converting model outputs to real-life quantities of interest. For example, I like to supplement a logistic regression model table with predicted probabilities for a given set of explanatory variable levels. This can be more intuitive than odds ratios, particularly for a lay audience.
For example, say I have run a logistic regression model for predicted 5 year survival after colon cancer. What is the actual probability of death for a patient under 40 with a small cancer that has not perforated? How does that probability differ for a patient over 40?
I’ve tried this various ways. I used Zelig for a while including here, but it started trying to do too much and was always broken (I updated it the other day in the hope that things were better, but was met with a string of errors again).
I also used rms, including here (checkout the nice plots!). I like it and respect the package. But I don’t use it as standard and so need to convert all the models first, e.g. to lrm. Again, for my needs it tries to do too much and I find datadist awkward.
Thirdly, I love Stan for this, e.g. used in this paper. The generated quantities block allows great flexibility to simulate whatever you wish from the posterior. I’m a Bayesian at heart will always come back to this. But for some applications it’s a bit much, and takes some time to get running as I want.
I often simply want to predicty-hat from lm and glm with bootstrapped intervals and ideally a comparison of explanatory levels sets. Just like sim does in Zelig. But I want it in a format I can immediately use in a publication.
Well now I can with finalfit.
You need to use the github version of the package until CRAN is updated
R
1
devtools::install_github("ewenharrison/finalfit")
There’s two main functions with some new internals to help expand to other models in the future.
Create new dataframe of explanatory variable levels
finalfit_newdata is used to generate a new dataframe. I usually want to set 4 or 5 combinations of x levels and often find it difficult to get this formatted for predict. Pass the original dataset, the names of explanatory variables used in the model, and a list of levels for these. For the latter, they can be included as rows or columns. If the data type is incorrect or you try to pass factor levels that don’t exist, it will fail with a useful warning.
boot_predict takes standard lm and glm model objects, together with finalfitlmlist and glmlist objects from fitters, e.g. lmmulti and glmmulti. In addition, it requires a newdata object generated from finalfit_newdata. If you’re new to this, don’t be put off by all those model acronyms, it is straightforward.
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colon_s%>%
glmmulti(dependent,explanatory)%>%
boot_predict(newdata,
estimate_name="Predicted probability of death",
R=100,boot_compare=FALSE,
digits=c(2,3))
Age Extent of spread Perforation Predicted probability of death
1<40years Submucosa No0.28(0.00to0.52)
2<40years Submucosa Yes0.29(0.00to0.61)
3<40years Adjacent structures No0.71(0.50to0.86)
4<40years Adjacent structures Yes0.72(0.45to0.89)
Note that the number of simulations (R) here is low for demonstration purposes. You should expect to use 1000 to 10000 to ensure you have stable estimates.
Output to Word, PDF, and html via RMarkdown
Simulations are produced using bootstrapping and everything is tidily outputted in a table/dataframe, which can be passed to knitr::kable.
Better still, by including boot_compare==TRUE, comparisons are made between the first row of newdata and each subsequent row. These can be first differences (e.g. absolute risk differences) or ratios (e.g. relative risk ratios). The comparisons are done on the individual bootstrap predictions and the distribution summarised as a mean with percentile confidence intervals (95% CI as default, e.g. 2.5 and 97.5 percentiles). A p-value is generated on the proportion of values on the other side of the null from the mean, e.g. for a ratio greater than 1.0, p is the number of bootstrapped predictions under 1.0. Multiplied by two so it is two-sided. (Sorry about including a p-value).
Scroll right here:
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colon_s%>%
glmmulti(dependent,explanatory)%>%
boot_predict(newdata,
estimate_name="Predicted probability of death",
compare_name="Absolute risk difference",
R=100,digits=c(2,3))
Age Extent of spread Perforation Predicted probability of death Absolute risk difference
It doesn’t yet include our other common models, such as coxph which I may add in. It doesn’t do lmer or glmer either. bootMer works well mixed-effects models which take a bit more care and thought, e.g. how are random effects to be handled in the simulations. So I don’t have immediate plans to add that in, better to do directly.
Plotting
Finally, as with all finalfit functions, results can be produced as individual variables using condense == FALSE. This is particularly useful for plotting
Note missing data in obstruct.factor. We will drop this variable for now (again, this is for demonstration only). Also see that nodes has not been labelled.
There are small numbers in some variables generating chisq.test warnings (predicted less than 5 in any cell). Generate final table.
Now, edit the Word template. Click on a table. The style should be compact. Right click > Modify... > font size = 9. Alter heading and text styles in the same way as desired. Save this as template.docx. Upload to your project folder. Add this reference to the .Rmd YAML heading, as below. Make sure you get the space correct.
The plot also doesn’t look quite right and it prints with warning messages. Experiment with fig.width to get it looking right.
Now paste this into your .Rmd file and run:
---
title: "Example knitr/R Markdown document"
author: "Ewen Harrison"
date: "21/5/2018"
output:
word_document:
reference_docx: template.docx
---
```{r setup, include=FALSE}
# Load data into global environment.
library(finalfit)
library(dplyr)
library(knitr)
load("out.rda")
```
## Table 1 - Demographics
```{r table1, echo = FALSE, results='asis'}
kable(table1, row.names=FALSE, align=c("l", "l", "r", "r", "r", "r"))
```
## Table 2 - Association between tumour factors and 5 year mortality
```{r table2, echo = FALSE, results='asis'}
kable(table2, row.names=FALSE, align=c("l", "l", "r", "r", "r", "r"))
```
## Figure 1 - Association between tumour factors and 5 year mortality
```{r figure1, echo = FALSE, warning=FALSE, message=FALSE, fig.width=10}
colon_s %>%
or_plot(dependent, explanatory)
```
---
title: "Example knitr/R Markdown document"
author: "Ewen Harrison"
date: "21/5/2018"
output:
pdf_document: default
---
```{r setup, include=FALSE}
# Load data into global environment.
library(finalfit)
library(dplyr)
library(knitr)
load("out.rda")
```
## Table 1 - Demographics
```{r table1, echo = FALSE, results='asis'}
kable(table1, row.names=FALSE, align=c("l", "l", "r", "r", "r", "r"))
```
## Table 2 - Association between tumour factors and 5 year mortality
```{r table2, echo = FALSE, results='asis'}
kable(table2, row.names=FALSE, align=c("l", "l", "r", "r", "r", "r"))
```
## Figure 1 - Association between tumour factors and 5 year mortality
```{r figure1, echo = FALSE}
colon_s %>%
or_plot(dependent, explanatory)
```
Again, ok but not great.
We can fix the plot in exactly the same way. But the table is off the side of the page. For this we use the kableExtra package. Install this in the normal manner. You may also want to alter the margins of your page using geometry in the preamble.
---
title: "Example knitr/R Markdown document"
author: "Ewen Harrison"
date: "21/5/2018"
output:
pdf_document: default
geometry: margin=0.75in
---
```{r setup, include=FALSE}
# Load data into global environment.
library(finalfit)
library(dplyr)
library(knitr)
library(kableExtra)
load("out.rda")
```
## Table 1 - Demographics
```{r table1, echo = FALSE, results='asis'}
kable(table1, row.names=FALSE, align=c("l", "l", "r", "r", "r", "r"),
booktabs=TRUE)
```
## Table 2 - Association between tumour factors and 5 year mortality
```{r table2, echo = FALSE, results='asis'}
kable(table2, row.names=FALSE, align=c("l", "l", "r", "r", "r", "r"),
booktabs=TRUE) %>%
kable_styling(font_size=8)
```
## Figure 1 - Association between tumour factors and 5 year mortality
```{r figure1, echo = FALSE, warning=FALSE, message=FALSE, fig.width=10}
colon_s %>%
or_plot(dependent, explanatory)
```
This is now looking pretty good for me as well.
There you have it. A pretty quick workflow to get final results into Word and a PDF.
The finafit package brings together the day-to-day functions we use to generate final results tables and plots when modelling. I spent many years repeatedly manually copying results from R analyses and built these functions to automate our standard healthcare data workflow. It is particularly useful when undertaking a large study involving multiple different regression analyses. When combined with RMarkdown, the reporting becomes entirely automated. Its design follows Hadley Wickham’s tidy tool manifesto.
It is recommended that this package is used together with dplyr, which is a dependent.
Some of the functions require rstan and boot. These have been left as Suggests rather than Depends to avoid unnecessary installation. If needed, they can be installed in the normal way:
1. Summarise variables/factors by a categorical variable
summary_factorlist() is a wrapper used to aggregate any number of explanatory variables by a single variable of interest. This is often “Table 1” of a published study. When categorical, the variable of interest can have a maximum of five levels. It uses Hmisc::summary.formula().
library(finalfit)
library(dplyr)
# Load example dataset, modified version of survival::colon
data(colon_s)
# Table 1 - Patient demographics by variable of interest ----
explanatory = c("age", "age.factor",
"sex.factor", "obstruct.factor")
dependent = "perfor.factor" # Bowel perforation
colon_s %>%
summary_factorlist(dependent, explanatory,
p=TRUE, add_dependent_label=TRUE)
See other options relating to inclusion of missing data, mean vs. median for continuous variables, column vs. row proportions, include a total column etc.
summary_factorlist() is also commonly used to summarise any number of variables by an outcome variable (say dead yes/no).
2. Summarise regression model results in final table format
The second main feature is the ability to create final tables for linear (lm()), logistic (glm()), hierarchical logistic (lme4::glmer()) and
Cox proportional hazards (survival::coxph()) regression models.
The finalfit() “all-in-one” function takes a single dependent variable with a vector of explanatory variable names (continuous or categorical variables) to produce a final table for publication including summary statistics, univariable and multivariable regression analyses. The first columns are those produced by summary_factorist(). The appropriate regression model is chosen on the basis of the dependent variable type and other arguments passed.
Logistic regression: glm()
Of the form: glm(depdendent ~ explanatory, family="binomial")
Of the form: lme4::glmer(dependent ~ explanatory + (1 | random_effect), family="binomial")
Hierarchical/mixed effects/multilevel logistic regression models can be specified using the argument random_effect. At the moment it is just set up for random intercepts (i.e. (1 | random_effect), but in the future I’ll adjust this to accommodate random gradients if needed (i.e. (variable1 | variable2).
Rather than going all-in-one, any number of subset models can be manually added on to a summary_factorlist() table using finalfit_merge(). This is particularly useful when models take a long-time to run or are complicated.
Note the requirement for fit_id=TRUE in summary_factorlist(). fit2df extracts, condenses, and add metrics to supported models.
Our own particular rstan models are supported and will be documented in the future. Broadly, if you are running (hierarchical) logistic regression models in [Stan](http://mc-stan.org/users/interfaces/rstan) with coefficients specified as a vector labelled beta, then fit2df() will work directly on the stanfit object in a similar manner to if it was a glm or glmerMod object.
3. Summarise regression model results in plot
Models can be summarized with odds ratio/hazard ratio plots using or_plot, hr_plot and surv_plot.
OR plot
# OR plot
explanatory = c("age.factor", "sex.factor",
"obstruct.factor", "perfor.factor")
dependent = 'mort_5yr'
colon_s %>%
or_plot(dependent, explanatory)
# Previously fitted models (`glmmulti()` or
# `glmmixed()`) can be provided directly to `glmfit`
