Riinu and I are sitting in Frankfurt airport discussing the paper retracted in JAMA this week.
During analysis, the treatment variable coded [1,2] was recoded in error to [1,0]. The results of the analysis were therefore reversed. The lung-disease self-management program actually resulted in more attendances at hospital, rather than fewer as had been originally reported.
Recode check
Checking of recoding is such an important part of data cleaning – we emphasise this a lot in HealthyR courses – but of course mistakes happen.
Our standard approach is this:
library(finalfit)
colon_s %>%
mutate(
sex.factor2 = forcats::fct_recode(sex.factor,
"F" = "Male",
"M" = "Female")
) %>%
count(sex.factor, sex.factor2)
# A tibble: 2 x 3
sex.factor sex.factor2 n
<fct> <fct> <int>
1 Female M 445
2 Male F 484
The miscode should be obvious.
check_recode()
However, mistakes may still happen and be missed. So we’ve bashed out a useful function that can be applied to your whole dataset. This is not to replace careful checking, but may catch something that has been missed.
The function takes a data frame or tibble and fuzzy matches variable names. It produces crosstables similar to above for all matched variables.
So if you have coded something from sex to sex.factor it will be matched. The match is hungry so it is more likely to match unrelated variables than to miss similar variables. But if you recode death to mortality it won’t be matched.
Here’s a walk through.
# Install
devtools::install_github('ewenharrison/finalfit')
library(finalfit)
library(dplyr)
# Recode example
colon_s_small = colon_s %>%
select(-id, -rx, -rx.factor) %>%
mutate(
age.factor2 = forcats::fct_collapse(age.factor,
"<60 years" = c("<40 years", "40-59 years")),
sex.factor2 = forcats::fct_recode(sex.factor,
# Intentional miscode
"F" = "Male",
"M" = "Female")
)
# Check
colon_s_small %>%
check_recode()
$index
# A tibble: 3 x 2
var1 var2
<chr> <chr>
1 sex.factor sex.factor2
2 age.factor age.factor2
3 sex.factor2 age.factor2
$counts
$counts[[1]]
# A tibble: 2 x 3
sex.factor sex.factor2 n
<fct> <fct> <int>
1 Female M 445
2 Male F 484
$counts[[2]]
# A tibble: 3 x 3
age.factor age.factor2 n
<fct> <fct> <int>
1 <40 years <60 years 70
2 40-59 years <60 years 344
3 60+ years 60+ years 515
$counts[[3]]
# A tibble: 4 x 3
sex.factor2 age.factor2 n
<fct> <fct> <int>
1 M <60 years 204
2 M 60+ years 241
3 F <60 years 210
4 F 60+ years 274
As can be seen, the output takes the form of a list length 2. The first is an index of matched variables. The second is crosstables as tibbles for each variable combination. sex.factor2 can be seen as being miscoded. sex.factor2 and age.factor2 have been matched, but should be ignored.
Numerics are not included by default. To do so:
out = colon_s_small %>%
select(-extent, -extent.factor,-time, -time.years) %>% # choose to exclude variables
check_recode(include_numerics = TRUE)
out
# Output not printed for space
Miscoding in survival::colon dataset?
When doing this just today, we noticed something strange in our example dataset, survival::colon.
The variable node4 should be a binary recode of nodes greater than 4. But as can be seen, something is not right!
We’re interested in any explanations those working with this dataset might have.
There we are then, a function that may be useful in detecting miscoding. So useful in fact, that we have immediately found probable miscoding in a standard R dataset.
We are using multiple imputation more frequently to “fill in” missing data in clinical datasets. Multiple datasets are created, models run, and results pooled so conclusions can be drawn.
We’ve put some improvements into Finalfit on GitHub to make it easier to use with the mice package. These will go to CRAN soon but not immediately.
Multivariate Imputation by Chained Equations (mice)
miceis a great package and contains lots of useful functions for diagnosing and working with missing data. The purpose here is to demonstrate how mice can be integrated into the Finalfit workflow with inclusion of model from imputed datasets in tables and plots.
Choose variables to impute and variables to impute from
finalfit::missing_predictorMatrix()makes it easy to specify which variables do what. For instance, we often do not want to impute our outcome or explanatory variable of interest (exposure), but do want to use them to impute other variables.
This is straightforward to code using the arguments drop_from_imputed and drop_from_imputer.
library(mice)
# Specify model
explanatory = c("age", "sex.factor", "nodes",
"obstruct.factor", "smoking_mar")
dependent = "mort_5yr"
# Choose not to impute missing values
# for explanatory variable of interest and
# outcome variable.
# But include in algorithm for imputation.
predM = colon_s %>%
select(dependent, explanatory) %>%
missing_predictorMatrix(
drop_from_imputed = c("obstruct.factor", "mort_5yr")
)
Create imputed datasets
A set of multiple imputed datasets (mids) can be created as below. Various checks should be performed to ensure you understand the data that has been created. See here.
mids = colon_s %>%
select(dependent, explanatory) %>%
mice(m = 4, predictorMatrix = predM) # Usually m = 10
Run models
Here we sill use a logistic regression model. The with.mids() function takes a model with a formula object, so use base R functions rather than Finalfit wrappers.
We now have multiple models run with each of the imputed datasets. We haven’t found good methods for combining common model metrics like AIC and c-statistic. I’d be interested to hear from anyone working on methods for this. Metrics can be extracted for each individual model to give an idea of goodness-of-fit and discrimination. We’re not suggesting you use these to compare imputed datasets, but could use them to compare models containing different variables created using the imputed datasets, e.g.
fits %>%
getfit() %>%
purrr::map(AIC)
[[1]]
[1] 1192.57
[[2]]
[1] 1191.09
[[3]]
[1] 1195.49
[[4]]
[1] 1193.729
# C-statistic
fits %>%
getfit() %>%
purrr::map(~ pROC::roc(.x$y, .x$fitted)$auc)
[[1]]
Area under the curve: 0.6839
[[2]]
Area under the curve: 0.6818
[[3]]
Area under the curve: 0.6789
[[4]]
Area under the curve: 0.6836
Pool results
Rubin’s rules are used to combine results of multiple models.
# Pool results
fits_pool = fits %>%
pool()
Plot results
Pooled results can be passed directly to Finalfit plotting functions.
# Can be passed to or_plot
colon_s %>%
or_plot(dependent, explanatory, glmfit = fits_pool, table_text_size=4)
Put results in table
The pooled result can be passed directly to fit2df() as can many common models such as lm(), glm(), lmer(), glmer(), coxph(), crr(), etc.
# Summarise and put in table
fit_imputed = fits_pool %>%
fit2df(estimate_name = "OR (multiple imputation)", exp = TRUE)
fit_imputed
explanatory OR (multiple imputation)
1 age 1.01 (1.00-1.02, p=0.212)
2 sex.factorMale 1.01 (0.77-1.34, p=0.917)
3 nodes 1.24 (1.18-1.31, p<0.001)
4 obstruct.factorYes 1.34 (0.94-1.91, p=0.105)
5 smoking_marSmoker 1.28 (0.88-1.85, p=0.192)
Combine results with summary data
Any model passed through fit2df() can be combined with a summary table generated with summary_factorlist() and any number of other models.
In healthcare, we deal with a lot of binary outcomes. Death yes/no, disease recurrence yes/no, for instance. These outcomes are often easily analysed using binary logistic regression via finalfit().
When the time taken for the outcome to occur is important, we need a different approach. For instance, in patients with cancer, the time taken until recurrence of the cancer is often just as important as the fact it has recurred.
Finalfit wraps a number of functions to make these analyses easy to perform and output into PDFs and Word documents.
Installation
# Make sure finalfit is up-to-date
install.packages("finalfit")
Dataset
We’ll use the classic “Survival from Malignant Melanoma” dataset from the boot package to illustrate. The data consist of measurements made on patients with malignant melanoma. Each patient had their tumour removed by surgery at the Department of Plastic Surgery, University Hospital of Odense, Denmark during the period 1962 to 1977.
For the purposes of demonstration, we are interested in the association between tumour ulceration and survival after surgery.
Get data and check
library(finalfit)
melanoma = boot::melanoma #F1 here for help page with data dictionary
ff_glimpse(melanoma)
#> Continuous
#> label var_type n missing_n missing_percent mean sd
#> time time <dbl> 205 0 0.0 2152.8 1122.1
#> status status <dbl> 205 0 0.0 1.8 0.6
#> sex sex <dbl> 205 0 0.0 0.4 0.5
#> age age <dbl> 205 0 0.0 52.5 16.7
#> year year <dbl> 205 0 0.0 1969.9 2.6
#> thickness thickness <dbl> 205 0 0.0 2.9 3.0
#> ulcer ulcer <dbl> 205 0 0.0 0.4 0.5
#> min quartile_25 median quartile_75 max
#> time 10.0 1525.0 2005.0 3042.0 5565.0
#> status 1.0 1.0 2.0 2.0 3.0
#> sex 0.0 0.0 0.0 1.0 1.0
#> age 4.0 42.0 54.0 65.0 95.0
#> year 1962.0 1968.0 1970.0 1972.0 1977.0
#> thickness 0.1 1.0 1.9 3.6 17.4
#> ulcer 0.0 0.0 0.0 1.0 1.0
#>
#> Categorical
#> data frame with 0 columns and 205 rows
As can be seen, all variables are coded as numeric and some need recoding to factors.
Death status
status is the the patients status at the end of the study.
1 indicates that they had died from melanoma;
2 indicates that they were still alive and;
3 indicates that they had died from causes unrelated to their melanoma.
Competing risks: comparing 2 (alive) with 1 (died melanoma) accounting for 3 (died other); see more below.
Time and censoring
time is the number of days from surgery until either the occurrence of the event (death) or the last time the patient was known to be alive. For instance, if a patient had surgery and was seen to be well in a clinic 30 days later, but there had been no contact since, then the patient’s status would be considered 30 days. This patient is censored from the analysis at day 30, an important feature of time-to-event analyses.
Recode
library(dplyr)
library(forcats)
melanoma = melanoma %>%
mutate(
# Overall survival
status_os = case_when(
status == 2 ~ 0, # "still alive"
TRUE ~ 1), # "died melanoma" or "died other causes"
# Diease-specific survival
status_dss = case_when(
status == 2 ~ 0, # "still alive"
status == 1 ~ 1, # "died of melanoma"
status == 3 ~ 0), # "died of other causes is censored"
# Competing risks regression
status_crr = case_when(
status == 2 ~ 0, # "still alive"
status == 1 ~ 1, # "died of melanoma"
status == 3 ~ 2), # "died of other causes"
# Label and recode other variables
age = ff_label(age, "Age (years)"), # table friendly labels
thickness = ff_label(thickness, "Tumour thickness (mm)"),
sex = factor(sex) %>%
fct_recode("Male" = "1",
"Female" = "0") %>%
ff_label("Sex"),
ulcer = factor(ulcer) %>%
fct_recode("No" = "0",
"Yes" = "1") %>%
ff_label("Ulcerated tumour")
)
Kaplan-Meier survival estimator
We can use the excellent survival package to produce the Kaplan-Meier (KM) survival estimator. This is a non-parametric statistic used to estimate the survival function from time-to-event data. Note use of %$% to expose left-side of pipe to older-style R functions on right-hand side.
library(survival)
survival_object = melanoma %$%
Surv(time, status_os)
# Explore:
head(survival_object) # + marks censoring, in this case "Alive"
#> [1] 10 30 35+ 99 185 204
# Expressing time in years
survival_object = melanoma %$%
Surv(time/365, status_os)
KM analysis for whole cohort
Model
The survival object is the first step to performing univariable and multivariable survival analyses.
If you want to plot survival stratified by a single grouping variable, you can substitute “survival_object ~ 1” by “survival_object ~ factor”
# Overall survival in whole cohort
my_survfit = survfit(survival_object ~ 1, data = melanoma)
my_survfit # 205 patients, 71 events
#> Call: survfit(formula = survival_object ~ 1, data = melanoma)
#>
#> n events median 0.95LCL 0.95UCL
#> 205.00 71.00 NA 9.15 NA
Life table
A life table is the tabular form of a KM plot, which you may be familiar with. It shows survival as a proportion, together with confidence limits. The whole table is shown with summary(my_survfit).
We can plot survival curves using the finalfit wrapper for the package excellent package survminer. There are numerous options available on the help page. You should always include a number-at-risk table under these plots as it is essential for interpretation.
As can be seen, the probability of dying is much greater if the tumour was ulcerated, compared to those that were not ulcerated.
CPH regression can be performed using the all-in-one finalfit() function. It produces a table containing counts (proportions) for factors, mean (SD) for continuous variables and a univariable and multivariable CPH regression.
A hazard is the term given to the rate at which events happen.
The probability that an event will happen over a period of time is the hazard multiplied by the time interval.
An assumption of CPH is that hazards are constant over time (see below).
It produces a table containing counts (proportions) for factors, mean (SD) for continuous variables and a univariable and multivariable CPH regression.
If you are using a backwards selection approach or similar, a reduced model can be directly specified and compared. The full model can be kept or dropped.
An assumption of CPH regression is that the hazard associated with a particular variable does not change over time. For example, is the magnitude of the increase in risk of death associated with tumour ulceration the same in the early post-operative period as it is in later years.
The cox.zph() function from the survival package allows us to test this assumption for each variable. The plot of scaled Schoenfeld residuals should be a horizontal line. The included hypothesis test identifies whether the gradient differs from zero for each variable. No variable significantly differs from zero at the 5% significance level.
zph_result
#> rho chisq p
#> age 0.1633 2.4544 0.1172
#> sexMale -0.0781 0.4473 0.5036
#> thickness -0.1493 1.3492 0.2454
#> ulcerYes -0.2044 2.8256 0.0928
#> year 0.0195 0.0284 0.8663
#> GLOBAL NA 8.4695 0.1322
Stratified models
One approach to dealing with a violation of the proportional hazards assumption is to stratify by that variable. Including a strata() term will result in a separate baseline hazard function being fit for each level in the stratification variable. It will be no longer possible to make direct inference on the effect associated with that variable.
This can be incorporated directly into the explanatory variable list.
As a general rule, you should always try to account for any higher structure in the data within the model. For instance, patients may be clustered within particular hospitals.
There are two broad approaches to dealing with correlated groups of observations.
Including a cluster() term is akin to using generalised estimating equations (GEE). Here, a standard CPH model is fitted but the standard errors of the estimated hazard ratios are adjusted to account for correlations.
Including a frailty() term is akin to using a mixed effects model, where specific random effects term(s) are directly incorporated into the model.
Both approaches achieve the same goal in different ways. Volumes have been written on GEE vs mixed effects models. We favour the latter approach because of its flexibility and our preference for mixed effects modelling in generalised linear modelling. Note cluster() and frailty() terms cannot be combined in the same model.
The frailty() method here is being superseded by the coxme package, and we’ll incorporate this soon.
Hazard ratio plot
A plot of any of the above models can be produced by passing the terms to hr_plot().
melanoma %>%
hr_plot(dependent_os, explanatory)
Competing risks regression
Competing-risks regression is an alternative to CPH regression. It can be useful if the outcome of interest may not be able to occur because something else (like death) has happened first. For instance, in our example it is obviously not possible for a patient to die from melanoma if they have died from another disease first. By simply looking at cause-specific mortality (deaths from melanoma) and considering other deaths as censored, bias may result in estimates of the influence of predictors.
The approach by Fine and Gray is one option for dealing with this. It is implemented in the package cmprsk. The crr() syntax differs from survival::coxph() but finalfit brings these together.
It uses the finalfit::ff_merge() function, which can join any number of models together.
So here we have various aspects of time-to-event analysis commonly used when looking at survival. There are many other applications, some which may not be obvious: for instance we use CPH for modelling length of stay in in hospital.
Stratification can be used to deal with non-proportional hazards in a particular variable.
Hierarchical structure in your data can be accommodated with cluster or frailty (random effects) terms.
Competing risks regression may be useful if your outcome is in competition with another, such as all-cause death, but is currently limited in its ability to accommodate hierarchical structures.
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.
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.
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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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.
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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.
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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.
R
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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.
R
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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.
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.
