Missing data

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:

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.

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-type 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_s 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() %>% 
    ff_label("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) %>% 
    ff_label("Smoking (MAR)")

# Examine with ff_glimpse
explanatory = c("age", "sex.factor", 
  "nodes", "obstruct.factor",  
  "smoking_mcar", "smoking_mar")
dependent = "mort_5yr"

colon_s %>% 
  ff_glimpse(dependent, explanatory)
#> $Continuous
#>             label var_type   n missing_n missing_percent mean   sd  min
#> age   Age (years)    <dbl> 929         0             0.0 59.8 11.9 18.0
#> nodes       nodes    <dbl> 911        18             1.9  3.7  3.6  0.0
#>       quartile_25 median quartile_75  max
#> age          53.0   61.0        69.0 85.0
#> nodes         1.0    2.0         5.0 33.0
#> 
#> $Categorical
#>                            label var_type   n missing_n missing_percent
#> mort_5yr        Mortality 5 year    <fct> 915        14             1.5
#> sex.factor                   Sex    <fct> 929         0             0.0
#> obstruct.factor      Obstruction    <fct> 908        21             2.3
#> smoking_mcar      Smoking (MCAR)    <fct> 828       101            10.9
#> smoking_mar        Smoking (MAR)    <fct> 719       210            22.6
#>                 levels_n                              levels  levels_count
#> mort_5yr               2        "Alive", "Died", "(Missing)"  511, 404, 14
#> sex.factor             2                    "Female", "Male"      445, 484
#> obstruct.factor        2            "No", "Yes", "(Missing)"  732, 176, 21
#> smoking_mcar           2 "Non-smoker", "Smoker", "(Missing)" 645, 183, 101
#> smoking_mar            2 "Non-smoker", "Smoker", "(Missing)" 591, 128, 210
#>                   levels_percent
#> mort_5yr        55.0, 43.5,  1.5
#> sex.factor                48, 52
#> obstruct.factor 78.8, 18.9,  2.3
#> smoking_mcar          69, 20, 11
#> smoking_mar           64, 14, 23

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_s %>%
  ff_glimpse()

It doesn’t present well if you have factors with lots of levels, so you may want to remove these.

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.

colon_s %>%
  missing_plot()

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.

explanatory = c("age", "sex.factor", 
  "obstruct.factor",  
  "smoking_mcar", "smoking_mar")
dependent = "mort_5yr"

colon_s %>% 
  missing_pattern(dependent, explanatory)

#>     age sex.factor mort_5yr obstruct.factor smoking_mcar smoking_mar    
#> 617   1          1        1               1            1           1   0
#> 181   1          1        1               1            1           0   1
#> 74    1          1        1               1            0           1   1
#> 22    1          1        1               1            0           0   2
#> 16    1          1        1               0            1           1   1
#> 2     1          1        1               0            1           0   2
#> 2     1          1        1               0            0           1   2
#> 1     1          1        1               0            0           0   3
#> 8     1          1        0               1            1           1   1
#> 4     1          1        0               1            1           0   2
#> 2     1          1        0               1            0           1   2
#>       0          0       14              21          101         210 346

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.

# 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)
#> Note: dependent includes missing data. These are dropped.
#>           label     levels          No         Yes     p
#>     Age (years)  Mean (SD) 60.2 (11.5) 57.3 (13.3) 0.004
#>             Sex     Female  346 (47.3)   91 (51.7) 0.330
#>                       Male  386 (52.7)   85 (48.3)      
#>           nodes  Mean (SD)   3.7 (3.7)   3.5 (3.2) 0.435
#>  Smoking (MCAR) Non-smoker  500 (68.3)  130 (73.9) 0.080
#>                     Smoker  154 (21.0)   26 (14.8)      
#>                  (Missing)   78 (10.7)   20 (11.4)      
#>   Smoking (MAR) Non-smoker  467 (63.8)  110 (62.5) 0.077
#>                     Smoker   91 (12.4)   33 (18.8)      
#>                  (Missing)  174 (23.8)   33 (18.8)

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.

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:

colon_s %>% 
  missing_pairs(dependent, explanatory, position = "fill", )

Missing data

Ewen Harrison