| Author | |
|---|---|
| Name | Claire Descombes |
| Affiliation | Universitätsklinik für Neurochirurgie, Inselspital Bern |
| Degree | MSc Statistics and Data Science, University of Bern |
| Contact | claire.descombes@insel.ch |
The reference material for this course, as well as some useful literature to deepen your knowledge of R, can be found at the bottom of the page.
Always…
A few useful reminders:
Keep your statistical power for your primary endpoint(s). For that, keep their number to a minimum (ideally only one primary endpoint), and try to remain as descriptive (i.e. not statistical testing) as possible regarding your secondary endpoints.
Missing data is a very tense topic. In practice, they are almost unavoidable.
A first good step regarding missing data is to act preventively: if you are planing a prospective data analysis, is to design your study in a way that reduces as much as possible their occurrence. A few tips there:
But once the data collection is over or if you are working on retrospective data, the data which is missing is usually missing for good.
So, one thing you should always ask yourself, when encountering missing data is: Is this data “missing /completely) at random”? Meaning: are the missing data points absent by chance, or is there a more systematic pattern in their missingness?
Types of missingness (with examples)
Missing Completely At Random (MCAT): Data is missing independently of any observed or unobserved values.
You are missing replies to your QoL questionnaire at 6 months for a few patients. The data is missing because all those questionnaires should have been filled in during a specific week where the study nurse was on holiday (poor absence planning, but that is another topic). There is nothing specifically putting those few patients aside from the rest of the cohort: we call those cases MCAT.
Missing At Random (MAR): Missingness depends on observed data but not the missing values themselves.
You are collecting data on depression in a cohort composed of both men and women, and men filled in less surveys than women. After accounting for gender, the unbalanced completion of survey has nothing to do with the level of depression: we call those cases MAT.
Missing Not At Random (MNAR): Missing values are related to the missing data itself, leading to potential bias.
Now you are collecting questionnaires filled in at 12 months by patients that are suffering of brain cancer, among which the progress of the disease is very variable. At the end of the trial, some questionnaires are missing, and they all systematically belong to patients that were simply too ill/invalid to fill them in. If you just delete these cases for your analysis, you might introduce a bias, meaning that you have to think about an alternative way of dealing with this data than just dropping the missing rows.
If the data are missing MCAR (or MAR), then listwise deletion does not add any (strong) bias, but it does decrease the power of the analysis by decreasing the effective sample size. Another good option in that case is mean imputation, which is most effective when the data is MCAR, as it assumes that the missing values, on average, are similar to the observed ones.
If you are dealing with data MNAR, then you have to find a smart way to impute (“deduce”) by one way or another the value of the data which is missing. We call that imputation, and there are many approaches to do that, each of them having advantages and disadvantages. Choose the optimal one depending on your data, the analysis you aim for, and the proportion of missing data.
Mean/median imputation: you replace the missing values with the mean or median of the observed values in that column.
(+) does not change the sample mean/median for that variable
(-) attenuates any correlations involving the variable(s) that are imputed, can distort distributions and underestimate variance
Regression imputation: you use a regression model to predict the missing value based on other variables in the dataset.
(+) the estimates fit perfectly along the regression line without any residual variance
(-) opposite problem of mean imputation: the model predicts the most likely value of missing data but does not supply uncertainty about that value; by doing so, it may artificially strengthen relationships between variables
Last Observation Carried Forward (LOCF) imputation: an be used when the data are longitudinal (i.e. repeated measures have been taken per subject); the last observed non-missing value is used to fill in missing values at a later point in the study
(+) easy to apply
(-) can introduce bias if the last observed value is not representative of the participant’s state at the time of the missing data; underestimates variability (fails to account for natural fluctuations in the data)
K-Nearest Neighbours (KNN) imputation: you find the k-nearest neighbours to a data point with a missing value and using their values to impute the missing one.
(+) efficient for data sets with underlying patterns and relationships
(-) is computationally expensive for large datasets
Etc.
And if too many data points are missing for a variable, consider dropping the corresponding analysis completely.