Skip to main content

Missing Data

Missing data is common in epidemiology studies, and always observed in longitudinal studies. Inadequate handling of missing data may cause bias or lead to inefficient analyses. If a variable is heavily missing, it may be appropriate to remove the variable then remove all incomplete records.

There is a difference between missing and "unknown" data. Ex. someone refusing to report income on a survey would be considered  missing, but an individual who has no preference between republican and democrat candidates may be considered a new category of "do not know".

Missing Data Mechanisms

The way to analyze incomplete data depends on the underlying missing data mechanisms. Ex. Is the missing data the same between males and females? Are values which are higher or lower more likely to be missing?

  • Missing completely at random (MCAR): No systematic differences between the missing values and the observed values.
    •  Ex. Blood pressure measurements missing because of a broken tool
  • Missing at random (MAR): Any systemic difference between the missing values and the observed values can be explained by differences in observed data.
    • Ex. Missing blood pressure measurements may be lower than those measured because younger people are more likely to be missing measurements.
  • Missing not at random (MNAR): Even after the observed data are taken into account, systematic differences remain between the missing values and the observed values.
    • Ex. people with hypertension missing clinic appointment because of headaches

Missing Data Patterns

 (Univariate)

Suppose we have a sample of size n, with some missing data points where:
image-1670859174228.png

The pattern of missing data can be described via the distribution of the indicator variable R:
image-1670859228747.png

  • If the probability that Ri = 1 is independent of the value yi, for any index i, the missing data pattern is ignorable. Equivalently. data are MAR
    • The observed data are a random sample of complete but unobserved sample
    • We can remove the data with the only effect being a decrease in power due to sample size
  • If the probability that Ri = 1 is NOT independent of the value yi, for any index i, the missing data pattern is NOT ignorable, i.e. MNAR, the data are informatively missing
    • The observed data does not represent a random sample of complete data.
    • Missing data is not ignorable, removing it may introduce bias

Missing Data Patterns (Mutlivariate)

Assume we have a multivariate dataset with outcome Y and covariates X1-Xk

Suppose we only have missing data on Y. As in the univarite case, the patterns of missing data can be described via the distribution of the indicator variable R.image-1670860184831.png

 

Imputation

Imputation is the idea that we can fill in the missing data using either a deterministic or stochastic method or combination of both.

  • Deterministic imputation
    • Refers to the situation given specific values of other fields, when only one value of a field will cause the record to satisfy all of the edits, such as using the mean or median
  • Stochastic (regression) imputation
    • This method uses regression, it adds a random error term to the predicted value and is therefore able to reproduce the correlation of X and Y more appropriately.

Other procedure sprocedures include EM algorithm, Markov Chain Monte Carlo BatesianBayesian method, weighted methods (IPW), etc.

Back to top