Longitudinal Change and Missingness

Upon completing this topic

You will be able to distinguish subjects, time, and observations in longitudinal data, and document how dropout affects the time structure and missingness assumptions. You will distinguish simple average comparisons at each time point from questions about within-subject change.

Repeated time points are not independent samples

When measuring the same subject at multiple time points, values within a subject are correlated. The analytical structure depends on whether the research question concerns average time-point differences or individual change trajectories. Document time intervals, measurement order, and dropout together.

Longitudinal schema

subject_id | time | outcome | exposure | observed
S01        | 0    | ...     | A        | true
S01        | 1    | ...     | A        | false

observed=false merely indicates the state of having no value; it does not explain the cause of missingness. You must record whether the subject dropped out after the last observation, whether measurement failed, or whether the subject was excluded from the study.

Viewing change and missingness together

If missingness concentrates at specific time points or conditions, the observed average trajectory may differ from the true change. Do not confirm MCAR, MAR, or MNAR labels based on data alone; verify the dropout process and measurement reasons. Report the number of subjects included in the analysis and the number of observations per time point separately.

Analytical direction

Simple summaries can be used to explore the form of data at each time point. To model within-subject correlation and between-group variation, consider structures such as mixed models. Regardless of the method used, specify the time unit, baseline, missingness handling, and extrapolation range.

Table reporting time and dropout

Record the planned number of subjects, actual number of observations, and number of new dropouts separately for each time point. Reporting only the overall missingness rate makes it impossible to know when dropout began to concentrate. Also verify whether the number of observations by condition changes over time.

Time can be expressed as visit number, actual elapsed time, or categorical time points. Even for the same time=1, if the actual interval differs, the meaning of the rate of change may differ; therefore, specify the unit and reference point.

Returning to the research question for interpretation

Longitudinal results must distinguish between "the average at time 1 differs from the average at time 2" and "there was change within the same subject." Do not extend the trajectory of only the observed subjects in data with dropout to the change of the entire population.

Common failures

• Do not count time points of the same subject as independent samples.
• Do not automatically assume the last observed value is the final outcome.
• Do not group all dropout under the same missingness cause.
• Do not confirm missingness assumptions based on data alone.

Key takeaways

• Longitudinal data has a connection structure between subjects and time.
• Dropout is part of the time structure and missingness assumptions.
• Average change and within-subject change are different questions.

Next topic

The next module covers survival data using censoring, risk sets, and Kaplan–Meier.

References

• statsmodels API: https://www.statsmodels.org/stable/api.html
• Bioconductor OSTA experimental design: https://bioconductor.org/books/release/OSTA/pages/bkg-exp-design.html
• pandas User Guide: https://pandas.pydata.org/docs/user_guide/index.html

This module's longitudinal schema and examples were written independently by BioStatPy.