T-cell receptor (TCR) repertoire sequencing data provides quantitative insight into the distribution of T-cell clones. The diversity of the TCR repertoire in humans tends do decrease with age, which may be a key determinant explaining immune senescence in older individuals. To address this, we first analyze how the diversity of a potential T-cell response against an unseen pathogen changes with age. Next, we discuss the complications with interpreting the outcomes of such an analysis. Specifically, the changes in T-cell subset sizes confound analyses of TCR diversity, and typical sample sizes do not easily allow for a robust quantification of this diversity. Thus, explaining immune senescence as a result of decreasing TCR diversity is far from straightforward and requires a detailed, robust, and quantitative analysis