HIV viral load (VL) is an important quantitative marker of disease progression and treatment response in people living with HIV infection (PLHIV), including children with perinatally-acquired HIV. Measures of VL are often used to predict different outcomes of interest in this population such as HIV-associated neurocognitive disorder. One popular approach to summarizing historical viral burden is the area under a time-VL curve (AUC). However, alternative historical VL summaries (HVSs) may better answer the research question of interest. In this manuscript, we discuss and contrast AUC with alternative HVSs including the time-averaged AUC, duration of viremia, percent time with suppressed VL, peak VL, and age at peak VL. Using data on youth with perinatally-acquired HIV infection from the Pediatric HIV/AIDS Cohort Study (PHACS) Adolescent Master Protocol (AMP), we show that HVSs and their associations with full scale IQ depend on when the viral loads were measured. When viral load measurements are incomplete, as can be the case in observational studies, analysis results may be subject selection bias. To alleviate bias we detail an imputation strategy and we present a simulation study demonstrating that unbiased estimation of a historical VL summary is possible with a correctly specified imputation model.