In persons living with HIV, viral load is strongly associated with morbidity and mortality. Viral failure in a patient who is compliant to therapy indicates that the therapy is not working and that changing regimens might be required. Statistically, this means that time to viral failure and time to regimen change should be highly correlated. We suggest a method of measuring association between two time-to-event variables and apply our method to data from therapy initiators in the Caribbean, Central, and South America network for HIV epidemiology. Our method is an extension of Spearman's correlation for censored data. It permits covariate adjustment and can be used for continuous and discrete data. Our computations show relatively high correlation between time to viral failure and time to regimen change: 0.28 (95% confidence interval [CI] 0.25, 0.30) among adults and 0.33 (95% CI 0.24, 0.41) among children. The results are similar after adjustment for age, sex, study site, baseline CD4, and baseline viral load.