The world's first efficacy trial of a preventive HIV vaccine was completed in 2003. Study participants who became HIV infected were followed for 2 years and monitored for HIV viral load and initiation of antiretroviral therapy (ART). In order to determine if vaccination may have altered HIV progression in persons who acquired HIV, a pre-specified objective was to compare the time until a composite endpoint between the vaccine and placebo arms, where the composite endpoint is the first event of ART initiation or viral failure (HIV viral load exceeds a threshold x(vl) copies/ml). Specifically, with vaccine efficacy, VE(tau, x(vl)), defined as one minus the ratio (vaccine/placebo) of the cumulative probability of the composite endpoint (with failure threshold x(vl)) occurring by tau months, the aim was to estimate the four parameters {VE(tau, x(vl)): x(vl) is an element of {1500, 10,000, 20,000, 55,000} copies/ml} with simultaneous 95% confidence bands. A Gaussian multipliers simulation method is devised for constructing confidence bands for VE(tau, x(vl)) with x(vl) spanning multiple discrete values or a continuous range. The new method is evaluated in simulations and is applied to the vaccine trial data set.