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Longitudinal cancer biomarker studies aim to identify markers useful for long-term associations with cancer risk and early detection of cancer diagnosis. Early detection biomarkers show acute associations, meaning longitudinal trajectory changes sharply just before diagnosis, while long-term risk prediction biomarkers are often represented as changes in slopes or levels. We compare three common approaches to identify longitudinal biomarkers associated with survival outcomes: joint models, conditional models, and Cox models with time-varying covariates. Each of the three methods uses a different modeling framework for the joint density of the biomarkers and survival time. Thus, they have distinct advantages and disadvantages for detecting acute and long-term associations. We investigate the power and Type I error rates for the three approaches under different data-generating settings with regular yearly visits and moderate measurement error to evaluate robustness to assumptions and the power gain from using test statistics that match the data's association structure. The Cox model controlled Type I errors rates and maintained high power to detect associations across the scenarios considered. The conditional and joint models had inflated Type I errors under longitudinal model misspecification and only outperformed the Cox model for power when the correct model is used. However, only the conditional model can effectively disentangle the acute and long-term effects. The Cox model's convex likelihood also provides the fastest convergence. We apply all three approaches to a study of the association between CA-125 and ovarian cancer in the National Cancer Institute Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial. The results follow similar patterns to those of our simulations.