We present a computational framework to analyze MALDI-TOF mass spectrometry data for quantitative comparison of peptides and glycans in serum. In particular, we introduce an algorithm that detects peaks that are differentially abundant in a subgroup of patients. The method is applied to identify candidate biomarkers in serum samples of 203 participants from Egypt; 73 hepatocellular carcinoma (HCC) cases, 52 patients with chronic liver disease (CLD), and 78 healthy individuals. Mass spectra were generated using two experiments: (1) low molecular weight (LMW) enriched serum samples were used for MALDI-TOF quantification of peptides, and (2) glycans were enzymatically released from proteins in serum and permethylated prior to MALDI-TOF quantification. A subset of the participants (35 HCC and 35 CLD cases) was used to select the most useful peaks. The peak selection step is preceded by peak screening, where we eliminated peaks that seem to have association with covariates such as age, gender, and viral infection based on the 78 spectra from healthy individuals. The performance of the selected peaks was evaluated in terms of detecting the disease state of a blinded independent set that comprised of 38 HCC and 17 CLD cases. Further evaluation of the potential clinical utility of the selected candidate peptide and glycan markers is needed.