As multi-drug resistant tuberculosis (MDR-TB) continues to spread, investigating the transmission potential of different drug-resistant strains becomes an ever more pressing topic in public health. While phylogenetic and transmission tree inferences provide valuable insight into possible transmission chains, phylodynamic inference combines evolutionary and epidemiological analyses to estimate the parameters of the underlying epidemiological processes, allowing us to describe the overall dynamics of disease spread in the population. In this study, we introduce an approach to Mycobacterium tuberculosis (M. tuberculosis) phylodynamic analysis employing an existing computationally efficient model to quantify the transmission fitness costs of drug resistance with respect to drug-sensitive strains. To determine the accuracy and precision of our approach, we first perform a simulation study, mimicking the simultaneous spread of drug-sensitive and drug-resistant tuberculosis (TB) strains. We analyse the simulated transmission trees using the phylodynamic multi-type birth-death model (MTBD, (Kuhnert et al., 2016)) within the BEAST2 framework and show that this model can estimate the parameters of the epidemic well, despite the simplifying assumptions that MTBD makes compared to the complex TB transmission dynamics used for simulation. We then apply the MTBD model to an M. tuberculosis lineage 4 dataset that primarily consists of MDR sequences. Some of the MDR strains additionally exhibit resistance to pyrazinamide - an important first-line anti-tuberculosis drug. Our results support the previously proposed hypothesis that pyrazinamide resistance confers a transmission fitness cost to the bacterium, which we quantify for the given dataset. Importantly, our sensitivity analyses show that the estimates are robust to different prior distributions on the resistance acquisition rate, but are affected by the size of the dataset - i.e. we estimate a higher fitness cost when using fewer sequences for analysis. Overall, we propose that MTBD can be used to quantify the transmission fitness cost for a wide range of pathogens where the strains can be appropriately divided into two or more categories with distinct properties.