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$\textbf{Background:}$ Circulating tumour DNA (ctDNA) carrying tumour-specific sequence alterations may provide a minimally invasive means to dynamically assess tumour burden and response to treatment in cancer patients. Somatic $\textit{TP53}$ mutations are a defining feature of high-grade serous ovarian carcinoma (HGSOC). We tested whether these mutations could be used as personalised markers to monitor tumour burden and early changes as a predictor of response and time to progression (TTP). $\textbf{Methods and Findings:}$ We performed a retrospective analysis of serial plasma samples collected during routine clinical visits from 40 patients with HGSOC undergoing heterogeneous standard of care treatment. Patient-specific $\textit{TP53}$ assays were developed for 31 unique mutations identified in formalin-fixed paraffin-embedded tumour DNA from these patients. These assays were used to quantify ctDNA in 318 plasma samples using microfluidic digital PCR. The $\textit{TP53}$ mutant allele fraction (TP53MAF) was compared to serum CA-125, the current gold-standard response marker for HGSOC in blood, as well as to disease volume on computed tomography scans by volumetric analysis. Changes after one cycle of treatment were compared with TTP. The median TP53MAF prior to treatment in 51 relapsed treatment courses was 8% (interquartile range [IQR] 1.2%-22%) compared to 0.7% (IQR 0.3%-2.0%) for seven untreated newly diagnosed stage IIIC/IV patients. TP53MAF correlated with volumetric measurements (Pearson $r$ = 0.59, $p$ < 0.001), and this correlation improved when patients with ascites were excluded ($r$ = 0.82). The ratio of TP53MAF to volume of disease was higher in relapsed patients (0.04% per cm$^3$) than in untreated patients (0.0008% per cm$^3$, $p$ = 0.004). In nearly all relapsed patients with disease volume > 32 cm$^3$, ctDNA was detected at ≥20 amplifiable copies per millilitre of plasma. In 49 treatment courses for relapsed disease, pre-treatment TP53MAF concentration, but not CA-125, was associated with TTP. Response to chemotherapy was seen earlier with ctDNA, with a median time to nadir of 37 d (IQR 28-54) compared with a median time to nadir of 84 d (IQR 42-116) for CA-125. In 32 relapsed treatment courses evaluable for response after one cycle of chemotherapy, a decrease in TP53MAF of >60% was an independent predictor of TTP in multivariable analysis (hazard ratio 0.22, 95% CI 0.07-0.67, $p$ = 0.008). Conversely, a decrease in TP53MAF of ≤60% was associated with poor response and identified cases with TTP < 6 mo with 71% sensitivity (95% CI 42%-92%) and 88% specificity (95% CI 64%-99%). Specificity was improved when patients with recent drainage of ascites were excluded. Ascites drainage led to a reduction of TP53MAF concentration. The limitations of this study include retrospective design, small sample size, and heterogeneity of treatment within the cohort. $\textbf{Conclusions:}$ In this retrospective study, we demonstrated that ctDNA is correlated with volume of disease at the start of treatment in women with HGSOC and that a decrease of ≤60% in TP53MAF after one cycle of chemotherapy was associated with shorter TTP. These results provide evidence that ctDNA has the potential to be a highly specific early molecular response marker in HGSOC and warrants further investigation in larger cohorts receiving uniform treatment.