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The COVID-19 pandemic has had high mortality rates in the elderly and frail worldwide, particularly in care homes. This is driven by the difficulty of isolating care homes from the wider community, the large population sizes within care facilities (relative to typical households), and the age/frailty of the residents. To quantify the mortality risk posed by disease, the case fatality risk (CFR) is an important tool. This quantifies the proportion of cases that result in death. Throughout the pandemic, CFR amongst care home residents in England has been monitored closely. To estimate CFR, we apply both novel and existing methods to data on deaths in care homes, collected by Public Health England and the Care Quality Commission. We compare these different methods, evaluating their relative strengths and weaknesses. Using these methods, we estimate temporal trends in the instantaneous CFR (at both daily and weekly resolutions) and the overall CFR across the whole of England, and dis-aggregated at regional level. We also investigate how the CFR varies based on age and on the type of care required, dis-aggregating by whether care homes include nursing staff and by age of residents. This work has contributed to the summary of measures used for monitoring the UK epidemic. Author summary: During an epidemic, the case fatality risk (CFR), i.e. the probability that an individual dies after testing positive for a disease, is a key parameter informing the public health response. However, calculating the CFR is not trivial, since there are cases who may die in the future but have not died yet. Therefore, statistical methods are required to correct for the distribution of times between testing positive and dying. In this paper, we derive multiple methods, some existing and some novel, within a consistent methodological framework. This allows us to understand how these different approaches are related and their relative strengths and weaknesses. During the COVID-19 pandemic, care homes have been particularly affected, due to the high risk of COVID-19-associated mortality in the frail and elderly. We apply our CFR methods to data from English care homes to analyse changes in the care home CFR throughout the pandemic. [ABSTRACT FROM AUTHOR]