[A] final sample of 1849 households in 47 randomly selected clusters. In 16 (0·9%) dwellings, residents were absent; 15 (0·8%) households refused to participate.
I am unable to find web-based standard definitions for survey terms (suggestions welcome). So, I define the contact rate as the percentage of households (of those that the interviewers attempted to contact) in which residents were not absent. In this survey, the contact rate was 1833/1849 or 99.1%. The participation rate is the percentage of households (of those contacted) which agree to participate in the survey. In this case, it is 1818/1833 or 99.2%. The response rate is then the number of participating households divided by the number of households at which contact was attempted, or 1818/1849 = 98.3%
One confusing aspect is that the Lancet authors do not explain how they handled the head of household issue. On page 2 we have "The survey purpose was explained to the head of household or spouse, and oral consent was obtained." This implies that either the head of household or the spouse was the source of the information. This makes sense since such people are likely to have knowledge of the inhabitants over the last couple of years. But how often were the household head and spouse both absent? It would seem unlikely that this never happened. Did the interviewers code this as "residents" being "absent" and include these in those 16 cases? Or did they just get information from whatever adult was present?
I do not think that this is a critical issue, but there is value in getting all the details correct.