Dear anonymous 730:
I don’t really know much about the sampling methodology you mention (QTR+EPIx); the only description I can find in this forum from 2012. In that short description, it appears to spread the sample of households throughout the primary sampling unit better than the original EPI method, but it is still subject to many of the same biases.
The QTR+EPIx method, like the original EPI method, chooses the next house by counting houses closest to the house just completed. If dwelling density is greater toward the centre of the primary sampling unit, which is true in many populations, this method will move the sample toward the centre of the primary sampling, thus biasing the sample within each primary sampling unit. In addition, one of the biggest problems with the original EPI method is that it leaves the selection of households up to the survey team members. As a result, less accessible or less desirable households will have a lower probability of selection. For example, if 2 households appear to be equally eligible, the survey team will choose the household without the large, angry dog chained in the front yard. In order to be independent and random, household selection must be as independent as possible of any decision-making by members of the survey data collection teams.
Another problem with the original EPI method and all its adaptations is confusion regarding the basic sampling unit. The EPI method selects houses or dwellings, it does not select households. If a dwelling is selected which contains more than one household, either all households in that dwelling can be included in the sample, or 1 household can be selected at random. In the former case, selection of a single small apartment building will complete the number of households required in that cluster, thus providing a relatively non-representative sample which inflates the design effect. In the latter case, because the probability of selection of a single household chosen from a multiple-household dwelling is different from the probability of selection of a household in a single-household dwelling, sample weighting must be employed during analysis. This complicates data analysis and lowers precision.
I will repeat that we have done household listing in many different circumstances and populations without expenditure of exorbitant time, energy, or resources. I would recommend household listing and simple or systematic random household selection in all population survey assessments except perhaps in urgent rapid assessments during acute humanitarian emergencies.