LQAS refers to a sequential sampling technique that classifies rather than estimates a proportion, mean, or other summary statistic. Mostly we use LQAS to classify prevalence, coverage, or food-basket completeness. The term used to describe the type of LQAS are a little arbitrary. Here are some definitions that might be of use: (A) Conventional LQAS : This is usually a simple two-class method in which classification rules are decided by inspection of cumulative binomial probabilities and the sample is a simple random sample or a systematic sample. Variants include using different probability distributions (e.g. The normal for classifying a mean, the hypergeometric for classifying a proportion in a small population, the Poisson for classifying a count or a rate, ... and so on). (B) Cluster LQAS : This can refer to LQAS with a cluster sample in which the whole sample is classified. It can also refer to making classification at the cluster level. If the latter method is used with a spatial sample then a map can be made. (C) Modified LQAS : This is a catch-all for something that is done a bit different. The SLEAC coverage method (e.g.) uses a "modified" (and simplified) LQAS method to give three or more classes and uses simple rules-of-thumb for calculating decision rules. Truncated LQAS uses a complicated decision rule to allow three classes and considerable savings in sample sizes at low and high prevalences. It should be noted that, in public health, we tend to lump all forms of sequential sampling under the term LQAS. Sometimes we see a "modified LQAS" which might be described as (e.g.) "SPRT sequential classification" when used in ecology or crop-protection. WRT your question about sampling procedures: (A) Would use simple random or systematic samples. Some clinical audit applications use consecutive samples (e.g. the next patient and the next patient). (B) The first variant might use PPS and proximity sampling (as SMART does). The second variant might use a stratified spatial sample (e.g. CSAS, S3M) and a random sample or a map-segment-sample approach with the PSU. (C) SLEAC (and SQUEAC in some circumstances) use an active and adaptive / snowball / respondent driven sample. Truncated sequential sampling for HIV and TB drug resistance have used consecutive sampling. I hope this helps.

Dear Mark, Thank you very much for the detail feedback. I was wondering if you clarify further on the following issues; 1. Sample size – is the sample size calculation the same for classical LQAS and Cluster/modified LQAS? the classical or conventional LQAS applies pure simple random sampling whereas the cluster/modified LQAS introduced parts of cluster sampling. According the typical LQAS guide, the recommended sample size is 95. The size per super supervision area differ according to the number defined areas (normal is 5x19). However, the WHO cluster LQAS field manual – (2012 vaccination coverage) recommends differently, sample of 60 children. The manual recommends the lot should be divided into ten areas of each six children. With regard to modified LQAS (almost similar to Cluster LQAS), I read an assessment conducted in USAID funded grants in Madagascar and Guatemala. What they did is modify of each supervision by clustering into seven of each three interviews, total of 21 per supervision areas. 2. Analysis – my question is analysis for cluster/modified LQAS. In typical LQAS, the analysis (coverage, decision rule) is done independently (by SA) and then can be aggregated to get overall. How about in cluster LQAS? As per the 30by30 cluster/SMART guides, it is not recommended to analyze by cluster level. If this is so, how can we know the coverage of each SA? Thanks

(1) Sequential sampling techniques have been shown to be robust to deviations from ideal sampling. In ecological and agricultural applications (e.g.) there is usually spatial and temporal clustering. For example, a fish farm might use traps to take samples in small batches. This robustness is one reason for their popularity (the other being simplicity of analysis). Cluster / modified LQAS may or may not use cluster sampling. The term "modified LQAS" is a catch-all term - it could mean almost anything. The term "cluster LQAS" may refer to a sample in which a sample sufficient to make a classification is taken from each primary sampling unit (PSU) or when a small sample is taken from each PSU which, when combined, is large enough to make a wide-area classification. In the first case we would use a map-segment-sample technique within each PSU to get close to a simple random sample. In the second case we would have a large number of small clusters so any effect of the sample design is likely to be small. I am not sure where n = 95 comes from. That is quite a large sample size for most LQAS applications. I have used sample sizes as large as n = 96 but most commonly I have used sample sizes on between n = 30 and n = 50. I think you need not take these guidelines as law. It is typical to make your own sampling plans depending on what levels of indicators are important and levels of error and what balance of errors you are willing to tolerate. In a current application of LQAS that I am working on for UNHCR (e.g.) we find that n = 60 (with a number of different decision rules) is good enough for all WASH indicators. (2) One approach would be to look at the indicator and decided on class boundaries and acceptable errors and work out the sampling plan (i.e. sample size and decision rule). If this is (e.g.) n = 30, d = 21 then I would plan to take n = 30 split among as many PSUs as was practicable / affordable from each SA and the classify each SA separately. I would then combine the sample as a stratified sample of SAs and make a wide-area estimate. This way I'd get a wide-area estimate and a map showing (e.g.) SAs with good and bad coverage. Perhaps you should let use know your application and we could work through the issues / processes. I hope this is of some use.

Dear Mark, Thanks. These different versions with different confusing terminology is creating problem for people working at the ground. I think there has to be a uniform system across the board. there is no way referring different manuals (FANTA, WHO, Core group, UNHCR etc) where each use different approach. I think we have to take lesson from SMART, CMAM, and SQUEAC where things are now harmonized. Thanks

There is a confusion of terms throughout the field not just with LQAS. For example, we think of SMART as using a "cluster sampling" approach. I picked three standards reference texts (not guidebooks) from my bookshelves and looked at the definition of "cluster sampling". I found: KIRKWOOD : PSUs are selected using a simple random sample and a census sample is taken within the PSU. This is similar to the approach taken with CSAS, SLEAC, and SQUEAC stage III surveys (a systematic rather than random first stage sample is used). MOSER & KALTON : As per KIRKWOOD. THOMPSON : As per KIRKWOOD and MOSER & KALTON but with a method similar to that used by SMART as a variant. The point that I am trying to make is that we only think of "cluster sampling" and "PPS" as simple and uncontroversial terms because we have (in emergency nutrition) a rather limited repertoire of methods. The type of sample we use in SMART is derived from the EPI coverage survey method. EPI has a "modified cluster sample". It uses PPS in the way that SMART does, has a fixed number of clusters (m = 30), has a fixed sample size (n = 210) which is collected as m = 30 quota samples of n = 7 from each cluster using a proximity sampling method). Methods such as SMART may be properly termed "two-stage cluster sampled surveys of modified EPI design". The KIRKWOOD definition (used in CSAS, SLEAC, and SQUEAC) is a PPS design but does not used the PPS mechanism or sample design that we are familiar with from EPI and SMART. Back to LQAS ... One source of confusion with LQAS comes from that final "S" (for "Sampling"). This makes us think that LQAS is about sampling when it is really an approach to data analysis (that can go hand-in-hand with sampling). We can use LQAS with (just about) any sample. It can get worse ... there are also (e.g.) BSS (binomial sequential sampling) and TSS (truncated sequential sampling) which are related to LQAS. These methods have the additional confusion of "sequential sampling" in their names which has led some users (even in the CDC and WHO) to advocate the use of these methods only with consecutive samples (i.e. a systematic sample with a sampling interval of one) when such a restriction about sampling does not apply. Here the confusion is between "sequential analysis" (analysing data as it is collected) and consecutive sampling. Another source of confusion is that LQAS is just one of a family of methods which might best be described as "sequential analysis" techniques. A few of these different methods are used for public health applications and given the name "LQAS" or get called "modified-LQAS". I suppose the latter is correct as LQAS was the earliest method. Id does not help that different field have different names for the same method or use the same name for different methods (this is not just a problem for LQAS). Yet another source of confusion arises from operationalising the methods. For example, some applications use "d" (the "acceptance number") but others use "r" (the "rejection number") in decision rules. I know this is probably no help but it may reconcile you to the confusion. There is also the consolation of religion. Here is something apposite from the Judeo-Christian creation myth (Genesis 11:1-9): 11:1 Now the whole world had one language and a common speech. 11:2 As people moved eastward, they found a plain in Shinar and settled there. 11:3 They said to each other, "Come, let’s make bricks and bake them thoroughly". They used brick instead of stone, and tar for mortar. 11:4 Then they said, "Come, let us build ourselves a city, with a tower that reaches to the heavens, so that we may make a name for ourselves; otherwise we will be scattered over the face of the whole earth". 11:5 But the Lord came down to see the city and the tower the people were building. 11:6 The Lord said, "If as one people speaking the same language they have begun to do this, then nothing they plan to do will be impossible for them". 11:7 "Come, let us go down and confuse their language so they will not understand each other". 11:8 So the Lord scattered them from there over all the earth, and they stopped building the city. 11:9 That is why it was called Babel - because there the Lord confused the language of the whole world. From there the Lord scattered them over the face of the whole earth. I think we can agree that if we could remove all this terminological confusion then nothing we plan would be impossible.

love it! thanks for making me smile, Mark.