# Estimating Coverage

This question was posted the Coverage assessment forum area and has 4 replies. You can also reply via email – be sure to leave the subject unchanged.

### Anonymous 1527

ITA

Normal user

23 Jul 2012, 09:16

Dear Advisors

We are currently finishing a SQUEAC assessment in a high SAM prevalence area. Because of a number of reasons, we decided not to do Stage 3, but rather end the SQUEAC assessment with the testing of our hypothesis. Nevertheless, the sample size we reached during the small area survey is quite large (>1000 cases) so we would like to estimate coverage for the area based solely on these results (and without a prior). The sample was collected from the 4 areas were we work (1 sub-section of each, chosen at random), so we are confident that it is representative. A few questions

1. Can we do this (use small area survey sample to estimate overall coverage if this is very large and spatially representative)?

2. Should we use the BayesCalculator for this? If so, we would need to change the numerator to more than 256 (c.1200). I checked on BrixtonHealth and it states that this can be achieved by changing the TCL. I dont know how this is done - any guidance?

### Ernest Guevarra

Valid International

Technical expert

24 Jul 2012, 10:15

Thanks for sharing your current coverage experience. I will try to provide some guidance and/or ideas that may help you arrive at an answer / solution to your questions. I just have 2 follow-up queries:

1) Usually, when we test our hypothesis through small area surveys, the sampling is purposive i.e. we select areas we believe to be high coverage or areas we believe to be low coverage and then find cases in those areas to see whether our hypotheses were correct. So, when you say you selected a sub-section randomly within the 4 areas you worked in, what hypothesis were you testing? Shouldn't you have known the areas you wanted to test beforehand already purposively?

2) By representativeness, what do you mean? Based on your description here, it seems that you had 4 working areas that are each divided in to sub-sections. Is that correct? You sampled in each of the 4 working areas by randomly selecting a sub-section in each? Is this correct?

Now, to try to answer your questions, I will assume that you were testing hypothesis you made for each of the 4 areas you are working by randomly selecting a sub-section in each of the areas and then doing exhaustive case finding in each sub-section. And by doing this, you found more than 1,000 SAM cases. Given this assumption, I will say that the sample you've gotten is not purposive and can be considered representative as you state.

So, for your question (1), I will say that you can do a coverage estimation given the sample size because this is a large sample size and will give you very good precision with your estimate.

For your question (2), I will say that you don't need BayesSQUEAC calculator for this because you just need to do simple arithmetic of dividing your total SAM cases IN the programme by the total SAM cases you have found. This will be your coverage estimate. To determine the 95% confidence intervals (please note this is confidence interval, not credible interval as with BayesSQUEAC), you just need to use the following simple formula for calculating this interval:

95% CI = p ± 1.96 x sqrt { ( p x (1 - p) ) / n }

where p = coverage proportion

n = sample size (total SAM cases found)

If the formula above is not clear the way it is presented here, click here to get a much better formatted presentation of the formula.

This means that you don't have to bother with changing the TCL of the BayesSQUEAC calculator.

What do the others think?

I hope this helps.

### Saul Guerrero

Director of Nutrition

Technical expert

24 Jul 2012, 10:30

Hi Ernest

Thanks for that answer - the team involved will appreciate it.

A point of clarification about the process: the project works in 4 "sectors" of a city. The hypothesis was about the coverage within the entire sector (i.e. 3 were high coverage sectors, 1 was low coverage sector). Each sector has about 4-5 sub-sectors; what the team did was to randomly select a sub-sector from each of the 4 sectors, and to do house-to-house case-finding there. I hope that clarifies how the process was carried out

Appreciate the support on the calculation of the CI

S

### Saul Guerrero

Director of Nutrition

Technical expert

24 Jul 2012, 10:30

Hi Ernest

Thanks for that answer - the team involved will appreciate it.

A point of clarification about the process: the project works in 4 "sectors" of a city. The hypothesis was about the coverage within the entire sector (i.e. 3 were high coverage sectors, 1 was low coverage sector). Each sector has about 4-5 sub-sectors; what the team did was to randomly select a sub-sector from each of the 4 sectors, and to do house-to-house case-finding there. I hope that clarifies how the process was carried out

Appreciate the support on the calculation of the CI

S

### Mark Myatt

Frequent user

24 Jul 2012, 18:51

I think you could just use the data you have.

Assuming that ...

n = number of cases c = number of covered cases

The coverage proportion

*p*can be estimated as:

p = c / n

with

*c*and

*n*calculated for point of period coverage as appropriate.

Given that you have such a large sample size, a 95% CI can be can be calculated as:

95% CI = p +/- 1.96 * sqrt((p * (1 - p) / n))

A worked example:

n = 600 c = 240 p = c / n = 240 / 600 = 0.4 95% CI = 0.4 +/- 1.96 * sqrt((0.4 * (1 - 0.4) / 600)) = 0.4 +/- 1.96 * sqrt((0.4 * 0.6) / 600) = 0.4 +/- 0.0392 = 0.3608; 0.4392

Multiply all by 100 to get percentages (in the worked example ... coverage = 40.0%, 95% CI = 36.1%; 43.9%).