Recommended sample size for rapid nutrition assessments/surveys including 0-59 m and for PLW

Dear Montse:

The simple answer is "It depends".  It depends on what assumptions you make about the population to be assessed.  The minimum sample size needed to make an estimate of prevalence depends on: a) the assumed prevalence of the condition, b) the precision needed for the final estimate of prevalence, c) the type of sampling done, d) the heterogeneity of distribution of the condition for which you are calculating sample size, and e) whether you are calculating sample size for a single survey or to compare 2 or more surveys. I will assume that you are calculating sample size for a single survey only.  

The formula for calculation of sample size in order to achieve a minimum precision for a single survey is:

n = DEFF * 3.84 * (p * (1-p)) / d squared. 

3.84 is the Z value for 1.96 which assumes that you will be calculating 95% confidence intervals (or using p<0.05 as the threshold for statistical significance).  p is the assumed prevalence and d is the 1/2 confidence interval you want for your final estimate of prevalence (for example, if you want a confidence interval of +/- 3 percentage points, d = 0.03).  DEFF is the design effect which reflects the loss of precision from doing cluster sampling instead of simple random sampling; it depends on the average cluster size and the inherent heterogeneity of distribution of the condition.  

So you can see that there is no universal "minimum sample size".  If we assume that the design effect for a cluster survey will be 1.5 (a reasonable assumption for many nutrition outcomes), the sample needed to achieve a precision of +/- 5 percentage points is 578 for a condition with a prevalence of 50% (perhaps stunting) and only 209 for a condition with a prevalence of 10% (perhaps wasting). Other outcomes which may be measured in nutrition assessment surveys, such as health care coverage or water source, have much higher design effects (as high as 4 or 5), so estimating the prevalence of these outcomes requires a much larger sample size given a given desired precision. If your survey will measure more than one important condition, you should calculate the sample size for each condition, then include the largest number in order to ensure adequate precision for all conditions measured.   

This is an entirely inadequate summary of a somewhat complicated topic. If you do not have training and/or experience in calculating sample size, I urge you to seek assistance from someone who does. It would be shame to carry out a survey, and then find that the results are uninterpretable because of inadequate precision. 

Dear Montse:

The formula for sample size to estimate a proportion or prevalence is the same regardless of the unit of analysis.  It applies to children 0-59 months of age, pregnant and lactating women, households, widgets being sampled from a factory's production line, or any other unit of analysis. 

Regarding the Rapid SMART Guide, I would still recommend that you calculate your own sample size. Cookbook guides for carrying out surveys are fraught with potential problems, and many of them, including the Rapid SMART Guide, contain incorrect information and recommendations. Moreover, each population to be surveyed is different, and cookbook guides do not the allow flexibility necessary to adapt your methodology to specific situations. Understanding the epidemiologic and statistical principles behind survey methodology makes it much more likely that any questions which arise during planning or execution are answered correctly.  

For future reference, you may be able to use this web-based course in emergency epidemiology to answer some questions about surveys in emergency-affected populations: http://conflict.lshtm.ac.uk/index.htm.  

I hope this is helpful, and I wish you luck in your work.