Basic sampling problem

[schniefen]

TL;DR Summary

Two approaches in estimating the proportion of the population with a certain gene mutation.

The proportion of individuals that carry a certain gene mutation in the population is unknown. A research assistant at a medical laboratory wants to estimate this proportion. The research assistant is thinking of two approaches:

A. Take blood samples from all individuals that come to the hospitals ER ward during a month, and test their gene status.

B. Sample people, by reaching them by cell phone or land line phone, and ask them to participate and have their gene status tested.

Suppose in both cases A. and B., all individuals that are asked will agree to have their blood sample taken and gene tested. Can you think of features in approaches A. and B. that may not fit into our setup for estimation?

Since the information in the problem is quite general, it is hard to make any definite conclusion about each approach. For instance, if one would like to use an MLE, one would like the sample to be i.i.d., however, this could probably be accomplished in both approaches. Maybe in A. there may be some issue with independence, since imagine a diseases that causes gene mutation and easily spreads, then every person that gets tested on the day when a person with that disease was present in the ward will likely turn out to also have a gene mutation.

 

[Dale]

Summary:: Two approaches in estimating the proportion of the population with a certain gene mutation.

Can you think of features in approaches A. and B. that may not fit into our setup for estimation?

The main issue is that A will not be a random sample of the population.

 

[FactChecker]

Both of these are, at least partially, what are called "self-selecting samples". They have done something that makes them more likely to end up in your selected sample. This is only safe if their actions are independent of the property that you want to test for. If certain gene mutations tend to put more people in the ER, then your results are biased. Likewise, if the gene mutation tends to influence whether they have a phone, your results are biased. I can think of situations where that can occur in either case, so it is best for you to consider it. This is a very treacherous subject and it is easy to overlook dependencies that will bias your results.