Adaptive Sampling

Adaptive Sampling

Bharadwaj S_2048101 

Introduction:

Adaptive sampling is a sampling technique that is implemented while a survey is being fielded that is, the sampling design is modified in real time as data collection continues based on what has been learned from previous sampling that has been completed. Its purpose is to improve the selection of elements during the remainder of the sampling, thereby improving the representativeness of the data that the entire sample yields.

 Adaptive sampling (also called response-adaptive designs) is where you adapt your selection criteria as the experiment progresses, based on preliminary results as they come in.

Adaptive sampling is especially important in medical research, where traditional sampling and research techniques may lead to ethical dilemmas and clinical trials that are not in the best interest of the patients involved.

In contrast, in an adaptive clinical trial, patient outcomes can be used as they become available to adjust the assignment of future patients, assigning more of them to the better treatment. This allows one to improve expected patient outcomes during the experiment, while still being able to reach good statistical decisions in a timely fashion. Thus, adaptive procedures can offer significant ethical and cost advantages over standard fixed procedures. A situation in which adaptive procedures have become particularly relevant are AIDS clinical trials, since many new drugs come to market, yet classical randomized studies may pose ethical dilemmas and time delays. The are also quite important in pre-clinical animal trials, phase I trials, and phase I/II trials. While there had been some opposition to their use quite some time ago, now NIH, FDA, EPA, etc. are encouraging their use.

 Real Life Examples of Adaptive Sampling

 One example is of a research project searching for gold in riverbeds in California. With no starting information on where gold is likely to be found, the researchers might begin by sampling river dust in a series of randomly chosen river locations spread out evenly throughout California. However, if a minuscule amount of gold was found in a river running through a certain valley from a certain mountain range, it would make sense to change the sampling distribution and run a larger proportion of samples in that area. This is adaptive sampling at its simplest.

Another example might be a study testing a new AIDS drug. In this blind study, volunteers might be placed randomly in either of two groups: the control group (taking a placebo), or the treatment group. Once the medicine begins to look promising, new participants could be added to the treatment group. You could also choose to divide this group into two sets, taking two different doses of the medicine. If the medicine seemed unpromising, the majority of new participants could be added to the placebo group.

 Adaptive Sampling Methodology

In standard sampling methods, you choose your whole sample before you even look at the data. In adaptive sampling, on the other hand, you stop part way through sampling and analyze/observe what you’ve recorded so far. Call your initial sample s₁, the initial values y_s1.

Now, choose the rest of the sample based on the data you’ve gathered. To do this, we want to choose data points that will minimize the mean squared error of the estimate given what you’ve observed so far. We can write this mathematically as
min E [ (Ẑ -Z )² | s₁, y_s1 ].

Why Aren't Adaptive Procedures Always Used?

Unfortunately, adaptive procedures are more complicated to design and to analyze, and in some settings are more difficult to implement. Most people using formal experimental designs use fixed sampling procedures where they decide in advance how many samples of each alternative they are going to collect. These fixed procedures are easier to design and analyze, because they don't have as many alternatives, but they are less efficient, sometimes significantly so. In many cases, however, users are unaware of the option to use adaptive designs because standard statistical courses and packages do not include them. In medical problems, people may be wary of adaptive designs because of the confusion between a controlled clinical trial using an adaptive design versus allowing the physicians to decide each patient's treatment based on professional experience. The latter can introduce many biases into the learning process, especially because physicians tend to use the exploitation approach for each patient, as opposed to including some exploration.

R Code:

Example:

n=5(n is sampling size)

N=10(N is population size)

mi	1	4	1	5	2
yi	0	12	1	15	7

 

n <- 5(sample size)

N <- 100(population size)

m <- c(1,4,1,5,2)

y <- c(0,12,1,15,7)

adaptive.sample.confint.fun <- function(y,m,n,N) {

  mu.hat <- 1/n * sum(y/m)

  s.y.2 <- var(y/m)

  v.mu <- (1 - n/N) * s.y.2/n

  c("mu.hat" = mu.hat,

    "s.y.2" = s.y.2,

    "v.mu" = v.mu,

    "var" = 2 * sqrt(v.mu),

    "lower" = mu.hat - 2 * sqrt(v.mu),

    "upper" = mu.hat + 2 * sqrt(v.mu))

}

adaptive.sample.confint.fun(y,m,n,N)

Reference:

Hardwick & Stout (2017). Adaptive Sampling Designs. Retrieved November 4, 2017 from: 

http://web.eecs.umich.edu/~qstout/AdaptSample.html

https://www.statisticshowto.com/adaptive-sampling/

https://www.sciencedirect.com/science/article/pii/S0169716105800082