ACMS 20340 Statistics for Life Sciences Chapter 8: Designing Experiments
Fisher’s Experiments
Experiment Terminology individuals (if human) subjects → explanatory variable factors → In conducting an experiment, we try to keep as many variables constant while only changing the designated factor variables. A treatment is a specific combination of factors applied to the subjects. The experiment compares the response to a given treatment to other treatments, no treatment, or a fake treatment.
Experiments versus Observational Studies Experiments are in many ways preferable to observational studies. ◮ With an experiment we can study the specific treatments we are interested in. ◮ With an experiment we can study the combined effects of many factors simultaneously.
Corn and chicks: an example How do two specific varieties of genetically modified corn and various protein-level diets affect the growth of newborn chicks? The factors are ◮ corn type: Opaque-2, Floury-2, Normal Corn ◮ protein level: 12%, 16%, 20% There are 9 different treatment groups between the two factors.
Control is important In medical experiments, there are usually at least two groups considered. One group serves as a baseline against which we compare the treatment we are interested in. This is called the control group. We would rather the subjects didn’t know which group they belong to, so a placebo is usually used. A placebo is a treatment given to the control group which is fake but otherwise indistinguishable from the treatment given to the experimental group. The placebo effect occurs when subjects feel the treatment worked just from the psychological impact of having a treatment.
Placebo A-Go-Go
Principles of Experimental Design Here are some basic principles of experimental design. ◮ Use a control group to keep lurking variables at bay. ◮ Randomize as much as possible to head off selection bias. ◮ Use enough subjects to reduce the effect any one subject has on the results. The goal is to see a difference between the experimental groups large enough to not be a chance variation. By using enough subjects and assigning enough to each group, the average response observed in each group becomes more likely to be representative the population with that treatment. An observed effect which is large enough to occur only rarely by chance is called statistically significant . How do we know what counts as chance variation? We use probability (chapter 9).
Types of experimental design These basic principles for experimental design describe randomized comparative experiments . A randomized comparative experiment uses both the comparison of two or more treatments and chance assignment of subjects to treatments. Three sub-categories of randomized comparative experiments which we will discuss are: ◮ Completely randomized design ◮ Matched pairs design ◮ Block design
Completely randomized design Each subject in a completely randomized design is assigned one of any of the possible groups at random. ◮ We always determine in advance how large each group should be. The chicks experiment is an example of a completely randomized design.
Gastric freezing: an example
Matched Pairs Design I Completely randomized designs are useful, but they don’t always give the most precise results. Sometimes it helps to match the subjects in various ways. For instance, a matched pairs design combines matching with randomization. A matched pairs design compares only two treatments. We choose pairs of subjects that are as closely matched as possible. ◮ E.g., individuals of the same sex, age, weight, etc. ◮ E.g., genetically related individuals such as twins or animals born in the same litter.
Matched Pairs Design II We assign one treatment to one member of the pair, and the other treatment to the other. How do we decide which member gets which treatment? CHANCE! Why do we randomize the order of treatment? The order of the treatment might influence the response of the subjects, so we randomize to rule out a possible bias. The pairs in matched pairs designs need not always consist of two distinct individuals. We can consider the same subject twice, applying one treatment after the other (in a randomized order, of course).
Drugs: an example Generics are brand-name drugs manufactured by a different company but with identical active ingredients and properties. Individuals are given either Brand X or its generic version on a given day so that drug absorption can be measured. One week later, each individual receives the other drug to measure drug absorption. A difference in absorption extent between Brand X and its generic is then calculated for each individual.
Block design Closely related to a matched pairs design is a block design. Here’s an example:
Block design The idea is to test blocks of individuals. A block is simply a group of individuals that are known before the experiment to be similar in some way that is expected to affect the response to the treatments. In a block design, the random assignment of individuals to treatments is carried out separately within each block.
Soybeans: an example We would like to study the effects of two different types of tillage and three different types of pesticides on soybean yields.
Soybeans: an example To do so, we first divide the area we are testing into smaller blocks.
Soybeans: an example Next, we subdivide each of these blocks into six smaller plots.
Soybeans: an example Lastly, we randomly apply each of the six treatments to one of the six plots in each block.
Some Cautions According to the text, “The logic of a randomized comparative experiment depends on our ability to treat all the subjects identically in every way except for the actual treatments being compared.” We can do better: “In performing a randomized comparative experiment, we should do our best to ensure that the subjects are treated identically in every way except for the actual treatments being compared.”
How can we achieve this? One way to treat the subjects identically in every way except for the treatments we give to them is by means of a double-blind experiment . In a double-blind experiment, neither the subjects nor the people who administer the experiment know which treatment each subject is receiving. Why be this careful? We don’t want the way the experiment is administered to give rise to some bias. For instance, a patient’s perception of his or her prognosis can be influenced by how he or she interacts with a doctor. This might create or reinforce a placebo effect.
Double-blind experiment: an example A study was conducted to determine whether the herbal supplement ginkgo biloba can help alleviate tinnitus, a ringing noise in the ears that doesn’t have an effective pharmaceutical treatment.
Double-blind experiment: an example 978 healthy adults with tinnitus were matched by age and sex. Within each pair, one individual received the ginkgo biloba treatment, while the other was given a placebo. Moreover, the experiment was double-blind, as neither the subjects nor the investigators knew who was receiving the ginkgo biloba and who was receiving the placebo, as the tablets were indistinguishable.
Double-blind experiment: an example The tablets were distributed to the subjects in coded bottles, and the code was revealed only after the experiment had concluded and the data had been collected.
Other issues: Replication Convincing evidence usually requires more than just a well-designed experiment that takes into account a number of potential sources of bias. It requires that the study be successfully replicated by the investigators as well as investigators from different locations. The environment of an experiment might influence the outcome of that experiment.
Other issues: Realism “The most serious potential weakness of experiments”: lack of realism That is, the subjects or treatment or setting of an experiment may not realistically duplicate the situations we want to study. For example, saccharin causes bladder cancer in rats, but it turns out that this cancer is specific to the rat urinary system and is related to saccharin consumption at concentrations higher than what is realistic for human consumption.
Other issues: Ethics Should we consider as acceptable all experiments that are performed in the name of science, or for the sake of knowledge, or for the sake of the public’s greater good? Is it morally right to include a placebo in a study design when there are safe and efficient treatments already available? Should we continue an experiment if we find that one of the treatments shows early signs of adverse effects? And what if one of the treatments shows early signs of clear superiority? Is it ever acceptable to leave subjects in the dark about the purpose and expected results of an experiment? Nope!
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