METHODS
The use of statistics in virology
When studying viral infections in hosts, scientists do not always obtain results that are so clear and obvious that everyone agrees with the conclusions. Often the effects are subtle, or the data are highly variable from sample to sample or from study to study (sometimes referred to as “noise”). This ambiguity is particularly true in epidemiological studies, given the large number of parameters and potential outcomes. How do you know if the data that you generated or are reading about in a paper are significant?
Statistical methods, properly employed, provide the common language of critical analysis to determine whether differences observed between or among groups are significant. Unfortunately, surveys of articles published in scientific journals indicate that statistical errors are common, making it even more difficult for the reader to interpret results. In fact, the term “significant difference” may be one of the most misused phrases in scientific papers, because the actual statistical support for the statement is often absent or incorrectly obtained. While a detailed presentation of basic statistical considerations is beyond the scope of this text, some guiding principles are offered.
It is essential to consider experimental de sign carefully before going to the bench or to the field. A fundamental challenge in study design is to predict correctly the number of observations required to obtain a reliable significant difference. The significance level is defined as the probability of mistakenly reporting that a difference is meaningful; by convention, this probability is minimally set at 0.05 (5%; see the table for hypothetical data). Scientists do not usually refer to experimental outcomes as “true” or “false” but rather use quantitative approaches to provide a sense of the significance between two data sets (e.g., experimental versus control). An important concept is statistical power, the probability of detecting a difference that truly is significant. In the simplest case, power can be increased by having a larger sample size (see table). Even when results seem black and white, having too few animals (or replicates) will be insufficient for drawing a statistically meaningful conclusion.
P values for the differences in infection rates between experimental and control groups a
| P value for indicated groupb | |||
|---|---|---|---|
| No. of animals per group | All control animals infected and no experimental animals infected | All control animals and one experimental animal infected or one control animal uninfected and no experimental animal infected | One control animal uninfected and one experimental animal infected |
| 3 | 0.1 | 0.4 | 1.0 |
| 4 | 0.03 | 0.1 | 0.5 |
| 5 | 0.008 | 0.05 | 0.2 |
| 6 | 0.002 | 0.02 | 0.08 |
| 7 | <0.001 | 0.005 | 0.03 |
| 8 | <0.001 | 0.001 | 0.01 |
aData from Richardson BA, Overbaugh J. 2005. J. Virol 79:669–676.
bDetermined by Fisher’s exact test, using a two-sided hypothesis test with the significance level fixed at 0.05.
Fisher’s exact test is used because it is appropriate for experiments with small numbers of observations.
It is essential to include a detailed description of how statistical analyses were per formed in all communications linked with the data. Benjamin Disraeli, a 19th-century British prime minister, once said, “There are three kinds of lies: lies, damned lies, and statistics.” Indeed, a gullible reader may be persuaded that a certain set of data is significant, but this conclusion depends on the stringency and appropriateness of the tests that were applied, as well as the data points included in the analysis.
While this text cannot define what tests are applicable for which assays, we can make a couple of strong suggestions. First, statistics should not be considered an afterthought or a painful process that one does after putting data together for a publication. Reliable studies that stand the test of time have considered statistics throughout the scientific process, and good statistics are essential for good study design. Second, be wary of reports in which an investigator inappropriately influences the statistical analyses to produce a “statistically significant” result. This process, sometimes referred to as “p-hacking,” can result in false positives or data that, while sufficiently different to qualify as “statistical,” in fact have no bearing on biological significance. Finally, while it is true that the field can be complex, most of the tests used by virologists are reasonably straightforward. Computer programs such as Excel and GraphPad have made the calculations easy, but you need to know which tests to apply. Fortunately, there are excellent books available that make statistics logical and accessible (e.g., Intuitive Biostatistics, by Harvey Motulsky). For more complex data, study design issues, and analyses, one may require consultation with a statistician.
Motulsky H. 2013. Intuitive Biostatistics: a Nonmathe matical Guide to Statistical Thinking, 3rd ed. Oxford University Press, Oxford, United Kingdom.
BACKGROUND
Descriptive epidemiology and the discovery of human immunodeficiency virus
Acquired immunodeficiency syndrome (AIDS) was first recognized as a new disease in the United States by physicians in New York, Los Angeles, and San Francisco, who independently noticed that some of the young homosexual male patients in their practices had developed unusual diseases, such as Pneumocystis carinii pneumonia and Kaposi’s sarcoma, which were typically associated with immunosuppressed patients. The first report in the medical literature that described this apparently new syndrome appeared in June 1981, and described five homosexual men in Los Angeles with P. carinii pneumonia. Other reports of a similar syndrome in individuals who injected drugs intravenously soon followed. While these “descriptive” observations raised many questions and incited much anxiety, they also laid the foundation for the subsequent, mechanistically focused work that identified the human immunodeficiency virus as a new human pathogen.
Centers for Disease Control (CDC). 1981. Pneumo cystis pneumonia—Los Angeles. MMWR Morb Mortal Wkly Rep 30:250–252.
METHODS
