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## Revista de Saúde Pública

*Print version* ISSN 0034-8910

### Rev. Saúde Pública vol.45 n.3 São Paulo Jun. 2011

#### http://dx.doi.org/10.1590/S0034-89102011000300021

**ORIGINAL
ARTICLES**

**The
role of plausibility in the evaluation of scientific research**

**El papel de
la plausibilidad en la evaluación de la investigación científica**

**Renan M V R
Almeida**

Programa de Engenharia Biomédica. Coppe. Universidade Federal do Rio de Janeiro. Rio de Janeiro, RJ, Brasil

**ABSTRACT**

The paper discusses
the impact of plausibility (the *a priori* probability) on the results
of scientific research, according to the approach proposed by Ioannidis, concerning
the percentage of null hypotheses erroneously classified as "positive" (statistically
significant). The question "what fraction of positive results are true-positives?",
which is equivalent to the positive predictive value, is dependent on the combination
of true and false hypotheses within a given area. For example, consider an area
in which 90% of hypotheses are false and α
= 0.05 and power = 0.8: for every 1,000 hypotheses, 45 (900 x 0.05) are false-positives
and 80 (100 x 0.8) are true-positives. Therefore, the probability of a positive
result being a false-positive is 45/125. In addition, the reporting of negative
results as if they were positive would contribute towards an increase in this
fraction. Although this analysis is difficult to quantify, and these results
are likely be overestimated, it has two implications: i) plausibility should
be considered in the analysis of the ethical adequacy of a research proposal,
and ii) mechanisms aimed at registering studies and protocols should be encouraged.

**Descriptors:**
Hypothesis-Testing. Reproducibility of Results. Statistical Methods and Procedures.

**RESUMEN**

El artículo
discute el impacto de la plausibilidad (probabilidad *a priori*) en el
resultado de investigaciones científicas, conforme abordaje de Ioannidis,
relacionado con el porcentaje de hipótesis nulas erróneamente
clasificadas como "positivas" (estadísticamente significativas). La interrogante
"cuál fracción de resultados positivos es verdaderamente positiva?",
equivalente al valor predictivo positivo, depende de la combinación de
hipótesis falsas y positivas en determinada área. Por ejemplo,
sea el 90% de las hipótesis falsas y α=
0,05, poder= 0,8: para cada 1000 hipótesis, 45 (900 x 0,05) serán
falsos positivos, y 80 (100 x 0,8) verdaderos positivos. Así, la probabilidad
de que un resultado sea un falso positivo es de 45/125. Adicionalmente, el relato
de estudios negativos como si fueran positivos contribuiría a la inflación
de esos valores. A pesar de que el análisis sea de difícil cuantificación
y probablemente super-estimado, el mismo tiene dos implicaciones: i) la plausibilidad
debe ser considerada en el análisis de la conformidad ética de
una investigación y ii) mecanismos de registro de estudio y protocolo
deben ser estimulados.

**Descriptores:**
Pruebas de Hipótesis. Reproducibilidad de Resultados. Métodos
y Procedimientos Estadísticos.

**INTRODUCTION**

In the contemporary
statistical methodology,^{11} which is widely in use across all fields
of science, the "null hypothesis" (H_{0}) represents the inexistence
of a given effect (therefore its name). H_{0} is either "rejected" or
"not rejected" based on an appropriate test statistic (for example, Student's
*t* for assessing the difference between two means). Thereafter, the analysis
strategy consists of calculating a probability - known as the p-value - associated
with this statistic. In cases in which this value is lower than a threshold
defined *a priori* (α),
the effect is considered to exist, or to be "statistically significant." Two
types of error are intrinsic to this procedure, and are known as Type I (rejecting
H_{0} when it is true) and Type II (not rejecting H_{0} when
it is false). These errors occur with probabilities "α"
and "β,"
respectively. In general, α
is set arbitrarily to 5%, and experimental designs often aim at a level of up
to 20% for β
(that is, 80% probability of correctly rejecting H_{0} when it is false,
or the test's "power").

Among other things,
a shortcoming of the traditional approach is that it does not consider the effect
of plausibility when evaluating a hypothesis. Especially among statisticians
of non-classical persuasion, there is the idea that a p-value may overestimate
the evidence against a hypothesis, since the effect of plausibility is not evident
in classical analyses (that is, p = 0.001 is considered as evidence for rejecting
both a plausible and an implausible hypothesis).^{3,4}

Thus, the present
article discusses the impact of initial plausibility in the results of scientific
research, based on the approach of Ioannidis.^{6-9} This approach relates
to the percentage of null hypothesis H_{0} erroneously classified as
"positive results" (statistically significant) in different fields of science.
According to this, the question "what proportion of positive results is truly
positive?" essentially depends on the proportion of true and false hypotheses
tested within a given field of knowledge - or the *a priori* plausibility.
This analysis is important for our understanding of the limitations inherent
to scientific research, especially with respect to the *priors* (initial
probabilities) of a given study.

**THE IOANNIDIS
APPROACH**

In a recent series
of articles, Ioannidis analyzed the role of replication and initial plausibility
on the results of scientific research.^{6-9} His central argument was
presented in an article with the provocative title "Why most published research
findings are false,"^{6} in which the author states that "it can be
proven that most claimed research findings in most areas of research are false."
This article has been cited hundreds of times in the scientific literature.

Ioannidis systematized
observations initially made by others, such as Browner & Newman^{1}
and Sterne & Smith.^{15} Thus, the concepts of Type I and Type II
errors were presented in a conceptually equivalent manner, such that the probability
of a Type I error was defined as a the percentage of all H_{0} hypotheses
in a given field of research that are erroneously classified as statistically
significant; and Type II error was defined as the percentage of false H_{0}
erroneously classified as non-statistically significant. Given a positive finding
(that is, a rejected H_{0}), the probability that H_{0} is indeed
false is conditional upon the initial fraction of truly true and truly false
hypotheses tested. This statement - which is analogous to the concept of positive
predictive value, widely used in diagnostic testing^{1,2} - can be understood
by considering the following examples: i) all hypotheses tested in a given area
are in actuality false. In this case, 100% of positive results would be false.
ii) 100% of hypotheses tested are true. Analogously, all positive results would
be true. And iii) in a field in which 90% of tested hypotheses are false (and
maintaining the conventional values of α
= 0.05 and power = 0.8), for every 1,000 hypotheses, 45 will be false-positives
(900 x 0.05), and 80 will be true-positives (100 x 0.8). Thus, given a positive
result, the probability of it being a false positive is of roughly one-third
(45/125) (Figure).

Between the extremes
represented by cases i and ii, the relationship R = *true H _{0}*/

*false H*alters the equivalent to the positive predictive value for a given field of knowledge (given a positive result, the larger R is, the greater the probability of a true-positive). In other words, the lower a study's plausibility is, the greater the probability of a positive result being false. This phenomenon, according to Ioannidis, would help explain why even high-impact scientific publications often publish contradictory and non-replicable results.

_{0}^{6}

Ioannidis also
introduced the concept of "*u* bias," defined as the probability of a negative
result being erroneously reported as positive by selective use of secondary
outcomes, alteration of cutoff points, use of inappropriate statistical methods,
or fraud. Based on these concepts, a simulation of R and u for different types
of study led to the conclusion that "in the described framework, a positive
predictive value exceeding 50% is quite difficult to get"^{6} (p. 699),
and that "even well powered epidemiological studies may have only a one in five
chance of being true, if R =1:10"^{6} (p. 699). This justifies Ioannidis'
claims regarding the prevalence of non-replicable results in science.

**ANALYSIS AND
EVALUATION**

Ioannidis' analysis
is contingent on two fundamental aspects: i) that the number of false hypotheses
in any field is much greater than that of true hypotheses; and ii) that the
u rate is indeed high (Ioannidis assumed values ranging from 10% to 80%). The
former may be justified by the innovative nature of the scientific endeavor,
as well as by the constant pressure for results, even in sterile or slow-moving
fields, but is difficult to extrapolate to the majority of scientific fields.
On the other hand, in the absence of so-called "file drawer effect,"^{13,14}
the influence of the phenomenon discussed by Ioannidis is smaller, given that,
if the pattern of R were known, the assessment of the true importance of a positive
result would in principle be possible. However, as discussed above, the only
way to determine R would be if all negative and positive results in a field
were known (for example, if 100 hypotheses concerning a given phenomenon were
tested and 95 were determined to be negative, global results would be compatible
with a model that assumed the inexistence of this phenomenon). As to the u parameter,
Goodman & Greenland^{5,}ª pointed out that:
i) the definition of u is misleading, since it equates the selective reporting
of secondary outcomes with direct fraud; and ii) the values for u assumed by
Ioannidis (10%-80%) are speculative and dominated the simulation, that is, his
conclusions are dependent on a high prevalence of "fraud." It follows that Ioannidis'
assumptions are difficult to quantify, and that it is impossible to claim that
their effect applies to a substantial fraction of scientific results.

According to the
authors, Ioannidis' analysis failed to distinguish between different levels
of evidence (in terms of p-value) against H_{0}.^{5,8} Ioannidis
dichotomized of results as either "statistically significant" or "non-statistically
significant" based on the classically used α
cutoff of 0.05. However, in practice, such dichotomization of results is unusual,
the indication of specific p-values being generally preferred.

Irrespectively
of the criticisms made by Goodman & Greenland^{5,}ª
(who in fact agree with the central points of Ioannidis' analysis), the effect
discussed is highly dependent on the specific characteristics of each field
of research. Ioannidis suggests two fields as being critical: genomic research
and the search for associations between nutrients and epidemiological outcomes,
in which hypotheses are often tested using a heuristic approach and effects
are small and difficult to measure. Another important example^{b}
is that of the field known as Complementary and Alternative Medicine (CAM),
given that it is not difficult to conclude, despite a number of attempts,^{10}
that the only common, core principle among the countless trends that fall under
the CAM denomination is the clear implausibility of their claims. This argument
can be added to other points made in the literature (such as the lack of impact
of negative results on this field, the inadequate legitimacy conferred to implausible
ideas, and the inappropriate allocation of limited resources) to conclude that
is conducting CAM studies in human subjects is unjustifiable.^{12}

On the other hand, absence of an effect is impossible to prove, for there is always the possibility of the effect being below the threshold of detection. Furthermore, the amount of resources for research is infinitely smaller than what would be necessary to analyze all phenomena that can theoretically be proposed. Therefore, at least in the realm of human research, phenomena should only be investigated when they are both relevant and plausible.

**FINAL CONSIDERATIONS**

Problems inherent to the methods of contemporary science facilitate the improper publication of results that are apparently positive. These problems are related to the plausibility of studies in a given field, but are also linked to the so-called "file drawer effect." As discussed above, quantifying these effects is difficult, since they are also dependent on the particular conditions of a given research field.

However, two implications
are worth highlighting: the first relates to the importance of the operational
principle recognized by the Helsinki declaration, which in its 11^{th}
article states that "medical research involving human subjects must conform
to generally accepted scientific principles, be based on a thorough knowledge
of the scientific literature, other relevant sources of information, and adequate
laboratory and, as appropriate, animal experimentation."^{16} Lack of
plausibility should thus be regarded as an important violation of research ethics.
The second implication refers to the need to develop mechanisms for registering
study protocols,^{13} so as to minimize and facilitate the detection
of both the file drawer effect and of protocol alterations. Such registration
mechanisms would also help to identify duplicate studies and to expedite meta-analysis,
thus contributing to greater transparency and efficiency in scientific research.

**REFERENCES**

1. Browner W, Newman TB. Are all significant p values created equal? The analogy between diagnostic tests and clinical research. *JAMA.* 1987;257(18):2459-63. [ Links ]

2. Dawson B, Trapp RG. Basic & Clinical Biostatistics. New York: McGraw-Hill; 2004. [ Links ]

3. Goodman SN. Toward evidence-based medical statistics. 1: The P value fallacy. *Ann Intern Med.* 1999;130(12):995-1004. [ Links ]

4. Goodman SN. Toward evidence-based medical statistics. 2: The Bayes factor. *Ann Intern Med.* 1999;130(12):1005-13. [ Links ]

5. Goodman S, Greenland S. Why most published research findings are false: problems in the analysis. *PLoS Med.* 2007;4(4):e168. DOI:10.1371/journal.pmed.0040168 [ Links ]

6. Ioannidis JPA. Why most published research findings are false *PLoS Med.* 2005;2(8):e124. DOI:10.1371/journal.pmed.0020124 [ Links ]

7. Ioannidis JPA. Contradicted and initially stronger effects in highly cited clinical research *JAMA.* 2005;294(2):218-28. [ Links ]

8. Ioannidis JPA. Why most published research findings are false: author's reply to Goodman and Greenland. *PLoS Med.* 2007;4(6):e215. DOI:10.1371/journal.pmed.0040215 [ Links ]

9. Ioannidis JPA. Why most discovered true associations are inflated. *Epidemiology*. 2008;16(4) 640-8. DOI:10.1097/EDE.0b013e31818131e7 [ Links ]

10. Manzini T, Martinez EZ, Carvalho ACD. Conhecimento, crença e uso de medicina alternativa e complementar por fonoaudiólogas. *Rev Bras Epidemiol.* 2008;11(2):304-14. DOI:10.1590/S1415-790X2008000200012 [ Links ]

11. Moore DS. Estatística Básica e sua Prática. Rio de Janeiro: LTC Editora; 2005. [ Links ]

12. Renkens CNM. Some complementary and alternative therapies are too implausible to be investigated. *Focus Alternat Complement Ther.* 2003;8(3):307-8. Disponível em: [ Links ]

13. Yamey G. Scientists who do not publish trial results are "unethical". *BMJ*. 1999; 319(7215):939. [ Links ]

14. Young NS, Ioannidis JPA, Al-Ubaydli O. Why current publication practices may distort science. *PLoS Med.* 2008;5(10):e201. DOI:10.1371/journal.pmed.0050201 [ Links ]

15. Sterne JAC, Smith GD. Sifting the evidence: what is wrong with significance tests? *BMJ.* 2001;322:226-31. [ Links ]

16. World Medical Association. Declaration of Helsinki - Ethical Principles for Medical Research Involving Human Subjects - 2008 version. Ferney-Voltaire; 2008[citado 2010 jul]. Disponível em: http://www.wma.net/en/30publications/10policies/b3/index.html [ Links ]

** Correspondence:
** Renan MVR Almeida

Programa de Engenharia Biomédica

Universidade Federal do Rio de Janeiro

Caixa Postal 68510

Cidade Universitária

21945-970 Rio de Janeiro, RJ, Brasil

E-mail: renan.m.v.r.almeida@gmail.com

Received: 7/14/2010

Accepted: 11/14/2010

Study presented
at the 8th Congresso Brasileiro de Bioética, held in Buzios, Brazil,
en 2009.

The author declares no conflict of interests.

a Goodman S, Greenland S. Assessing the unreliability of
the medical literature: a response to "Why most published research findings
are false". Baltimore: Johns Hopkins University; 2007[citado 2010 jul].
(Working paper, 135). Disponível em: http://www.bepress.com/jhubiostat/paper135

b Novella S. Are most medical studies
wrong? *Neurologica Blog.* 2007[citado 2010 jul]. Disponível
em: http://theness.com/neurologicablog/?p=8