Biostatistics

Last updated

Biostatistics (also known as biometry) is a branch of statistics that applies statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results.

Contents

History

Biostatistics and genetics

Biostatistical modeling forms an important part of numerous modern biological theories. Genetics studies, since its beginning, used statistical concepts to understand observed experimental results. Some genetics scientists even contributed with statistical advances with the development of methods and tools. Gregor Mendel started the genetics studies investigating genetics segregation patterns in families of peas and used statistics to explain the collected data. In the early 1900s, after the rediscovery of Mendel's Mendelian inheritance work, there were gaps in understanding between genetics and evolutionary Darwinism. Francis Galton tried to expand Mendel's discoveries with human data and proposed a different model with fractions of the heredity coming from each ancestral composing an infinite series. He called this the theory of "Law of Ancestral Heredity". His ideas were strongly disagreed by William Bateson, who followed Mendel's conclusions, that genetic inheritance were exclusively from the parents, half from each of them. This led to a vigorous debate between the biometricians, who supported Galton's ideas, as Raphael Weldon, Arthur Dukinfield Darbishire and Karl Pearson, and Mendelians, who supported Bateson's (and Mendel's) ideas, such as Charles Davenport and Wilhelm Johannsen. Later, biometricians could not reproduce Galton conclusions in different experiments, and Mendel's ideas prevailed. By the 1930s, models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian modern evolutionary synthesis.

Solving these differences also allowed to define the concept of population genetics and brought together genetics and evolution. The three leading figures in the establishment of population genetics and this synthesis all relied on statistics and developed its use in biology.

These and other biostatisticians, mathematical biologists, and statistically inclined geneticists helped bring together evolutionary biology and genetics into a consistent, coherent whole that could begin to be quantitatively modeled.

In parallel to this overall development, the pioneering work of D'Arcy Thompson in On Growth and Form also helped to add quantitative discipline to biological study.

Despite the fundamental importance and frequent necessity of statistical reasoning, there may nonetheless have been a tendency among biologists to distrust or deprecate results which are not qualitatively apparent. One anecdote describes Thomas Hunt Morgan banning the Friden calculator from his department at Caltech, saying "Well, I am like a guy who is prospecting for gold along the banks of the Sacramento River in 1849. With a little intelligence, I can reach down and pick up big nuggets of gold. And as long as I can do that, I'm not going to let any people in my department waste scarce resources in placer mining." [3]

Research planning

Any research in life sciences is proposed to answer a scientific question we might have. To answer this question with a high certainty, we need accurate results. The correct definition of the main hypothesis and the research plan will reduce errors while taking a decision in understanding a phenomenon. The research plan might include the research question, the hypothesis to be tested, the experimental design, data collection methods, data analysis perspectives and costs involved. It is essential to carry the study based on the three basic principles of experimental statistics: randomization, replication, and local control.

Research question

The research question will define the objective of a study. The research will be headed by the question, so it needs to be concise, at the same time it is focused on interesting and novel topics that may improve science and knowledge and that field. To define the way to ask the scientific question, an exhaustive literature review might be necessary. So the research can be useful to add value to the scientific community. [4]

Hypothesis definition

Once the aim of the study is defined, the possible answers to the research question can be proposed, transforming this question into a hypothesis. The main propose is called null hypothesis (H0) and is usually based on a permanent knowledge about the topic or an obvious occurrence of the phenomena, sustained by a deep literature review. We can say it is the standard expected answer for the data under the situation in test. In general, HO assumes no association between treatments. On the other hand, the alternative hypothesis is the denial of HO. It assumes some degree of association between the treatment and the outcome. Although, the hypothesis is sustained by question research and its expected and unexpected answers. [4]

As an example, consider groups of similar animals (mice, for example) under two different diet systems. The research question would be: what is the best diet? In this case, H0 would be that there is no difference between the two diets in mice metabolism (H0: μ1 = μ2) and the alternative hypothesis would be that the diets have different effects over animals metabolism (H1: μ1 ≠ μ2).

The hypothesis is defined by the researcher, according to his/her interests in answering the main question. Besides that, the alternative hypothesis can be more than one hypothesis. It can assume not only differences across observed parameters, but their degree of differences (i.e. higher or shorter).

Sampling

Usually, a study aims to understand an effect of a phenomenon over a population. In biology, a population is defined as all the individuals of a given species, in a specific area at a given time. In biostatistics, this concept is extended to a variety of collections possible of study. Although, in biostatistics, a population is not only the individuals, but the total of one specific component of their organisms, as the whole genome, or all the sperm cells, for animals, or the total leaf area, for a plant, for example.

It is not possible to take the measures from all the elements of a population. Because of that, the sampling process is very important for statistical inference. Sampling is defined as to randomly get a representative part of the entire population, to make posterior inferences about the population. So, the sample might catch the most variability across a population. [5] The sample size is determined by several things, since the scope of the research to the resources available. In clinical research, the trial type, as inferiority, equivalence, and superiority is a key in determining sample size. [4]

Experimental design

Experimental designs sustain those basic principles of experimental statistics. There are three basic experimental designs to randomly allocate treatments in all plots of the experiment. They are completely randomized design, randomized block design, and factorial designs. Treatments can be arranged in many ways inside the experiment. In agriculture, the correct experimental design is the root of a good study and the arrangement of treatments within the study is essential because environment largely affects the plots (plants, livestock, microorganisms). These main arrangements can be found in the literature under the names of "lattices", "incomplete blocks", "split plot", "augmented blocks", and many others. All of the designs might include control plots, determined by the researcher, to provide an error estimation during inference.

In clinical studies, the samples are usually smaller than in other biological studies, and in most cases, the environment effect can be controlled or measured. It is common to use randomized controlled clinical trials, where results are usually compared with observational study designs such as case–control or cohort. [6]

Data collection

Data collection methods must be considered in research planning, because it highly influences the sample size and experimental design.

Data collection varies according to type of data. For qualitative data, collection can be done with structured questionnaires or by observation, considering presence or intensity of disease, using score criterion to categorize levels of occurrence. [7] For quantitative data, collection is done by measuring numerical information using instruments.

In agriculture and biology studies, yield data and its components can be obtained by metric measures. However, pest and disease injuries in plats are obtained by observation, considering score scales for levels of damage. Especially, in genetic studies, modern methods for data collection in field and laboratory should be considered, as high-throughput platforms for phenotyping and genotyping. These tools allow bigger experiments, while turn possible evaluate many plots in lower time than a human-based only method for data collection. Finally, all data collected of interest must be stored in an organized data frame for further analysis.

Analysis and data interpretation

Descriptive tools

Data can be represented through tables or graphical representation, such as line charts, bar charts, histograms, scatter plot. Also, measures of central tendency and variability can be very useful to describe an overview of the data. Follow some examples:

Frequency tables

One type of table is the frequency table, which consists of data arranged in rows and columns, where the frequency is the number of occurrences or repetitions of data. Frequency can be: [8]

Absolute: represents the number of times that a determined value appear;

Relative: obtained by the division of the absolute frequency by the total number;

In the next example, we have the number of genes in ten operons of the same organism.

Genes = {2,3,3,4,5,3,3,3,3,4}
Genes numberAbsolute frequencyRelative frequency
100
210.1
360.6
420.2
510.1

Line graph

Figure A: Line graph example. The birth rate in Brazil (2010-2016); Figure B: Bar chart example. The birth rate in Brazil for the December months from 2010 to 2016; Figure C: Example of Box Plot: number of glycines in the proteome of eight different organisms (A-H); Figure D: Example of a scatter plot. Examples of descriptive tools.png
Figure A: Line graph example. The birth rate in Brazil (2010–2016); Figure B: Bar chart example. The birth rate in Brazil for the December months from 2010 to 2016; Figure C: Example of Box Plot: number of glycines in the proteome of eight different organisms (A-H); Figure D: Example of a scatter plot.

Line graphs represent the variation of a value over another metric, such as time. In general, values are represented in the vertical axis, while the time variation is represented in the horizontal axis. [10]

Bar chart

A bar chart is a graph that shows categorical data as bars presenting heights (vertical bar) or widths (horizontal bar) proportional to represent values. Bar charts provide an image that could also be represented in a tabular format. [10]

In the bar chart example, we have the birth rate in Brazil for the December months from 2010 to 2016. [9] The sharp fall in December 2016 reflects the outbreak of Zika virus in the birth rate in Brazil.

Histograms

Example of a histogram. Example histogram.png
Example of a histogram.

The histogram (or frequency distribution) is a graphical representation of a dataset tabulated and divided into uniform or non-uniform classes. It was first introduced by Karl Pearson. [11]

Scatter plot

A scatter plot is a mathematical diagram that uses Cartesian coordinates to display values of a dataset. A scatter plot shows the data as a set of points, each one presenting the value of one variable determining the position on the horizontal axis and another variable on the vertical axis. [12] They are also called scatter graph, scatter chart, scattergram, or scatter diagram. [13]

Mean

The arithmetic mean is the sum of a collection of values () divided by the number of items of this collection ().

Median

The median is the value in the middle of a dataset.

Mode

The mode is the value of a set of data that appears most often. [14]

Comparison among mean, median and mode
Values = { 2,3,3,3,3,3,4,4,11 }
TypeExampleResult
Mean ( 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 11 ) / 94
Median 2, 3, 3, 3, 3, 3, 4, 4, 113
Mode2, 3, 3, 3, 3, 3, 4, 4, 113

Box plot

Box plot is a method for graphically depicting groups of numerical data. The maximum and minimum values are represented by the lines, and the interquartile range (IQR) represent 25–75% of the data. Outliers may be plotted as circles.

Correlation coefficients

Although correlations between two different kinds of data could be inferred by graphs, such as scatter plot, it is necessary validate this though numerical information. For this reason, correlation coefficients are required. They provide a numerical value that reflects the strength of an association. [10]

Pearson correlation coefficient

Scatter diagram that demonstrates the Pearson correlation for different values of r. Correlation coefficient.png
Scatter diagram that demonstrates the Pearson correlation for different values of ρ.

Pearson correlation coefficient is a measure of association between two variables, X and Y. This coefficient, usually represented by ρ (rho) for the population and r for the sample, assumes values between −1 and 1, where ρ = 1 represents a perfect positive correlation, ρ = −1 represents a perfect negative correlation, and ρ = 0 is no linear correlation. [10]

Inferential statistics

It is used to make inferences [15] about an unknown population, by estimation and/or hypothesis testing. In other words, it is desirable to obtain parameters to describe the population of interest, but since the data is limited, it is necessary to make use of a representative sample in order to estimate them. With that, it is possible to test previously defined hypotheses and apply the conclusions to the entire population. The standard error of the mean is a measure of variability that is crucial to do inferences. [5]

Hypothesis testing is essential to make inferences about populations aiming to answer research questions, as settled in "Research planning" section. Authors defined four steps to be set: [5]

  1. The hypothesis to be tested: as stated earlier, we have to work with the definition of a null hypothesis (H0), that is going to be tested, and an alternative hypothesis. But they must be defined before the experiment implementation.
  2. Significance level and decision rule: A decision rule depends on the level of significance, or in other words, the acceptable error rate (α). It is easier to think that we define a critical value that determines the statistical significance when a test statistic is compared with it. So, α also has to be predefined before the experiment.
  3. Experiment and statistical analysis: This is when the experiment is really implemented following the appropriate experimental design, data is collected and the more suitable statistical tests are evaluated.
  4. Inference: Is made when the null hypothesis is rejected or not rejected, based on the evidence that the comparison of p-values and α brings. It is pointed that the failure to reject H0 just means that there is not enough evidence to support its rejection, but not that this hypothesis is true.

A confidence interval is a range of values that can contain the true real parameter value in given a certain level of confidence. The first step is to estimate the best-unbiased estimate of the population parameter. The upper value of the interval is obtained by the sum of this estimate with the multiplication between the standard error of the mean and the confidence level. The calculation of lower value is similar, but instead of a sum, a subtraction must be applied. [5]

Statistical considerations

Power and statistical error

When testing a hypothesis, there are two types of statistic errors possible: Type I error and Type II error. The type I error or false positive is the incorrect rejection of a true null hypothesis and the type II error or false negative is the failure to reject a false null hypothesis. The significance level denoted by α is the type I error rate and should be chosen before performing the test. The type II error rate is denoted by β and statistical power of the test is 1 − β.

p-value

The p-value is the probability of obtaining results as extreme as or more extreme than those observed, assuming the null hypothesis (H0) is true. It is also called the calculated probability. It is common to confuse the p-value with the significance level (α), but, the α is a predefined threshold for calling significant results. If p is less than α, the null hypothesis (H0) is rejected. [16]

Multiple testing

In multiple tests of the same hypothesis, the probability of the occurrence of falses positives (familywise error rate) increase and some strategy are used to control this occurrence. This is commonly achieved by using a more stringent threshold to reject null hypotheses. The Bonferroni correction defines an acceptable global significance level, denoted by α* and each test is individually compared with a value of α = α*/m. This ensures that the familywise error rate in all m tests, is less than or equal to α*. When m is large, the Bonferroni correction may be overly conservative. An alternative to the Bonferroni correction is to control the false discovery rate (FDR). The FDR controls the expected proportion of the rejected null hypotheses (the so-called discoveries) that are false (incorrect rejections). This procedure ensures that, for independent tests, the false discovery rate is at most q*. Thus, the FDR is less conservative than the Bonferroni correction and have more power, at the cost of more false positives. [17]

Mis-specification and robustness checks

The main hypothesis being tested (e.g., no association between treatments and outcomes) is often accompanied by other technical assumptions (e.g., about the form of the probability distribution of the outcomes) that are also part of the null hypothesis. When the technical assumptions are violated in practice, then the null may be frequently rejected even if the main hypothesis is true. Such rejections are said to be due to model mis-specification. [18] Verifying whether the outcome of a statistical test does not change when the technical assumptions are slightly altered (so-called robustness checks) is the main way of combating mis-specification.

Model selection criteria

Model criteria selection will select or model that more approximate true model. The Akaike's Information Criterion (AIC) and The Bayesian Information Criterion (BIC) are examples of asymptotically efficient criteria.

Developments and big data

Recent developments have made a large impact on biostatistics. Two important changes have been the ability to collect data on a high-throughput scale, and the ability to perform much more complex analysis using computational techniques. This comes from the development in areas as sequencing technologies, Bioinformatics and Machine learning (Machine learning in bioinformatics).

Use in high-throughput data

New biomedical technologies like microarrays, next-generation sequencers (for genomics) and mass spectrometry (for proteomics) generate enormous amounts of data, allowing many tests to be performed simultaneously. [19] Careful analysis with biostatistical methods is required to separate the signal from the noise. For example, a microarray could be used to measure many thousands of genes simultaneously, determining which of them have different expression in diseased cells compared to normal cells. However, only a fraction of genes will be differentially expressed. [20]

Multicollinearity often occurs in high-throughput biostatistical settings. Due to high intercorrelation between the predictors (such as gene expression levels), the information of one predictor might be contained in another one. It could be that only 5% of the predictors are responsible for 90% of the variability of the response. In such a case, one could apply the biostatistical technique of dimension reduction (for example via principal component analysis). Classical statistical techniques like linear or logistic regression and linear discriminant analysis do not work well for high dimensional data (i.e. when the number of observations n is smaller than the number of features or predictors p: n < p). As a matter of fact, one can get quite high R2-values despite very low predictive power of the statistical model. These classical statistical techniques (esp. least squares linear regression) were developed for low dimensional data (i.e. where the number of observations n is much larger than the number of predictors p: n >> p). In cases of high dimensionality, one should always consider an independent validation test set and the corresponding residual sum of squares (RSS) and R2 of the validation test set, not those of the training set.

Often, it is useful to pool information from multiple predictors together. For example, Gene Set Enrichment Analysis (GSEA) considers the perturbation of whole (functionally related) gene sets rather than of single genes. [21] These gene sets might be known biochemical pathways or otherwise functionally related genes. The advantage of this approach is that it is more robust: It is more likely that a single gene is found to be falsely perturbed than it is that a whole pathway is falsely perturbed. Furthermore, one can integrate the accumulated knowledge about biochemical pathways (like the JAK-STAT signaling pathway) using this approach.

Bioinformatics advances in databases, data mining, and biological interpretation

The development of biological databases enables storage and management of biological data with the possibility of ensuring access for users around the world. They are useful for researchers depositing data, retrieve information and files (raw or processed) originated from other experiments or indexing scientific articles, as PubMed. Another possibility is search for the desired term (a gene, a protein, a disease, an organism, and so on) and check all results related to this search. There are databases dedicated to SNPs (dbSNP), the knowledge on genes characterization and their pathways (KEGG) and the description of gene function classifying it by cellular component, molecular function and biological process (Gene Ontology). [22] In addition to databases that contain specific molecular information, there are others that are ample in the sense that they store information about an organism or group of organisms. As an example of a database directed towards just one organism, but that contains much data about it, is the Arabidopsis thaliana genetic and molecular database – TAIR. [23] Phytozome, [24] in turn, stores the assemblies and annotation files of dozen of plant genomes, also containing visualization and analysis tools. Moreover, there is an interconnection between some databases in the information exchange/sharing and a major initiative was the International Nucleotide Sequence Database Collaboration (INSDC) [25] which relates data from DDBJ, [26] EMBL-EBI, [27] and NCBI. [28]

Nowadays, increase in size and complexity of molecular datasets leads to use of powerful statistical methods provided by computer science algorithms which are developed by machine learning area. Therefore, data mining and machine learning allow detection of patterns in data with a complex structure, as biological ones, by using methods of supervised and unsupervised learning, regression, detection of clusters and association rule mining, among others. [22] To indicate some of them, self-organizing maps and k-means are examples of cluster algorithms; neural networks implementation and support vector machines models are examples of common machine learning algorithms.

Collaborative work among molecular biologists, bioinformaticians, statisticians and computer scientists is important to perform an experiment correctly, going from planning, passing through data generation and analysis, and ending with biological interpretation of the results. [22]

Use of computationally intensive methods

On the other hand, the advent of modern computer technology and relatively cheap computing resources have enabled computer-intensive biostatistical methods like bootstrapping and re-sampling methods.

In recent times, random forests have gained popularity as a method for performing statistical classification. Random forest techniques generate a panel of decision trees. Decision trees have the advantage that you can draw them and interpret them (even with a basic understanding of mathematics and statistics). Random Forests have thus been used for clinical decision support systems.[ citation needed ]

Applications

Public health

Public health, including epidemiology, health services research, nutrition, environmental health and health care policy & management. In these medicine contents, it's important to consider the design and analysis of the clinical trials. As one example, there is the assessment of severity state of a patient with a prognosis of an outcome of a disease.

With new technologies and genetics knowledge, biostatistics are now also used for Systems medicine, which consists in a more personalized medicine. For this, is made an integration of data from different sources, including conventional patient data, clinico-pathological parameters, molecular and genetic data as well as data generated by additional new-omics technologies. [29]

Quantitative genetics

The study of population genetics and statistical genetics in order to link variation in genotype with a variation in phenotype. In other words, it is desirable to discover the genetic basis of a measurable trait, a quantitative trait, that is under polygenic control. A genome region that is responsible for a continuous trait is called a quantitative trait locus (QTL). The study of QTLs become feasible by using molecular markers and measuring traits in populations, but their mapping needs the obtaining of a population from an experimental crossing, like an F2 or recombinant inbred strains/lines (RILs). To scan for QTLs regions in a genome, a gene map based on linkage have to be built. Some of the best-known QTL mapping algorithms are Interval Mapping, Composite Interval Mapping, and Multiple Interval Mapping. [30]

However, QTL mapping resolution is impaired by the amount of recombination assayed, a problem for species in which it is difficult to obtain large offspring. Furthermore, allele diversity is restricted to individuals originated from contrasting parents, which limit studies of allele diversity when we have a panel of individuals representing a natural population. [31] For this reason, the genome-wide association study was proposed in order to identify QTLs based on linkage disequilibrium, that is the non-random association between traits and molecular markers. It was leveraged by the development of high-throughput SNP genotyping. [32]

In animal and plant breeding, the use of markers in selection aiming for breeding, mainly the molecular ones, collaborated to the development of marker-assisted selection. While QTL mapping is limited due resolution, GWAS does not have enough power when rare variants of small effect that are also influenced by environment. So, the concept of Genomic Selection (GS) arises in order to use all molecular markers in the selection and allow the prediction of the performance of candidates in this selection. The proposal is to genotype and phenotype a training population, develop a model that can obtain the genomic estimated breeding values (GEBVs) of individuals belonging to a genotype and but not phenotype population, called testing population. [33] This kind of study could also include a validation population, thinking in the concept of cross-validation, in which the real phenotype results measured in this population are compared with the phenotype results based on the prediction, what used to check the accuracy of the model.

As a summary, some points about the application of quantitative genetics are:

Expression data

Studies for differential expression of genes from RNA-Seq data, as for RT-qPCR and microarrays, demands comparison of conditions. The goal is to identify genes which have a significant change in abundance between different conditions. Then, experiments are designed appropriately, with replicates for each condition/treatment, randomization and blocking, when necessary. In RNA-Seq, the quantification of expression uses the information of mapped reads that are summarized in some genetic unit, as exons that are part of a gene sequence. As microarray results can be approximated by a normal distribution, RNA-Seq counts data are better explained by other distributions. The first used distribution was the Poisson one, but it underestimate the sample error, leading to false positives. Currently, biological variation is considered by methods that estimate a dispersion parameter of a negative binomial distribution. Generalized linear models are used to perform the tests for statistical significance and as the number of genes is high, multiple tests correction have to be considered. [34] Some examples of other analysis on genomics data comes from microarray or proteomics experiments. [35] [36] Often concerning diseases or disease stages. [37]

Other studies

Tools

There are a lot of tools that can be used to do statistical analysis in biological data. Most of them are useful in other areas of knowledge, covering a large number of applications (alphabetical). Here are brief descriptions of some of them:

Scope and training programs

Almost all educational programmes in biostatistics are at postgraduate level. They are most often found in schools of public health, affiliated with schools of medicine, forestry, or agriculture, or as a focus of application in departments of statistics.

In the United States, where several universities have dedicated biostatistics departments, many other top-tier universities integrate biostatistics faculty into statistics or other departments, such as epidemiology. Thus, departments carrying the name "biostatistics" may exist under quite different structures. For instance, relatively new biostatistics departments have been founded with a focus on bioinformatics and computational biology, whereas older departments, typically affiliated with schools of public health, will have more traditional lines of research involving epidemiological studies and clinical trials as well as bioinformatics. In larger universities around the world, where both a statistics and a biostatistics department exist, the degree of integration between the two departments may range from the bare minimum to very close collaboration. In general, the difference between a statistics program and a biostatistics program is twofold: (i) statistics departments will often host theoretical/methodological research which are less common in biostatistics programs and (ii) statistics departments have lines of research that may include biomedical applications but also other areas such as industry (quality control), business and economics and biological areas other than medicine.

Specialized journals

See also

Related Research Articles

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.

<span class="mw-page-title-main">Kolmogorov–Smirnov test</span> Non-parametric statistical test between two distributions

In statistics, the Kolmogorov–Smirnov test is a nonparametric test of the equality of continuous, one-dimensional probability distributions that can be used to test whether a sample came from a given reference probability distribution, or to test whether two samples came from the same distribution. Intuitively, the test provides a method to qualitatively answer the question "How likely is it that we would see a collection of samples like this if they were drawn from that probability distribution?" or, in the second case, "How likely is it that we would see two sets of samples like this if they were drawn from the same probability distribution?". It is named after Andrey Kolmogorov and Nikolai Smirnov.

<span class="mw-page-title-main">Statistics</span> Study of the collection, analysis, interpretation, and presentation of data

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

<span class="mw-page-title-main">Statistical hypothesis test</span> Method of statistical inference

A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently support a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a p-value computed from the test statistic. Roughly 100 specialized statistical tests have been defined.

In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value of a result, , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when . The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study.

In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis when a specific alternative hypothesis is true. It is commonly denoted by , and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability of making a type II error by wrongly failing to reject the null hypothesis decreases.

In null-hypothesis significance testing, the -value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Even though reporting p-values of statistical tests is common practice in academic publications of many quantitative fields, misinterpretation and misuse of p-values is widespread and has been a major topic in mathematics and metascience. In 2016, the American Statistical Association (ASA) made a formal statement that "p-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone" and that "a p-value, or statistical significance, does not measure the size of an effect or the importance of a result" or "evidence regarding a model or hypothesis." That said, a 2019 task force by ASA has issued a statement on statistical significance and replicability, concluding with: "p-values and significance tests, when properly applied and interpreted, increase the rigor of the conclusions drawn from data."

In statistical hypothesis testing, the alternative hypothesis is one of the proposed proposition in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test. It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc. However, the research hypothesis is sometimes consistent with the null hypothesis.

Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complex studies, different sample sizes may be allocated, such as in stratified surveys or experimental designs with multiple treatment groups. In a census, data is sought for an entire population, hence the intended sample size is equal to the population. In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group.

A permutation test is an exact statistical hypothesis test making use of the proof by contradiction. A permutation test involves two or more samples. The null hypothesis is that all samples come from the same distribution . Under the null hypothesis, the distribution of the test statistic is obtained by calculating all possible values of the test statistic under possible rearrangements of the observed data. Permutation tests are, therefore, a form of resampling.

Exact (significance) test is a test such that if the null hypothesis is true, then all assumptions made during the derivation of the distribution of the test statistic are met. Using an exact test provides a significance test that maintains the type I error rate of the test at the desired significance level of the test. For example, an exact test at a significance level of , when repeated over many samples where the null hypothesis is true, will reject at most of the time. This is in contrast to an approximate test in which the desired type I error rate is only approximately maintained, while this approximation may be made as close to as desired by making the sample size sufficiently large.

In statistics, the false discovery rate (FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling procedures are designed to control the FDR, which is the expected proportion of "discoveries" that are false. Equivalently, the FDR is the expected ratio of the number of false positive classifications to the total number of positive classifications. The total number of rejections of the null include both the number of false positives (FP) and true positives (TP). Simply put, FDR = FP /. FDR-controlling procedures provide less stringent control of Type I errors compared to family-wise error rate (FWER) controlling procedures, which control the probability of at least one Type I error. Thus, FDR-controlling procedures have greater power, at the cost of increased numbers of Type I errors.

In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. For example, an innocent person may be convicted. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false. For example: a guilty person may be not convicted.

Omnibus tests are a kind of statistical test. They test whether the explained variance in a set of data is significantly greater than the unexplained variance, overall. One example is the F-test in the analysis of variance. There can be legitimate significant effects within a model even if the omnibus test is not significant. For instance, in a model with two independent variables, if only one variable exerts a significant effect on the dependent variable and the other does not, then the omnibus test may be non-significant. This fact does not affect the conclusions that may be drawn from the one significant variable. In order to test effects within an omnibus test, researchers often use contrasts.

<span class="mw-page-title-main">Multiple comparisons problem</span> Statistical interpretation with many tests

In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or estimates a subset of parameters selected based on the observed values.

Medical statistics deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research. Medical statistics has been a recognized branch of statistics in the United Kingdom for more than 40 years, but the term has not come into general use in North America, where the wider term 'biostatistics' is more commonly used. However, "biostatistics" more commonly connotes all applications of statistics to biology. Medical statistics is a subdiscipline of statistics.

It is the science of summarizing, collecting, presenting and interpreting data in medical practice, and using them to estimate the magnitude of associations and test hypotheses. It has a central role in medical investigations. It not only provides a way of organizing information on a wider and more formal basis than relying on the exchange of anecdotes and personal experience, but also takes into account the intrinsic variation inherent in most biological processes.

The Newman–Keuls or Student–Newman–Keuls (SNK)method is a stepwise multiple comparisons procedure used to identify sample means that are significantly different from each other. It was named after Student (1927), D. Newman, and M. Keuls. This procedure is often used as a post-hoc test whenever a significant difference between three or more sample means has been revealed by an analysis of variance (ANOVA). The Newman–Keuls method is similar to Tukey's range test as both procedures use studentized range statistics. Unlike Tukey's range test, the Newman–Keuls method uses different critical values for different pairs of mean comparisons. Thus, the procedure is more likely to reveal significant differences between group means and to commit type I errors by incorrectly rejecting a null hypothesis when it is true. In other words, the Neuman-Keuls procedure is more powerful but less conservative than Tukey's range test.

Energy distance is a statistical distance between probability distributions. If X and Y are independent random vectors in Rd with cumulative distribution functions (cdf) F and G respectively, then the energy distance between the distributions F and G is defined to be the square root of

The McDonald–Kreitman test is a statistical test often used by evolutionary and population biologists to detect and measure the amount of adaptive evolution within a species by determining whether adaptive evolution has occurred, and the proportion of substitutions that resulted from positive selection. To do this, the McDonald–Kreitman test compares the amount of variation within a species (polymorphism) to the divergence between species (substitutions) at two types of sites, neutral and nonneutral. A substitution refers to a nucleotide that is fixed within one species, but a different nucleotide is fixed within a second species at the same base pair of homologous DNA sequences. A site is nonneutral if it is either advantageous or deleterious. The two types of sites can be either synonymous or nonsynonymous within a protein-coding region. In a protein-coding sequence of DNA, a site is synonymous if a point mutation at that site would not change the amino acid, also known as a silent mutation. Because the mutation did not result in a change in the amino acid that was originally coded for by the protein-coding sequence, the phenotype, or the observable trait, of the organism is generally unchanged by the silent mutation. A site in a protein-coding sequence of DNA is nonsynonymous if a point mutation at that site results in a change in the amino acid, resulting in a change in the organism's phenotype. Typically, silent mutations in protein-coding regions are used as the "control" in the McDonald–Kreitman test.

Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning, and meta-analysis to plan experiments, analyze data and interpret results. It complements hypothesis testing approaches such as null hypothesis significance testing (NHST), by going beyond the question is an effect present or not, and provides information about how large an effect is. Estimation statistics is sometimes referred to as the new statistics.

References

  1. Centre for Transformative Innovation, Swinburne University of Technology. "Allan, Frances Elizabeth (Betty) - Person - Encyclopedia of Australian Science and Innovation". www.eoas.info. Retrieved 2022-10-26.
  2. Gunter, Chris (10 December 2008). "Quantitative Genetics". Nature. 456 (7223): 719. Bibcode:2008Natur.456..719G. doi: 10.1038/456719a . PMID   19079046.
  3. Charles T. Munger (2003-10-03). "Academic Economics: Strengths and Faults After Considering Interdisciplinary Needs" (PDF). Archived (PDF) from the original on 2022-10-09.
  4. 1 2 3 Nizamuddin, Sarah L.; Nizamuddin, Junaid; Mueller, Ariel; Ramakrishna, Harish; Shahul, Sajid S. (October 2017). "Developing a Hypothesis and Statistical Planning". Journal of Cardiothoracic and Vascular Anesthesia. 31 (5): 1878–1882. doi:10.1053/j.jvca.2017.04.020. PMID   28778775.
  5. 1 2 3 4 Overholser, Brian R; Sowinski, Kevin M (2017). "Biostatistics Primer: Part I". Nutrition in Clinical Practice. 22 (6): 629–35. doi:10.1177/0115426507022006629. PMID   18042950.
  6. Szczech, Lynda Anne; Coladonato, Joseph A.; Owen, William F. (4 October 2002). "Key Concepts in Biostatistics: Using Statistics to Answer the Question "Is There a Difference?"". Seminars in Dialysis. 15 (5): 347–351. doi:10.1046/j.1525-139X.2002.00085.x. PMID   12358639. S2CID   30875225.
  7. Sandelowski, Margarete (2000). "Combining Qualitative and Quantitative Sampling, Data Collection, and Analysis Techniques in Mixed-Method Studies". Research in Nursing & Health. 23 (3): 246–255. CiteSeerX   10.1.1.472.7825 . doi:10.1002/1098-240X(200006)23:3<246::AID-NUR9>3.0.CO;2-H. PMID   10871540. S2CID   10733556.
  8. Maths, Sangaku. "Absolute, relative, cumulative frequency and statistical tables – Probability and Statistics". www.sangakoo.com. Retrieved 2018-04-10.
  9. 1 2 "DATASUS: TabNet Win32 3.0: Nascidos vivos – Brasil". DATASUS: Tecnologia da Informação a Serviço do SUS.
  10. 1 2 3 4 Forthofer, Ronald N.; Lee, Eun Sul (1995). Introduction to Biostatistics. A Guide to Design, Analysis, and Discovery. Academic Press. ISBN   978-0-12-262270-0.
  11. Pearson, Karl (1895-01-01). "X. Contributions to the mathematical theory of evolution.—II. Skew variation in homogeneous material". Phil. Trans. R. Soc. Lond. A. 186: 343–414. Bibcode:1895RSPTA.186..343P. doi: 10.1098/rsta.1895.0010 . ISSN   0264-3820.
  12. Utts, Jessica M. (2005). Seeing through statistics (3rd ed.). Belmont, CA: Thomson, Brooks/Cole. ISBN   978-0534394028. OCLC   56568530.
  13. Jarrell, Stephen B. (1994). Basic statistics. Dubuque, Iowa: Wm. C. Brown Pub. ISBN   978-0697215956. OCLC   30301196.
  14. Gujarati, Damodar N. (2006). Econometrics. McGraw-Hill Irwin.
  15. Watson, Lyndsey (2009). "Essentials of Biostatistics in Public Health & Essentials of Biostatistics Workbook: Statistical Computing Using Excel". Australian and New Zealand Journal of Public Health. 33 (2): 196–197. doi: 10.1111/j.1753-6405.2009.00372.x . ISSN   1326-0200.
  16. Baker, Monya (2016). "Statisticians issue warning over misuse of P values". Nature. 531 (7593): 151. Bibcode:2016Natur.531..151B. doi: 10.1038/nature.2016.19503 . PMID   26961635.
  17. Benjamini, Y. & Hochberg, Y. Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society. Series B (Methodological) 57, 289–300 (1995).
  18. "Null hypothesis". www.statlect.com. Retrieved 2018-05-08.
  19. Hayden, Erika Check (8 February 2012). "Biostatistics: Revealing analysis". Nature. 482 (7384): 263–265. doi: 10.1038/nj7384-263a . PMID   22329008.
  20. Efron, Bradley (February 2008). "Microarrays, Empirical Bayes and the Two-Groups Model". Statistical Science. 23 (1): 1–22. arXiv: 0808.0572 . doi:10.1214/07-STS236. S2CID   8417479.
  21. Subramanian, A.; Tamayo, P.; Mootha, V. K.; Mukherjee, S.; Ebert, B. L.; Gillette, M. A.; Paulovich, A.; Pomeroy, S. L.; Golub, T. R.; Lander, E. S.; Mesirov, J. P. (30 September 2005). "Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles". Proceedings of the National Academy of Sciences. 102 (43): 15545–15550. Bibcode:2005PNAS..10215545S. doi: 10.1073/pnas.0506580102 . PMC   1239896 . PMID   16199517.
  22. 1 2 3 4 5 Moore, Jason H (2007). "Bioinformatics". Journal of Cellular Physiology. 213 (2): 365–9. doi: 10.1002/jcp.21218 . PMID   17654500. S2CID   221831488.
  23. "TAIR - Home Page". www.arabidopsis.org.
  24. "Phytozome". phytozome.jgi.doe.gov.
  25. "International Nucleotide Sequence Database Collaboration - INSDC". www.insdc.org.
  26. "Top". www.ddbj.nig.ac.jp. 11 January 2024.
  27. "The European Bioinformatics Institute < EMBL-EBI". www.ebi.ac.uk.
  28. "National Center for Biotechnology Information". www.ncbi.nlm.nih.gov. U. S. National Library of Medicine –.
  29. Apweiler, Rolf; et al. (2018). "Whither systems medicine?". Experimental & Molecular Medicine. 50 (3): e453. doi:10.1038/emm.2017.290. PMC   5898894 . PMID   29497170.
  30. Zeng, Zhao-Bang (2005). "QTL mapping and the genetic basis of adaptation: Recent developments". Genetica. 123 (1–2): 25–37. doi:10.1007/s10709-004-2705-0. PMID   15881678. S2CID   1094152.
  31. Korte, Arthur; Farlow, Ashley (2013). "The advantages and limitations of trait analysis with GWAS: A review". Plant Methods. 9: 29. doi: 10.1186/1746-4811-9-29 . PMC   3750305 . PMID   23876160.
  32. Zhu, Chengsong; Gore, Michael; Buckler, Edward S; Yu, Jianming (2008). "Status and Prospects of Association Mapping in Plants". The Plant Genome. 1: 5–20. doi: 10.3835/plantgenome2008.02.0089 .
  33. Crossa, José; Pérez-Rodríguez, Paulino; Cuevas, Jaime; Montesinos-López, Osval; Jarquín, Diego; De Los Campos, Gustavo; Burgueño, Juan; González-Camacho, Juan M; Pérez-Elizalde, Sergio; Beyene, Yoseph; Dreisigacker, Susanne; Singh, Ravi; Zhang, Xuecai; Gowda, Manje; Roorkiwal, Manish; Rutkoski, Jessica; Varshney, Rajeev K (2017). "Genomic Selection in Plant Breeding: Methods, Models, and Perspectives" (PDF). Trends in Plant Science. 22 (11): 961–975. doi:10.1016/j.tplants.2017.08.011. PMID   28965742. Archived (PDF) from the original on 2022-10-09.
  34. Oshlack, Alicia; Robinson, Mark D; Young, Matthew D (2010). "From RNA-seq reads to differential expression results". Genome Biology. 11 (12): 220. doi: 10.1186/gb-2010-11-12-220 . PMC   3046478 . PMID   21176179.
  35. Helen Causton; John Quackenbush; Alvis Brazma (2003). Statistical Analysis of Gene Expression Microarray Data. Wiley-Blackwell.
  36. Terry Speed (2003). Microarray Gene Expression Data Analysis: A Beginner's Guide. Chapman & Hall/CRC.
  37. Frank Emmert-Streib; Matthias Dehmer (2010). Medical Biostatistics for Complex Diseases. Wiley-Blackwell. ISBN   978-3-527-32585-6.
  38. Warren J. Ewens; Gregory R. Grant (2004). Statistical Methods in Bioinformatics: An Introduction. Springer.
  39. Matthias Dehmer; Frank Emmert-Streib; Armin Graber; Armindo Salvador (2011). Applied Statistics for Network Biology: Methods in Systems Biology. Wiley-Blackwell. ISBN   978-3-527-32750-8.
  40. 1 2 "Home - VSN International". www.vsni.co.uk.
  41. "CycDesigN - VSN International". www.vsni.co.uk.
  42. Piepho, Hans-Peter; Williams, Emlyn R; Michel, Volker (2015). "Beyond Latin Squares: A Brief Tour of Row-Column Designs". Agronomy Journal. 107 (6): 2263. doi:10.2134/agronj15.0144.
  43. "The Comprehensive R Archive Network". cran.r-project.org.
  44. Renganathan V (2021). Biostatistics explored through R software: An overview. Vinaitheerthan Renganathan. ISBN   9789354936586.
  45. Stegmann, Dr Ralf (2019-07-01). "PLA 3.0". PLA 3.0 – Software for Biostatistical Analysis. Retrieved 2019-07-02.
  46. "Biostatistics - Oxford Academic". OUP Academic.
  47. "The International Journal of Biostatistics".
  48. "PubMed Journals will be shut down". 15 June 2018.
  49. https://ebph.it/ Epidemiology
  50. "Biometrics". onlinelibrary.wiley.com. doi:10.1111/(ISSN)1541-0420.
  51. "Biometrika - Oxford Academic". OUP Academic.
  52. "Biometrical Journal". onlinelibrary.wiley.com. doi:10.1002/(ISSN)1521-4036.
  53. "Communications in Biometry and Crop Science". agrobiol.sggw.waw.pl.
  54. "Statistical Applications in Genetics and Molecular Biology". www.degruyter.com. 1 May 2002.
  55. "Statistical Methods in Medical Research". SAGE Journals.
  56. "Pharmaceutical Statistics". onlinelibrary.wiley.com.
  57. "Statistics in Medicine". onlinelibrary.wiley.com. doi:10.1002/(ISSN)1097-0258.

Commons-logo.svg Media related to Biostatistics at Wikimedia Commons