Quantitative biology, biostatistics and mathematical modeling

Summary

To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of.

Sir Ronald A. Fisher, FRS

Many experiments fail because the data collectors have not been properly trained and many statisticians have their own horror stories to illustrate this.

John A. Nelder, FRS

Modeling is sometimes regarded as primarily a task for subject matter specialists, but in most fields requisite knowledge and understanding of statistics remains thinly spread.

Arthur P. Dempster

This chapter begins by defining reproducibility and discussing non-statistical – mainly psychological – sources of experimental bias. The next section assesses the quality of the published literature and discusses statistical sources of bias. The discussion will be familiar if you have been following the ‘reproducibility crisis’ over the past several years. The above topics are included to stimulate reflection about your own research practices and to bring together ideas that have been discussed in separate disciplines. The chapter ends with a refresher on statistical inference and a discussion on statistics software.

What is reproducibility?

An experiment is reproducible when subsequent experiments, by the same or different scientists, confirm the results. The terms repeatability and replicability are sometimes used interchangeably or with related meanings, but we will use reproducibility as an allencompassing term. Reproducibility can occur at several levels.

Analytical: Analytical or computational reproducibility refers to obtaining the same results using the original data and a description of the analysis. This is a minimum standard but is impossible to achieve when the data are unavailable. Even if the data are provided in the supplementary material or in public databases, reproducing the results may be hard if the description of the analysis is incomplete [173]. A minimum requirement for analytical reproducibility is to provide the data underlying the results and the scripts that produced them. This is simple when using R because the code can be integrated into documents such as reports and publications. For example, large portions of this book have embedded R code, which is evaluated, and then the outputs are inserted into the text document. The knitr and rmarkdown R packages make this process straightforward [402].

Summary

I believe sanity and realism can be restored to the teaching of Mathematical Statistics most easily and directly by entrusting such teaching largely to men and women who have had personal experience of research in the Natural Sciences.

Sir Ronald A. Fisher, FRS

Replication is a fundamental concept in both science and statistics and is used in the everyday sense of the term to mean ‘doing something more than once’. The ‘more than once’ part is straightforward, but it is often unclear what exactly needs to be done multiple times, especially when many parts of an experiment can be replicated. In the experimental sciences, there is always a treatment or intervention applied to an entity, which in our case will be a biological entity such as a person, animal, or cell. A basic requirement for replication is to have multiple independent entity–intervention pairs. Suppose that the intervention is a drug given orally to a patient. Each patient–drug pair is considered one replication and provides independent information about the effect of the drug. The effect is then compared with placebo–patient pairs. If the question is ‘what is the effect of the drug on patients’ then replicating the patient–drug pair and patient–placebo pair enables the question to be addressed.

Other aspects of this experiment could be replicated. For example, we could measure the outcome on each person more than once and replicate the measurement procedure. Or, we could give the drug to the same person multiple times and on each occasion record the outcome. Alternatively, we could even conduct the whole experiment multiple times, say once in England and once in America. Experimenters need to decide what to replicate and often the wrong part is chosen, wasting time and resources. In addition, one occasionally sees that the critical aspect of the experiment is not replicated at all, or only replicated a few times. In such cases it is either impossible to test the hypothesis of interest or the power is so low that the objectives of the experiment are unlikely to be met. A clever statistical analysis cannot fix the problem; it needs to be planned at the design stage.

Summary

Page references indicate where the entry is discussed in greater detail and words in bold indicate terms defined elsewhere in the glossary.

Aliased effects Occur when some main or interaction effects cannot be estimated because they are confounded. Aliasing is done on purpose to simplify the design of the experiment. [p. 91]

Alpha (α) See Critical value.

Alternative hypothesis (H1) Is the hypothesis that an association between variables is present or that an effect exists. It can be a general statement that the null hypothesis is not true, or it can be more specific and state the direction of the association or effect.

Analysis of covariance (ANCOVA) Is a statistical model with at least one categorical and one continuous predictor variable and a continuous outcome.

Analysis of variance (ANOVA) Is a statistical model with one or more categorical predictor variables and a continuous outcome.

Ancillary variable An outcome variable that is unrelated to the hypothesis or research question but is measured to provide more information about the subjects or the experimental system. Such variables are useful for quality control checks.

Argument Is an input into an R function. For example, if a function takes a number and returns the square root, the number is an argument to the square-root function.

Autocorrelation Is the ‘self-correlation’ of a vector across time or space.

Bias Is the difference between a measured or calculated value and the true value.

Biological effects Are variations that arise from intrinsic differences between biological samples or sample material. Examples include the sex or age of the subjects. [p. 52]

Biological unit Is the entity about which we would like to make an inference, test a hypothesis, estimate some property, or draw a conclusion in an experiment. This may or may not be the same as the experimental unit. [p. 95]

Blinding Occurs when either the experimenter, the subject, or both are unaware of the treatment conditions while the experiment is being conducted. Blinding can remove some sources of bias.

Summary

Everything of importance has been said before by somebody who did not discover it.

Alfred North Whitehead

Everything that needs to be said has already been said. But since no one was listening, everything must be said again.

André Gide

True to the above quotes, most of this book's contents have appeared in print before, but often where biologists are unlikely to look – statistics journals and books, and methods papers in other fields. My task is to translate ideas known to statisticians into the language of experimental biology. With a background in both biology (BSc, PhD, postdoc) and data analysis (MPhil in Computational Biology and over seven years working as a preclinical statistician in the pharmaceutical industry), hopefully I am fluent enough in both languages to perform a successful translation.

The contents of this book have little overlap with other statistics-for-biologists books because they mostly focus on statistical analysis. Analysis is but one step of the scientific workflow (Figure 0.1), and before you can analyse data you need to do an experiment. This requires planning, good execution, and quality control checks. These critical topics are rarely taught to biologists, who are expected to learn them on their own. The consequence of this approach is predictable; some biologists obtain the necessary skills, but many do not. This book focuses on the first three steps of the scientific workflow, and data analysis is briefly discussed in Chapter 4.

This book was written to improve the quality of research conducted in academic, government, and industrial labs and institutions. Scientists and funders now recognise that bias and irreproducibility are undermining preclinical biomedical research [2, 5, 28, 30, 42, 80, 83, 84, 123, 172, 240, 251, 305, 316, 342]. There are many reasons why experiments cannot be reproduced (discussed in Chapter 1) and this book focuses on the role that experimental design and data analysis have on making results reproducible.

This book is for experimental biologists, at any level, conducting basic research or with an applied, clinical, or translational focus. Knowledge covered in an introductory statisticsfor- biologists course is assumed, and concepts like the standard deviation and common statistical tests such as the t-test, analysis of variance (ANOVA), regression, and correlation should be familiar. It is fine if some time has passed since you formally covered these topics.

Summary

The development of the design of experiments is one of the greatest contributions of statistical science to science and technology. Yet, almost nobody knows anything about it!

John A. Nelder, FRS

… if all our engineers and scientists had some understanding of even the simplest principles of efficient experimental design a quantum leap could occur in the rate of development of our knowledge and of our ability to solve our problems.

George Box, FRS

This chapter introduces concepts and principles from the branch of statistics known as the design of experiments (DoE). A well-designed experiment has the following characteristics:

Summary

This chapter provides a basic introduction to R, focusing only on the features that are relevant for this book. Many topics are omitted and since there are many resources both online and in print, there is no need to duplicate them here. Quick-R is a great website that can be consulted in addition to this appendix to learn the basics.

Installing R

R is available for Windows, Mac, and Linux operating systems and can be downloaded from the Comprehensive R Archive Network (CRAN). For Windows and Mac users, download and install as you would any other program. For Linux users, packages are available for Debian, Redhat, SUSE, and Ubuntu. Ubuntu users can also install R from the synaptic package manager. Installation instructions are provided on the CRAN website. To run R, click the icon on the desktop or under a menu. Alternatively, R can be started on the Linux command line by typing R (capital).

In addition to the base installation there are over 7000 add-on packages contributed by R users. They provide additional functionality and can be installed by typing

at the R command prompt. You will then be asked to specify a location, and choosing one close to you will result in a faster download. Once successfully downloaded and installed, the package will need to be loaded into the R session before it can be used by typing

Periodically running

will download newer versions of all of your installed packages. The packages listed in Table A.1 are used in this book but are not part of the base installation. You may wish to install them all at once with the following code

A word of warning about packages: the quality and documentation can vary, and there is usually no guarantee that functions work as advertised. Packages submitted to CRAN by package developers must pass many checks before being accepted. These checks however do not test whether functions work properly. For example, a function called reciprocal() takes a number x and is supposed to return the number, but it might return by accident. Package developers are responsible for ensuring that functions return the correct values. Do not let this warning put you off R.

Specifically intended for lab-based biomedical researchers, this practical guide shows how to design experiments that are reproducible, with low bias, high precision, and widely applicable results. With specific examples from research using both cell cultures and model organisms, it explores key ideas in experimental design, assesses common designs, and shows how to plan a successful experiment. It demonstrates how to control biological and technical factors that can introduce bias or add noise, and covers rarely discussed topics such as graphical data exploration, choosing outcome variables, data quality control checks, and data pre-processing. It also shows how to use R for analysis, and is designed for those with no prior experience. An accompanying website (https://stanlazic.github.io/EDLB.html) includes all R code, data sets, and the labstats R package. This is an ideal guide for anyone conducting lab-based biological research, from students to principle investigators working in either academia or industry.

In Singapore, influenza vaccination is recommended for persons at higher risk of complications of seasonal influenza, including those with chronic medical conditions and the elderly (individuals aged ⩾65 years). We investigated the factors associated with influenza vaccine uptake based on a nationally representative sample of community-dwelling adults aged >50 years. The data for this study were obtained from the National Health Surveillance Survey (NHSS) 2013. The association between influenza vaccine uptake and socio-demographic and health-related variables was analysed using univariable and multivariable logistic regression models. Of 3700 respondents aged ⩾50 years in the NHSS, 15·2% had received seasonal influenza vaccination in the past year. Older age, single marital status and economic inactivity were the socio-demographic variables independently associated with vaccine uptake. Health-related factors which were predictive of influenza vaccine uptake were sufficient total physical activity, better self-rated health, having at least one medical condition at risk of influenza complications and a regular family doctor/general practitioner. Influenza vaccine uptake in community-dwelling older adults was low. Our findings are of relevance in the formulation of public health policies and targeted health promotion strategies to increase vaccine uptake in this population group.

Australian abattoir workers, farmers, veterinarians and people handling animal birthing products or slaughtering animals continue to be at high risk of Q fever despite an effective vaccine being available. National Notifiable Diseases Surveillance System data were analysed for the period 1991–2014, along with enhanced risk factor data from notified cases in the states of New South Wales and Queensland, to examine changes in the epidemiology of Q fever in Australia. The national Q fever notification rate reduced by 20% [incident rate ratio (IRR) 0·82] following the end of the National Q fever Management Program in 2006, and has increased since 2009 (IRR 1·01–1·34). Highest rates were in males aged 40–59 years (5·9/100 000) and 87% of Q fever cases occurred in New South Wales and Queensland. The age of Q fever cases and proportion of females increased over the study period. Based on the enhanced risk factor data, the most frequently listed occupation for Q fever cases involved contact with livestock, followed by ‘no known risk’ occupations. More complete and comparable enhanced risk factor data, at the State/Territory and national levels, would aid in further understanding of the epidemiology of Q fever.

We studied the evolution, genotypes, and the molecular clock of dengue virus serotype 1 (DENV-1), between 2001 and 2014 in Guangzhou, China. The analysis of the envelope (E) gene sequences of 67 DENV-1 strains isolated in Guangzhou, together with 58 representative sequences downloaded from NCBI, have shown shifts in viral genotypes. The genotype changed several times, from genotype I to IV in 2002, from IV to I in 2005, and from I to V in 2014. These genotype shifts may be the cause of DENV outbreaks. The diversity of genotypes and clades demonstrates a high risk of future outbreaks in Guangzhou. The mean rate of virus nucleotide substitution in Guangzhou was determined to be 7·77 × 10−4 per site per year, which represents a medium substitution rate compared to two other countries. Our research can point to different ancestors of the isolated strains, which may further reveal the different origins and transmission of DENV-1 strains in Guangzhou.

Although most non-typhoidal Salmonella illnesses are self-limiting, antimicrobial treatment is critical for invasive infections. To describe resistance in Salmonella that caused foodborne outbreaks in the United States, we linked outbreaks submitted to the Foodborne Disease Outbreak Surveillance System to isolate susceptibility data in the National Antimicrobial Resistance Monitoring System. Resistant outbreaks were defined as those linked to one or more isolates with resistance to at least one antimicrobial drug. Multidrug resistant (MDR) outbreaks had at least one isolate resistant to three or more antimicrobial classes. Twenty-one per cent (37/176) of linked outbreaks were resistant. In outbreaks attributed to a single food group, 73% (16/22) of resistant outbreaks and 46% (31/68) of non-resistant outbreaks were attributed to foods from land animals (P < 0·05). MDR Salmonella with clinically important resistance caused 29% (14/48) of outbreaks from land animals and 8% (3/40) of outbreaks from plant products (P < 0·01). In our study, resistant Salmonella infections were more common in outbreaks attributed to foods from land animals than outbreaks from foods from plants or aquatic animals. Antimicrobial susceptibility data on isolates from foodborne Salmonella outbreaks can help determine which foods are associated with resistant infections.

A recent countrywide MRSA spa-type 1081 outbreak in The Netherlands predominantly affected nursing homes, generating questions on how infection spreads within and between nursing homes despite a low national prevalence. Since the transfer of residents between nursing homes is uncommon in The Netherlands, we hypothesized that staff exchange plays an important role in transmission. This exploratory study investigated the extent of former (last 2 years) and current staff exchange within and between nursing homes in The Netherlands. We relied on a questionnaire that was targeted towards nursing-home staff members who had contact with residents. We found that 17·9% and 12·4% of the nursing-home staff formerly (last 2 years) or currently worked in other healthcare institutes besides their job in the nursing home through which they were selected to participate in this study. Moreover, 39·7% of study participants worked on more than one ward. Our study shows that, in The Netherlands, nursing-home staff form a substantial number of links between wards within nursing homes and nursing homes are linked to a large network of healthcare institutes through their staff members potentially providing a pathway for MRSA transmission between nursing homes and throughout the country.

More than 2 million visits for skin and soft tissue infections (SSTIs) are seen in US emergency departments (EDs) yearly. Up to 50% of patients with SSTIs, suffer from recurrences, but associated factors remain poorly understood. We performed a retrospective study of patients with primary diagnosis of SSTI between 2005 and 2011 using California ED discharge data from the State Emergency Department Databases and State Inpatient Databases. Using a multivariable logistic regression, we examined factors associated with a repeat SSTI ED visits up to 6 months after the initial SSTI. Among 197 371 SSTIs, 16·3% were associated with a recurrent ED visit. We found no trend in recurrent visits over time (χ 2 trend = 0·68, P = 0·4). Race/ethnicity, age, geographical location, household income, and comorbidities were all associated with recurrent visits. Recurrent ED visits were associated with drug/alcohol abuse or liver disease [odds ratio (OR) 1·4, 95% confidence interval (CI) 1·3–1·4], obesity (OR 1·3, 95% CI 1·2–1·4), and in infections that were drained (OR 1·1, 95% CI 1·1–1·1) and inversely associated with hospitalization after initial ED visit (OR 0·4, 95% CI 0·3–0·4). In conclusion, we found several patient-level factors associated with recurrent ED visits. Identification of these high-risk groups is critical for future ED-based interventions.

The intensity of annual Spanish influenza activity is currently estimated from historical data of the Spanish Influenza Sentinel Surveillance System (SISSS) using qualitative indicators from the European Influenza Surveillance Network. However, these indicators are subjective, based on qualitative comparison with historical data of influenza-like illness rates. This pilot study assesses the implementation of Moving Epidemic Method (MEM) intensity levels during the 2014–2015 influenza season within the 17 sentinel networks covered by SISSS, comparing them to historically reported indicators. Intensity levels reported and those obtained with MEM at the epidemic peak of the influenza wave, and at national and regional levels did not show statistical difference (P = 0·74, Wilcoxon signed-rank test), suggesting that the implementation of MEM would have limited disrupting effects on the dynamic of notification within the surveillance system. MEM allows objective influenza surveillance monitoring and standardization of criteria for comparing the intensity of influenza epidemics in regions in Spain. Following this pilot study, MEM has been adopted to harmonize the reporting of intensity levels of influenza activity in Spain, starting in the 2015–2016 season.

Quantitative biology, biostatistics and mathematical modeling

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Contents

1 - Introduction

Summary

3 - Replication (what is ‘N’?)

Summary

Appendix B - Glossary

Summary

Preface

Summary

5 - Planning for Success

Frontmatter

2 - Key Ideas in Experimental Design

Summary

Appendix A - Introduction to R

Summary

Experimental Design for Laboratory Biologists

Abbreviations

Factors associated with influenza vaccine uptake in older adults living in the community in Singapore

Trends and risk factors for human Q fever in Australia, 1991–2014

References

Dedication

Molecular characterization and genotype shift of dengue virus strains between 2001 and 2014 in Guangzhou

Antimicrobial resistance in Salmonella that caused foodborne disease outbreaks: United States, 2003–2012

Staff exchange within and between nursing homes in The Netherlands and potential implications for MRSA transmission

Incidence and factors associated with emergency department visits for recurrent skin and soft tissue infections in patients in California, 2005–2011

Pilot study to harmonize the reported influenza intensity levels within the Spanish Influenza Sentinel Surveillance System (SISSS) using the Moving Epidemic Method (MEM)

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Experimental Design for Laboratory Biologists