Scientific Methods for Health Sciences

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Scientific Methods for Health Sciences EBook

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Preface

The Scientific Methods for Health Sciences (SMHS) EBook is designed to support a 4-course training curriculum emphasizing the fundamentals, applications and practice of scientific methods specifically for graduate students in the health sciences.

Format

Follow the instructions in this page to expand, revise or improve the materials in this EBook.

Learning and Instructional Usage

This section describes the means of traversing, searching, discovering and utilizing the SMHS EBook resources in both formal and informal learning setting.

Copyrights

The SMHS EBook is a freely and openly accessible electronic book developed by SOCR and the general health sciences community.

Chapter I: Fundamentals

Exploratory Data Analysis, Plots and Charts

Review of data types, exploratory data analyses and graphical representation of information.

Ubiquitous Variation

There are many ways to quantify variability, which is present in all natural processes.

Parametric Inference

Foundations of parametric (model-based) statistical inference.

Probability Theory

Random variables, stochastic processes, and events are the core concepts necessary to define likelihoods of certain outcomes or results to be observed. We define event manipulations and present the fundamental principles of probability theory including conditional probability, total and Bayesian probability laws, and various combinatorial ideas.

Odds Ratio/Relative Risk

The relative risk, RR, (a measure of dependence comparing two probabilities in terms of their ratio) and the odds ratio, OR, (the fraction of one probability and its complement) are widely applicable in many healthcare studies.

Probability Distributions

Probability distributions are mathematical models for processes that we observe in nature. Although there are different types of distributions, they have common features and properties that make them useful in various scientific applications.

Resampling and Simulation

Resampling is a technique for estimation of sample statistics (e.g., medians, percentiles) by using subsets of available data or by randomly drawing replacement data. Simulation is a computational technique addressing specific imitations of what’s happening in the real world or system over time without awaiting it to happen by chance.

Design of Experiments

Design of experiments (DOE) is a technique for systematic and rigorous problem solving that applies data collection principles to ensure the generation of valid, supportable and reproducible conclusions.

Intro to Epidemiology

Epidemiology is the study of the distribution and determinants of disease frequency in human populations. This section presents the basic epidemiology concepts. More advanced epidemiological methodologies are discussed in the next chapter.

Experiments vs. Observational Studies

Experimental and observational studies have different characteristics and are useful in complementary investigations of association and causality.

Estimation

Estimation is a method of using sample data to approximate the values of specific population parameters of interest like population mean, variability or 97^th percentile. Estimated parameters are expected to be interpretable, accurate and optimal, in some form.

Hypothesis Testing

Hypothesis testing is a quantitative decision-making technique for examining the characteristics (e.g., centrality, span) of populations or processes based on observed experimental data.

Statistical Power, Sensitivity and Specificity

The fundamental concepts of type I (false-positive) and type II (false-negative) errors lead to the important study-specific notions of statistical power, sample size, effect size, sensitivity and specificity.

Data Management

All modern data-driven scientific inquiries demand deep understanding of tabular, ASCII, binary, streaming, and cloud data management, processing and interpretation.

Bias and Precision

Bias and precision are two important and complementary characteristics of estimated parameters that quantify the accuracy and variability of approximated quantities.

Association and Causality

An association is a relationship between two, or more, measured quantities that renders them statistically dependent so that the occurrence of one does affect the probability of the other. A causal relation is a specific type of association between an event (the cause) and a second event (the effect) that is considered to be a consequence of the first event.

Rate-of-change

Rate of change is a technical indicator describing the rate in which one quantity changes in relation to another quantity.

Clinical vs. Statistical Significance

Statistical significance addresses the question of whether or not the results of a statistical test meet an accepted quantitative criterion, whereas clinical significance is answers the question of whether the observed difference between two treatments (e.g., new and old therapy) found in the study large enough to alter the clinical practice.

Correction for Multiple Testing

Multiple testing refers to analytical protocols involving testing of several (typically more then two) hypotheses. Multiple testing studies require correction for type I (false-positive rate), which can be done using Bonferroni's method, Tukey’s procedure, family-wise error rate (FWER), or false discovery rate (FDR).

Chapter II: Applied Inference

Epidemiology

This section expands the Epidemiology Introduction from the previous chapter. Here we will discuss numbers needed to treat and various likelihoods related to genetic association studies, including linkage and association, LOD scores and Hardy-Weinberg equilibrium.

Correlation and Regression (ρ and slope inference, 1-2 samples)

Studies of correlations between two, or more, variables and regression modeling are important in many scientific inquiries. The simplest situation such situation is exploring the association and correlation of bivariate data ($X$ and $Y$).

ROC Curve

The receiver operating characteristic (ROC) curve is a graphical tool for investigating the performance of a binary classifier system as its discrimination threshold varies.

ANOVA

Analysis of Variance (ANOVA) is a statistical method fpr examining the differences between group means. ANOVA is a generalization of the t-test for more than 2 groups. It splits the observed variance into components attributed to different sources of variation.

Non-parametric inference

Nonparametric inference involves a class of methods for descriptive and inferential statistics that are not based on parametrized families of probability distributions, which is the basis of the parametric inference we discussed earlier.

Instrument Performance Evaluation: Cronbach's α

Cronbach’s alpha (α) is a measure of internal consistency used to estimate the reliability of a cumulative psychometric test.

Measurement Reliability and Validity

Measures of Validity include: Construct validity (extent to which the operation actually measures what the theory intends to), Content validity (the extent to which the content of the test matches the content associated with the construct), Criterion validity (the correlation between the test and a variable representative of the construct), experimental validity (validity of design of experimental research studies). Similarly, there many alternate strategies to assess instrument Reliability (or repeatability) -- test-retest reliability, administering different versions of an assessment tool to the same group of individuals, inter-rater reliability, internal consistency reliability.

Survival Analysis

Survival analysis is used for analyzing longitudinal data on the occurrence of events (e.g., death, injury, onset of illness, recovery from illness). In this section we discuss data structure, survival/hazard functions, parametric versus semi-parametric regression techniques and introduction to Kaplan-Meier methods (non-parametric).

Decision Theory

Decision theory helps determining the optimal course of action among a number of alternatives, when consequences cannot be forecasted with certainty. There are different types of loss-functions and decision principles (e.g., frequentist vs. Bayesian).

CLT/LLNs – limiting results and misconceptions

The Law of Large Numbers (LLT) and the Central Limit Theorem (CLT) are the first and second fundamental laws of probability. CLT yields that the arithmetic mean of a sufficiently large number of iterates of independent random variables given certain conditions will be approximately normally distributed. LLT states that in performing the same experiment a large number of times, the average of the results obtained should be close to the expected value and tends to get closer to the expected value with increasing number of trials.

Association Tests

There are alternative methods to measure association two quantities (e.g., relative risk, risk ratio, efficacy, prevalence ratio).

Bayesian Inference

Bayes’ rule connects the theories of conditional and compound probability and provides a way to update probability estimates for a hypothesis as additional evidence is observed.

PCA/ICA/Factor Analysis

Principal component analysis is a mathematical procedure that transforms a number of possibly correlated variables into a fewer number of uncorrelated variables through a process known as orthogonal transformation. Independent component analysis is a computational tool to separate a multivariate signal into additive subcomponents by assuming that the subcomponents are non-Gaussian signals and are statistically independent from each other. Factor analysis is a statistical method, which describes variability among observed correlated variables in terms of potentially lower number of unobserved variables.

Point/Interval Estimation (CI) – MoM, MLE

Estimation of population parameters is critical in many applications. In statistics, estimation is commonly accomplished in terms of point-estimates or interval-estimates for specific (unknown) population parameters of interest. The method of moments (MOM) and maximum likelihood estimation (MLE) techniques are used frequently in practice.

Chapter III: Linear Modeling

Analysis of Covariance (ANCOVA)

First, see the ANOVA section above.

Chapter IV: Special Topics

Network Analysis

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