Start Date: 07/05/2020
Course Type: Common Course |
Course Link: https://www.coursera.org/learn/simple-regression-analysis-public-health
Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more.Biostatistics is the application of statistical reasoning to the life sciences, and it's the key to unlocking the data gathered by researchers and the evidence presented in the scientific public health literature. In this course, we'll focus on the use of simple regression methods to determine the relationship between an outcome of interest and a single predictor via a linear equation. Along the way, you'll be introduced to a variety of methods, and you'll practice interpreting data and performing calculations on real data from published studies. Topics include logistic regression, confidence intervals, p-values, Cox regression, confounding, adjustment, and effect modification.
Simple Logistic Regression
Simple Cox Proportional Hazards Regression
Confounding, Adjustment, and Effect Modification
Course Project
Simple Regression Analysis in Public Health This course will cover the basic concepts and methods of regression analysis in public health. We will cover the different methods within a single course, focusing on the different types of regression models used to predict outcomes in various populations, such as in population-based or health-related diseases. We will also cover the different types of regression techniques that are used, including logistic regression, confidence intervals, Cox regression, and multiple regression, as well as the multivariable logistic regression model, the Cox regression model, and multiple regression, as appropriate. Upon completing this course, you will be able to: 1. Describe different regression models used to predict outcomes in various populations. 2. Choose appropriate regression method for a population using multiple variables. 3. Compute the indirect effects of covariance and confounding on the direct effects of covariance on outcomes in the population model. 4. Use multiple regression to predict outcomes in various populations using multiple variables. 5. Use multiple regression model to predict outcomes in various populations using multiple variables. 6. Deselect covariance and confounding from multiple regression models. 7. Use regression to predict outcomes in various populations using multiple variables. ---------------- Please note that the free version of this class gives you access to all of the instructional videos and handouts. The peer feedback and quizzes are only available in the paid version.Numerical Modeling and Modeling Strategy Multiple Regression Direct Effects and
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Regression analysis | All major statistical software packages perform least squares regression analysis and inference. Simple linear regression and multiple regression using least squares can be done in some spreadsheet applications and on some calculators. While many statistical software packages can perform various types of nonparametric and robust regression, these methods are less standardized; different software packages implement different methods, and a method with a given name may be implemented differently in different packages. Specialized regression software has been developed for use in fields such as survey analysis and neuroimaging. |
Regression analysis | Classical assumptions for regression analysis include: |
Regression analysis | In the last case, the regression analysis provides the tools for: |
Regression analysis | In the case of simple regression, the formulas for the least squares estimates are |
Regression analysis | Many techniques for carrying out regression analysis have been developed. Familiar methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional. |
Regression analysis | The performance of regression analysis methods in practice depends on the form of the data generating process, and how it relates to the regression approach being used. Since the true form of the data-generating process is generally not known, regression analysis often depends to some extent on making assumptions about this process. These assumptions are sometimes testable if a sufficient quantity of data is available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, in many applications, especially with small effects or questions of causality based on observational data, regression methods can give misleading results. |
Regression analysis | Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable; for example, correlation does not imply causation. |
Meta-regression | Meta-regression analysis (MRA) is a quantitative method of conducting literature surveys. Meta-regression has gained popularity in social, behavioral and economic sciences. Important applications have focused on qualifying estimates of policy-relevant parameters, testing economic theories, explaining heterogeneity, and qualifying potential biases. Generally, three types of models can be distinguished in the literature on meta-analysis: simple regression, fixed effect meta-regression and random effects meta-regression. |
Polynomial regression | The goal of regression analysis is to model the expected value of a dependent variable "y" in terms of the value of an independent variable (or vector of independent variables) "x". In simple linear regression, the model |
Regression analysis | In statistical modeling, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors'). More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution. A related but distinct approach is necessary condition analysis (NCA), which estimates the maximum (rather than average) value of the dependent variable for a given value of the independent variable (ceiling line rather than central line) in order to identify what value of the independent variable is necessary but not sufficient for a given value of the dependent variable. |
Regression analysis | In linear regression, the model specification is that the dependent variable, formula_2 is a linear combination of the "parameters" (but need not be linear in the "independent variables"). For example, in simple linear regression for modeling formula_3 data points there is one independent variable: formula_4, and two parameters, formula_5 and formula_6: |
Regression analysis | If the experimenter had performed measurements at three different values of the independent variable vector X, then regression analysis would provide a unique set of estimates for the three unknown parameters in β. |
Outline of regression analysis | The following outline is provided as an overview of and topical guide to regression analysis: |
Regression analysis | Assume now that the vector of unknown parameters β is of length "k". In order to perform a regression analysis the user must provide information about the dependent variable "Y": |
Regression analysis | Regression methods continue to be an area of active research. In recent decades, new methods have been developed for robust regression, regression involving correlated responses such as time series and growth curves, regression in which the predictor (independent variable) or response variables are curves, images, graphs, or other complex data objects, regression methods accommodating various types of missing data, nonparametric regression, Bayesian methods for regression, regression in which the predictor variables are measured with error, regression with more predictor variables than observations, and causal inference with regression. |
Regression analysis | Consider a regression model which has three unknown parameters, β, β, and β. Suppose an experimenter performs 10 measurements all at exactly the same value of independent variable vector X (which contains the independent variables "X", "X", and "X"). In this case, regression analysis fails to give a unique set of estimated values for the three unknown parameters; the experimenter did not provide enough information. The best one can do is to estimate the average value and the standard deviation of the dependent variable "Y". Similarly, measuring at two different values of X would give enough data for a regression with two unknowns, but not for three or more unknowns. |
Segmented regression | Segmented regression, also known as piecewise regression or "broken-stick regression", is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions. The boundaries between the segments are "breakpoints". |
Sensitivity analysis | Regression analysis, in the context of sensitivity analysis, involves fitting a linear regression to the model response and using standardized regression coefficients as direct measures of sensitivity. The regression is required to be linear with respect to the data (i.e. a hyperplane, hence with no quadratic terms, etc., as regressors) because otherwise it is difficult to interpret the standardised coefficients. This method is therefore most suitable when the model response is in fact linear; linearity can be confirmed, for instance, if the coefficient of determination is large. The advantages of regression analysis are that it is simple and has a low computational cost. |
Public health law | Population-based legal analysis is the theoretical foundation of public health law. The law of populations is a relatively new theoretical framework in jurisprudence that seeks to analyze legal problems using the tools of epidemiology. Population-based legal analysis can be applied to traditional public health problems but also has application in environmental law, zoning, evidence, and complex tort. |
Public health | Public health refers to "the science and art of preventing disease, prolonging life and promoting human health through organized efforts and informed choices of society, organizations, public and private, communities and individuals." It is concerned with threats to health based on population health analysis. The population in question can be as small as a handful of people, or as large as all the inhabitants of several continents (for instance, in the case of a pandemic). The dimensions of health can encompass "a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity," as defined by the United Nations' World Health Organization. Public health incorporates the interdisciplinary approaches of epidemiology, biostatistics and health services. Environmental health, community health, behavioral health, health economics, public policy, mental health and occupational safety and health are other important subfields. |