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Gregor Mendel was an Austrian Monk in the late 1800s who experimented with pea plants to find trait inheritance patterns in successive generations. Mendel's Laws Principle of Segregation - Two alleles of a homologous pair of chromosomes separate (segrega...

Multiple Linear Regression analysis can be looked upon as an extension of simple linear regression analysis to the situation in which more than one independent variables must be considered. The general model with response Y and regressors X1, X2,... Xp: Su...

Which Summary Measure to Use? Weighted averages are usually best Mantel-Haenszel is easy to compute and can handle zeros MLE measures are difficult and typically require a computer Weighted Average in MH Summaries Consider the following table: ...

The primary goal of linkage analysis is to determine the location (chromosome and region) of genes influencing a specific trait. We accomplish this by looking for evidence of co-inheritance of the trait with other genes or markers whose locations are known, an...

Given several predictors and a response, we need to figure out whether all are needed. Consider a large model, Ω, and a smaller model, 𝜔, which consist of a subset of predictors in Ω. If there is not much difference in fit, we perfer the smaller model. ...

The objective of standardization is the compare the rates of a disease (or outcome) between population which differ in underlying characteristics (age, sex, race, etc) that may affect the overall rate of disease; In essence it's another way to account for conf...

A phenotype is the appearance of an individual, which results from the interaction of the person's genetic makeup and their environment. Phenotypes can be categorical or numerical. If we are interested in the genetic component of a trait  there are different m...

So far we have mostly seen quantitative variables in regression models, but many variables of interest are qualitative (sex, status, etc). To add such information to a model, we can set up a indicator/dummy variable. For example, we could set up a variable X...

Transformations of the response and predictors can improve the fit and correct violations of model assumptions such as non-constant error variance. This chapter focuses on the transformation of predictors. The idea behind Broken Stick Regression/Segmented Reg...

The aim of matching is remove confounding by matching subjects to be similar on a potential confounder. Doing so eliminates (or reduces) confounding, as well as reducing variability thereby increasing power. Recall a paired t-test with two independent samples...

Genotype and Allele Frequency Estimation is the first step in studying a polymorphism. Used for family data and independent individuals in a population. We can use a subset of individuals who are independent and count alleles, or use the maximum likelihood met...

The estimation and inference from the regression model depends on several assumptions. These assumptions need to be checked using regression diagnostics. We divide the potential problems into three categories: Error: 𝜀 ~ N(0, 𝜎2I); i.e. the errors are: ...

Stratified analysis can be used to adjust for confounding, but the results can be difficult to adjust multiple confounders. If we have too many strata, we could end up with very small tables or 0 counts for some cells. We can instead use Logistic Regression wh...

In association testing we are interested in the effect of a specific allele in the population. We ask the question: "Is allele X1 more common in affected individuals than unaffected individuals?" We do not need family data to answer this, but we can use it if ...

Variable selection is intended to select the "best subset" of predictors. Variable selection shouldn't be separated from the rest of the model; Outliers and influential points can change the model we select. Transformations of the variables can have an impact ...

In case-control studies matching cases and controls on a potential confounder improves the efficiency of a study and removes/reduces bias. Logistic regression controlling for a stratification variable allows us to examine multiple risk factors and control for...

In 1978 Restricted Fragment Linked Polymorphisms (RFLPSs) were used for linkage analysis. In 1987 the first human genetic map was created. In 1989 microstellite markers made genome-wide linkage studies possible. 1990-2003 the human genome project was sequ...

Linear Regression Predicting a CI new obs adds a 1 to se(y): 𝛽0 + 𝛽2x +/- t* Multiple Linear Regression and Estimation 𝐻0 : 𝛽1 = 𝛽2 = 𝛽3 = ⋯ = 𝛽𝑝 = 0  v.s.  𝐻1 : not all 𝛽𝑘 = 0, 𝑘 = 1, … , 𝑝 rejection ...

Classification and regression trees can be generated from multivariable data sets using recursive partitioning with: Gini index or entropy for a categorical outcome Residual sum of squares for a continuous outcome We can use cross-validation to assess t...

Survival analysis is a measure of time until an event occurs. It doesn't only measure death as an outcome, and can adjust for covariates just as a logistic regression. But while a logistic regression only requires knowledge of whether an outcome occurred, surv...