Search Results

In the frequentist approach, estimated probabilities are viewed as one of an infinite sequence of possible data of the same experiment, while Bayesian analysis is based on expressing uncertainty about unknown quantities as formal probability distributions. Ba...

Generalized linear models are extensions of classical linear models. Classes of generalized linear models include linear regression, logistic regression for binary and binomial data, nominal and ordinal multi-nomial logistic regression, Poisson regression for ...

Are the mean response profiles similar in the groups, or in other words, are the mean response profiles parallel?This is a question that concerns the group × time interaction effect Assuming that the mean response profiles are parallel, are the means consta...

Subjects are assigned to study groups by a random mechanism not controlled by the patient or the investigator. Randomization increases the likelihood treatment groups are comparable with respect to distribution of measurable and measurable characteristics. Ra...

Let Y be an indicator for presence of disease ->    Y | p ~ Bin(p, 1) Logistic regression models the log-ODDS (also called logit) of the mean outcome using a linear predictor. In a case-control study beta_0 is not interpretable. But the estimate of log(OR) c...

Recall in the last section Generalized Linear Models (GLMs) were introduced as an extension of the traditional linear model, it eases the assumptions in the following ways: Drops the normality assumption The response variable is allowed to follow any dis...

Suppose we have a model of mean response as a product of time on a continuous value:The top is control and bottom is treatment. By allowing an index for the jth measurement we allow participants to have measurement in unequal time periods. Consider the 3 hypo...

Outcomes are either continuous or dichotomous. Primary and secondary outcomes must be defined a priori in the protocol. The sample size for the study is based on the primary outcome. When determining  if a clinical trial is effective we test a hypothesis of a...

By now we know what a linear regression looks like. Let's consider a special case where number of parameters, p = 0:Assume Y is distributed as a normal distribution with mean β0: Y|β0, τ ∼ N(β0, σ2 = 1/τ ) τ = 1 / σ2 , also called precision   <- Be aware this...

In studying the association between two variables we should control for variables that may influence the relationship. To do so we can create K strata to control for a third variable. When all involved variables are categorical, we can display the distributio...

Here we'll be considering an alternative approach for analyzing longitudinal data using linear mixed effects models. These models have some subset of the individual parameters vary randomly from one subject to another, thereby accounting for sources of natural...

Baseline covariates are variables expected to influence the outcome, measured before the start of the intervention. They should describe the population enrolled in the study (Table 1 in all RCT papers). We need to decide what variables to measure, if the group...

Previously we have assumed given covariates, the observations are independent. However, there are many situations where this does not hold. Bayesian Hierarchical models can be used to cluster observations, where each cluster might have its own cluster-specific...

Frequently dichotomous outcomes are used in medical studies, such as presence of a disease or exposure to some factor. The classical model does not apply outcomes that are not continuous, and many other reasons: The variance of the dichotomous response is n...

The simplest mixed effect model is a random intercept model where Zi = 1; The random intercept model can be interpreted as the effect of all unobserved subject-specific variables (bi) on the linear predictor. Random slopes of time-varying covariates (δ) can b...

We've already covered survival analysis in great detail here. This will be review, application to clinical trials, and SAS implementation. Survival analysis uses class methods of studying occurrence and time of events; it was traditionally designed to study d...

In many biomedical applications outcomes are binary, ordinal or a count. In such cases we consider extension of generalized linear models for analyzing discrete longitudinal data. These non-linear models require that a linear transformation of the mean respons...

There are some situations where it may be necessary to have multiple hypothesis tests; ANOVA with more than 2 tables, genetic data, interim analysis, multiple outcomes, etc. Often times clinical trials may have 3 or more arms to reduce administrative burden an...

Effect modification can be modeled with logistic regression by including interaction terms. A significant interaction term implies a departure from heterogeneity between groups. Consider the following example were we wish to compare admission rates by sex per...

Generalized Linear Mixed Models (GLMMs) are an extension of linear mixed models to allow response variables from different distributions (such as binary or multi-nomial responses). Think of it as an extension of generalized linear models (e.g. logistic regress...