Refer to Data Set EAR.DAT (see Table 3.12 (on page 69), also...

Refer to Data Set EAR.DAT (see Table 3.12 (on page 69), also www.cengagebrain.com). Consider a subject "cured" if (1) the subject is a unilateral case and the ear clears by 14 days or (2) the subject is a bilateral case and both ears are clear by 14 days. Run a logistic regression with outcome variable = cured and independent variables (1) antibiotic, (2) age, and (3) type of case (unilateral or bilateral). Assess goodness of fit of the model you obtain.

Refer to Data Set EAR.DAT (see Table 3.12 (on page 69), also www.cengagebrain.com).
Consider a subject "cured" if (1) the subject is a unilateral case and the ear clears by 14 days or (2) the subject is a bilateral case and both ears are clear by 14 days. Run a logistic regression with outcome variable = cured and independent variables (1) antibiotic, (2) age, and (3) type of case (unilateral or bilateral). Assess goodness of fit of the model you obtain.

Key Concepts

Goodness-of-Fit Assessment

Goodness-of-fit assessment evaluates how well a model's predicted outcomes match the observed data. In logistic regression, this is typically done using tests such as the Hosmer-Lemeshow test, likelihood ratio tests, and by examining residuals. These methods help determine if the model is appropriately specified, if any key variables are missing, or if the model adequately captures the underlying relationships in the data.

Independent Variables in Regression

Independent variables, also known as predictors or covariates, are factors that are believed to influence the outcome in a regression model. In the context of logistic regression, these variables could be continuous, categorical, or binary, and they help determine the impact of different characteristics, like treatment type, age, or case classification, on the likelihood of the outcome.

Binary Outcome Modeling

Binary outcome modeling involves analyzing data where the dependent variable has only two possible values. This type of analysis is essential when the outcome is categorical, and methods like logistic regression transform predictor values into probabilities, enabling interpretation in contexts such as treatment effectiveness or condition resolution.

Logistic Regression

Logistic regression is a statistical method used for modeling a binary outcome, such as success/failure or cured/not cured, based on one or more predictor variables. It estimates the probability of an event occurring as a function of the independent variables by using the logistic function, thereby providing an approach to quantify relationships between predictors and the binary response.

Transcript

00:01 A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from.

00:07 The lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups.

00:13 One group received vaccinations, the other group did not.

00:16 During the following year, only 33 of 2004 and 55 vaccinated children had ear infections.

00:24 So those that did receive vaccinations, 33 out of 2455 had ear infections.

00:32 Infections compared to 499 out of 2 ,452 unvaccinated children in the control group.

00:48 Are the conditions for inference satisfied? well, first we can say that yes is because it's random.

01:13 The individuals were randomly divided into those two groups.

01:17 The 10 % condition is satisfied because both samples are less than 10 % of the population of all vaccinated and all.

01:25 Unvaccinated children.

01:29 So also they are independent because they were randomly divided into two groups and the success and failures are both greater than 10.

01:52 All the successes and failures for each are greater than are equal to 10.

01:59 And so all conditions are met.

02:02 B find a 95 % confidence interval for the difference in the rates of ear infection.

02:11 And so for the first sample proportion we get 333 out of 2455 and for our second sample proportion would be 499 out of 2452 and 333 out of 2455 is 0 .1356 and 499 out of 2452 is 0 .2035...

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