Statistics: Hosmer-Lemeshow Goodness of Fit Test and ROC Curve

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40 Questions

What is the primary purpose of a ROC curve?

To distinguish between high-risk and low-risk patients

What is the typical range of AUC values for a 'good' model?

0.75 to 0.92

When would you use survival analysis instead of logistic regression?

When the time to an event is important

What is the Kaplan-Meier estimation used for?

To estimate the survival function

What is the purpose of the Log Rank Test?

To compare the survival rates of two groups

What is the Cox Proportional Hazard Model used for?

To analyze the relationship between predictors and survival time

What does a high AUC value indicate?

The model is excellent

What is the Hosmer-Lemeshow test used for?

To evaluate the goodness of fit of a model

What is the primary focus of the medical perspective in disease management?

Prognostic

What is the risk of dying within 30 days post MI for a 75-year-old patient compared to a 50-year-old patient?

Lower for the 50-year-old patient

What is the primary function of diagnosis in disease management?

To determine signs and symptoms

What is the primary concern of the therapeutic perspective?

Treating the disease

What is the primary focus of the etiology perspective?

Determining the cause of the disease

What is the significance of the 30-day mortality rate post-MI?

It is a measure of the risk of dying within 30 days

What is the purpose of identifying risk factors in disease management?

To identify individuals at high risk of developing the disease

What is the significance of the population at risk in disease management?

It refers to the group of people who are at high risk of developing the disease

What is the 10-year risk of CHD event for a 45-year-old male with a total score of 7?

13%

What is the benefit of controlling BP and improving diet in the given scenario?

Reduce risk from 13% to 4%

What type of study design is typically used in prognostic research?

Cohort study

What is the goal of Phase I in a two-phase prognostic study?

To come up with the prediction rule

What is the relationship between the determinants and the outcome in a prognostic study?

Endpoint is a function of the combination of determinants

What is the first step in conducting a prognostic study?

Identify the research question

What is the purpose of Phase II in a two-phase prognostic study?

To test the predictive ability of the model

What is the characteristic of a prognostic study?

It is longitudinal in nature and involves multiple risk factors

What is the primary goal of a prognostic study?

To estimate the probability of a future outcome given all determinants

What type of risk does a prognostic study measure?

Absolute risk

What is the purpose of informing a patient about their prognosis?

To help decide whether to start an intervention or treatment

What is the characteristic of an individual patient that is considered non-clinical?

Age

What is the benefit of knowing an individual patient's risk of developing a specific outcome?

It helps in deciding whether to start an intervention or treatment

What is the purpose of a prognostic study in terms of treatment or intervention?

To predict how much changes in risk after the treatment or intervention

What is the term used to describe the risk of an individual patient having a specific outcome?

Individual prognosis

Why is it important to know an individual patient's characteristics?

To estimate the probability of a future outcome

What is the purpose of defining a relevant outcome in a prognostic study?

To measure the effect of the determinant status

Why is it essential to measure the outcome in all patients in a prognostic study?

To ensure the outcome is measured as precisely as possible

What is the purpose of checking for non-linearity of continuous variables in model development?

To determine the best model for the data

What is the formula for logistic regression analysis?

Y ~ α + βX

What is the purpose of regression coefficients in logistic regression analysis?

To calculate the risk of disease presence

What is the purpose of blinding in a prognostic study?

To eliminate bias in the study

What is the purpose of defining a relevant time period for prognosis?

To measure the effect of the determinant status

What is the formula to calculate the odds ratio in logistic regression analysis?

Exp(B) = odds ratio

Study Notes

Prognostic Study

  • Aims to predict the probability of an individual patient experiencing a particular outcome or event
  • Focuses on the risk of an individual patient, rather than the average population risk or relative risk compared to others

Types of Prognostic Study

  • Longitudinal in nature, involving multiple risk factors/predictors
  • Absolute risk prediction
  • Study design: Cohort study
  • Cohort is a group that is followed in time, where exposure is present before the outcome

Phases of Prognostic Study

  • Phase 1: Develop a prediction rule
  • Phase 2: Test the predictive ability of the prediction rule (validation of model in new population)

Steps in Prognostic Research

  • Identify research question
  • Define study population (domain/population)
  • Identify prognostic factors (determinants-indicator/intervention/control)
  • Follow clinical practice

Measuring Outcomes

  • Define a relevant outcome (e.g. death, disability, quality of life, MI)
  • Define a relevant time period for prognosis (e.g. days, weeks, years)
  • Measure outcome in all patients as precisely as possible

Analysis in Prognostic Study

  • Model development: univariate analysis, check non-linearity of continuous variables, multivariate analysis, check for interaction
  • Easy to use format of model
  • Performance of model

Logistic Regression Analysis

  • Y ~ α + βX
  • Y ~ intercept + coef* factor
  • Regression coefficients (beta, β) used to calculate risk of disease presence
  • Exp(β) = odds ratio

Hosmer-Lemeshow Goodness of Fit Test

  • Used to assess the goodness of fit of a logistic regression model
  • Measures the difference between observed and predicted outcomes

Discrimination

  • Ability of a model to distinguish between high-risk and low-risk patients
  • ROC curve (Receiver Operating Characteristic) and AUC (Area Under the Curve) used to evaluate discrimination
  • AUC values:
    • 0.50 to 0.75: fair
    • 0.75 to 0.92: good
    • 0.92 to 0.97: very good
    • 0.97 to 1.00: excellent

Survival Analysis

  • Used to analyze the time to an event (e.g. time to death, time to disease occurrence)
  • Kaplan-Meier estimation and Log Rank Test used to estimate survival function and compare survival curves between groups
  • Cox Proportional Hazard Model used to analyze the effect of multiple predictors on survival time

This quiz assesses understanding of statistical concepts, including the Hosmer-Lemeshow goodness of fit test and the ROC curve, used to measure model performance and discrimination in predicting outcomes.

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