Biostat / epi 537

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06 Jan 2009


  1. Introductions

    1. Instructor

    1. Teaching Assistant(s)

    1. Students

  1. Intro to Longitudinal Studies

    1. Event times (Biostat 537)

    1. Repeated measures (Biostat 540)

  1. Biostat 537 – Course Overview

  1. Introduction to Survival Data

    1. Examples

    1. Functions used to summarize distribution of times

My Introduction:

      • My statistical research does focus primarily on longitudinal studies – both repeated measures issues and survival.

      • Change is interesting!

      • Research and Teaching

      • Interested in B537/B540 in order to “bring together” and perhaps write a book.

Longitudinal Study – VPS

      • Prospective study with interest in both time-to-event and longitudinal health status measures.

      • Event = time-until-AIDS

        1. discrete time

        2. some drop-out

      • Longitudinal = knowledge

Longitudinal Study – Mayo PBC Data

      • outcome = time-until-death

      • Different research questions:

        1. Compare two treatment groups

        2. Predictive model?

        3. Accuracy of predictive model/marker?

Longitudinal Study – MACS data

      • Prospective cohort study

      • First Event: Incident infection (time scale?)

      • Second Event: AIDS or death given infected = t0

      • Longitudinal analysis of changes in immune status as part of natural history of infection and/or in response to treatment.

      • Idea of time-dependent covariates – can the current value of CD4 or viral load be used to predict risk of death?

Longitudinal Study – Breast Cancer Data

      • Prospective study subsequent to BC diagnosis

      • Event = time-until-death, but this is relatively rare (censoring!)

      • Some delay to enrollment (left truncation)

      • Compare the predictive ability of different cytometry measures.

Longitudinal Study – Cystic Fibrosis Registry

      • National registry of CF patients

      • Event = death

      • Goal = predict mortality, perhaps to guide selection of patients for lung transplantation.

      • Logistic regression with 5-year status (0=alive; 1=dead)

      • Survival analysis using time-dependent covariates to model the hazard of death.

      • Longitudinal analysis looks at performance status, FEV1, and changes over time – are some groups at great risk of decline in pulmonary function?


      • CHANGE

        1. In a monotone discrete status such as vital status, or disease (first occurrence).

        2. In continuous or discrete characteristics that are measured at regular time periods (e.g. yearly).

      • Survival methods are concerned with

        1. Summarizing risk of death using hazard regression methods

        2. Summarizing cumulative fraction that have died using survival curve methods (Kaplan-Meier)

        3. Missing data from censoring!

        4. Covariates may change with time (be careful!)

      • Longitudinal methods are concerned with

        1. Summarizing changes in the mean over time and group.

        2. Characterizing the sources of variation: between groups represented by covariate values (systematic); among individuals (random effects); and within-individuals over time (error, or drift).

Overview of Biostat 537

      • Contact hours: (2) lectures; (1) discussion section starting 13 Jan 2008.

      • Evaluation: (2) Quizes (45 min); midterm (take-home) and final (in-class).

      • Weekly exercises

      • Discussion section = review key content, discuss exercise details and/or issues.

      • Web page

Introduction to Censored Survival Data – Overview

      • Survival time, observation time, and censoring indicator.

      • Cause-specific and issues…

      • Hazard

      • Censoring and truncation

      • Recurrent events

Regression Methods

Mathematical Summaries of a Population of Event Times


      • Longitudinal studies generally offer two analyses that focus on time: survival; and repeated measures.

      • Survival data have a number of features that require some special methods:

        1. censoring

        2. cause-specific events

        3. models for time (or avoid it!)

      • Mathematically we can focus on any one of (5) key summaries – but for survival data we focus on the survival curve and the hazard function – much more about both of these

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