Biostatistics for Dummies

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Biostatistics for Dummies Biomedical Computing Cross- Training Seminar October 18 th , 2002

Transcript of Biostatistics for Dummies

Page 1: Biostatistics for Dummies

Biostatistics for Dummies

Biomedical Computing Cross-Training Seminar

October 18th, 2002

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What is “Biostatistics”?TechniquesMathematicsStatisticsComputing

DataMedicineBiology

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What is “Biostatistics”?

Biological data

Knowledge of biological process

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Common Applications(Medical and otherwise)

Clinical medicine

Epidemiologic studies

Biological laboratory research

Biological field research

Genetics

Environmental health

Health services

Ecology

Fisheries

Wildlife biology

Agriculture

Forestry

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Biostatisticians Work

Develop study design

Conduct analysis

Oversee and regulate

Determine policy

Training researchers

Development of new methods

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Some Statistics on Biostatistics

Internet search (Google)

> 210,000 hits

> 50 Graduate Programs in U.S.

Too much to cover in

one hour!

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Center Focus

MSU strengths Computational

simulation in physical sciences

Environmental health sciences

Bioinformatics is crowded

Computational simulation in environmental health sciences Build on appreciable

MSU strength Establish ourselves

Unique capability Particular appeal to

NIEHS

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Focus of Seminar

Statistical methodologiesComputational simulation in environmental

health sciencesCan be classified as “biostatistics”

Stochastic modelingTime seriesSpatial statistics*

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The Application

Of interest Cancer incidence rate Pesticide exposure

Of concern Age Gender Race Socioeconomic status

Objectives Suitably adjust

cancer incidence rate

Determine if relationship exists

Develop model Explain relationship Estimate cancer rate Predict cancer rate

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The Data

N.S.S. & U.S. Dept. of Commerce National T.I.S. (1972-2001, by county) Number of acres

harvested Type of crop

MS State Dept. Health Central Cancer Registry (1996 – 1998, by person) Tumor type Age Gender Race County of residence Cancer morbidity

Crude incidence/100,000

Age adjusted incidence/100,000

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Why (Bio)statistics?

Statistics Science of uncertainty Model order from

disorder

Disorder exists Large scale rational

explanation Smaller scale residual

uncertainty

Chaos

Deterministic equation Randomness

x0

Entropy

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(Bio)statistical Data

Independent identically distributed

Inhomogeneous data

Dependent dataTime seriesSpatial statistics

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Time SeriesIdentically distributed

Time dependent

Equally spaced Randomness

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Objectives in Time Series

Graphical descriptionTime plotsCorrelation plotsSpectral plots

Modeling

Inference

Prediction

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Time Series Models

Linear Models Covariance stationary Constant mean Constant variance Covariance function

of distance in time(t) ~ i.i.dZero meanFinite variance

square summable

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Nonlinear Time Series

Amplitude-frequency dependence

Jump phenomenon

Harmonics

Synchronization

Limit cycles

Biomedical applications Respiration Lupus-erythematosis Urinary introgen

excretion Neural science Human pupillary

system

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Some Nonlinear Models

Nonlinear AR Additive noise

Threshold AR Smoothed TAR Markov chain driven Fractals

Amplitude-dependent exponential AR

Bilinear

AR with conditional heteroscedasticity

Functional coefficient AR

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A Threshold Model

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A Threshold Model

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Describing Correlation

AutocorrelationAR: exponential decayMA: 0 past q

Partial autocorrelationAR: 0 past pMA: exponential decay

Cross-correlation

Relationship to spectral density

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Spatial Statistics*

Data components Spatial locations

S = {s1,s2,…,sn} Observable variable

{Z(s1),Z(s2),…,Z(sn)} s D Rk

Correlation

Data structures Geostatistical Lattice Point patterns or

marked spatial point processes

Objects

Assumptions on Z and D

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Biological Applications

Geostatistics Soil science Public health

Lattice Remote sensing Medical imaging

Point patterns Tumor growth rate In vitro cell growth

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Spatial Temporal Models

Combine time series with spatial data

ApplicationTime element

time Pesticide exposure develop cancer

Spatial element Proximity to pesticide use