J&J PRD Internship 2009

Nonclinical Statistician Intern

Cheryl Kilroy’s Account

The Right Recipe

• Past Experiences

• New Experiences

• Future Experiences

Internship Goals

• Learn

• Network

• Contribute

Learning

• Johnson and Johnson

• Nonclinical versus Clinical Trials

• Biology

• Statistics and Programming

Networking

• Nonclinical Statisticians

• Clinical Statisticians

• Programmers

• Scientists in all areas

Contributing

• Past Experiences

• Education – synergistic effect

• Documentation of my Internship

• Time Series and Forecasting presentation

Time Series and Forecasting

Objective of Presentation

• Gain a high level understanding of time series and forecasting.

What is a Time Series

• A set of observations where every observation has a time associated with it. source: Villanova University class notes from Dr. Frey’s fall 2009 lecture.

Examples:

-Life Expectancies each year

-Stock Market Prices each day

-Average Temperature each month

Main Goal of a Time Series

• Make accurate predictions

Analysis Process

• Goal is to obtain iid noise residuals

- Plot the Time Series

- Remove Trend and Seasonal Components and save residuals

- Choose Model to fit stationary residuals

- Forecast using sum of trend and seasonal model plus residual model

Life Expectancy Project

• Summary

• Data

• Questions

Life Expectancy by Gender

2002198519681951193419171900

80

70

60

50

40

Year

Data

MaleFemale

Variable

Time Series PlotLife Expectancy by Gender

from 1900 - 2004

Life Expectancy of Males

• Trend Analysis

210-1-2

99.9

99

90

50

10

1

0.1

Residual

Pe

rce

nt

75.072.570.067.565.0

1.0

0.5

0.0

-0.5

-1.0

Fitted Value

Re

sid

ua

l

1.00.50.0-0.5-1.0

12

9

6

3

0

Residual

Fre

qu

en

cy

605550454035302520151051

1.0

0.5

0.0

-0.5

-1.0

Observation Order

Re

sid

ua

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Male

2008199019721954193619181900

90

85

80

75

70

65

60

Year

Ma

le

MAPE 0.589357MAD 0.398487MSD 0.247695

Accuracy Measures

ActualFitsForecasts

Variable

Trend Analysis Plot for MaleQuadratic Trend Model

Yt = 64.371 + 0.0987*t + 0.001274*t**2

Fitting the Residuals

• Autoregressive Model (AR (p))

• Moving Average Model (MA (q))

• Autoregressive

– Moving Average (ARMA (p,q)

• ARIMA (p,d,q) – I stands for integrated

• SARIMA – S stands for seasonal

Life Expectancy - Males• Autocorrelation and

partial autocorrelation functions (ACF and PACF

605550454035302520151051

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Lag

Auto

corr

ela

tion

Male Residual ACF

605550454035302520151051

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Lag

Part

ial A

uto

corr

ela

tion

Male Residual PACF

Life Expectancy - Males

• Residual Model Output for various models

Gender p q d AR p-value MA p-value

MSE Comments

Male 1 0 1 .946 NA .0632 Insignificant for AR(1)

Male 1 1 0 .000 .678 .05893 Significant for AR(1)

Male 1 0 0 .000 NA .05814 Significant for AR(1)

Male 2 1 0 .000, .000 .000 .04764 Warnings - Diverging

Male 1 1 1 .986 .987 .0643 Nothing significant

Life Expectancy - Males

• ACF and PACF of Residuals from Residual Model

151413121110987654321

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Lag

Auto

corr

ela

tion

ACF of Residuals for RESI1(with 5% significance limits for the autocorrelations)

151413121110987654321

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Lag

Part

ial A

uto

corr

ela

tion

PACF of Residuals for RESI1(with 5% significance limits for the partial autocorrelations)

0.80.40.0-0.4-0.8

99.9

99

90

50

10

1

0.1

Residual

Perc

ent

1.00.50.0-0.5-1.0

0.50

0.25

0.00

-0.25

-0.50

Fitted Value

Resi

dual

0.60.30.0-0.3-0.6

20

15

10

5

0

Residual

Fre

quency

605550454035302520151051

0.50

0.25

0.00

-0.25

-0.50

Observation Order

Resi

dual

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for RESI1

Life Expectancy - Males

Final Model

Male Quadratic Trend

• Y(t) = 64.371 + .0987(t) + .001274(t)^2

Male Fitted Model of Residuals:

• X t = .8984 X (t – 1) + Z (t) ,

Z (t) ~ WN (0, σ^2)

Life Expectancy - Males

• Life Expectancy Forecast from years 2010 to 2025

Year

2010 76.70419 0.09394316 76.79813

2011 76.97488 -0.071157 76.90372

2012 77.24812 -0.2237467 77.02437

2013 77.52391 -0.3960779 77.12783

2014 77.80225 -0.5193993 77.28285

2015 78.08313 -0.5909878 77.49214

2016 78.36656 -0.6054504 77.76111

2017 78.65254 -0.6130346 78.03951

2018 78.94107 -0.6194339 78.32164

2019 79.23215 -0.5411478 78.691

2020 79.52577 -0.4852965 79.04047

2021 79.82194 -0.4126984 79.40924

2022 80.12066 -0.2947382 79.82592

2023 80.42192 -0.1786734 80.24325

2024 80.72574 -0.0312025 80.69453

2025 81.0321 0.11923508 81.15133

Questions

And/or

Suggestions

Thank you!