J&J Prd Internship 2009
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Transcript of J&J Prd Internship 2009
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!