Estimating and modelling cumulative incidence functions using time-dependent weights
|
|
|
- Joel French
- 7 years ago
- Views:
Transcription
1 Estimating and modelling cumulative incidence functions using time-dependent weights Paul C Lambert 1,2 1 Department of Health Sciences, University of Leicester, Leicester, UK 2 Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden UK Stata Users Group, London, September 2013 Paul Lambert Cumulative Incidence Functions UKSUG /32
2 Competing Risks In survival analysis individuals are often at risk of more than one event. For example, individuals diagnosed with breast cancer are, at risk of death from their cancer at risk of death from other causes Paul Lambert Cumulative Incidence Functions UKSUG /32
3 Competing Risks In survival analysis individuals are often at risk of more than one event. For example, individuals diagnosed with breast cancer are, at risk of death from their cancer at risk of death from other causes The probability of dying from cancer will depend upon the mortality rate due to cancer and the mortality rate due to other causes. This is a classic competing risks situation. Paul Lambert Cumulative Incidence Functions UKSUG /32
4 Competing risks schematic h 1 (t) Cancer Alive h 2 (t) CVD h 3 (t) Other Paul Lambert Cumulative Incidence Functions UKSUG /32
5 Cause specific hazard function For cause k, h k (t) = lim δ 0 P (t T < t + δ, event = k T > t) δ To still be at risk at time t a subject can not have died of cause k or any of the K 1 other causes. Total hazard (mortality) rate All cause survival ( S(t) = exp t 0 h(t) = K h k (t) k=1 ) ( t h(u)du = exp 0 ) K h k (u)du k=1 Paul Lambert Cumulative Incidence Functions UKSUG /32
6 Cause specific cumulative incidence function We want the probability of dying of cause k accounting for the competing risks. For cause k. CIF k (t) = P (T t, event = k) CIF k (t) = t 0 S(u)h k (u)du Paul Lambert Cumulative Incidence Functions UKSUG /32
7 Cause specific cumulative incidence function We want the probability of dying of cause k accounting for the competing risks. For cause k. CIF k (t) = P (T t, event = k) CIF k (t) = CIF (t) = t 0 S(u)h k (u)du K CIF k (t) k=1 Note: CIF does not require independence between causes. For further details on competing risks see references [1, 2, 3] Post estimation command stpm2cif will estimate CIFs and related measures after using stpm2 to model cause-specific hazards [4, 5] Paul Lambert Cumulative Incidence Functions UKSUG /32
8 Key Paper: Geskus 2011[8] Geskus showed estimation and modelling of the CIF can use weighted versions of standard estimators. crprep function in R to restructure data and calculate weights[6]. I will describe a new command stcrprep that has similar functionality to crprep, but also some extensions to enable parametric models for the CIF to be easily fitted. After expansion and weighting of the data, sts graph, failure will plot CIF. sts test will perform test for differences in CIFs[7]. stcox will fit a Fine and Gray model (same as stcrreg). estat phtest can be used to assess proportional subhazards. streg, stpm2 can be used to fit parametric models for CIF. Paul Lambert Cumulative Incidence Functions UKSUG /32
9 Data expansion and weighting Define event of interest. Subjects that have a competing event are kept in the risk set to the end of follow-up. However, there is a a chance that they would be censored after their competing event. Estimate censoring distribution. Weights depend on conditional probability of not being censored after competing event. Paul Lambert Cumulative Incidence Functions UKSUG /32
10 Data Expansion for Competing Events Time Censored Cancer Other Paul Lambert Cumulative Incidence Functions UKSUG /32
11 Data Expansion for Competing Events Time Censored Cancer Other Paul Lambert Cumulative Incidence Functions UKSUG /32
12 Data Expansion for Competing Events w41 w w81 w82 w83 w84 9 Time Censored Cancer Other Paul Lambert Cumulative Incidence Functions UKSUG /32
13 Data Expansion for Competing Events w41 w w81 w82 w83 w84 9 Time Censored Cancer Other Paul Lambert Cumulative Incidence Functions UKSUG /32
14 Initial data Competing event: d == 2. stset t, failure(d==1,2) id(id) (output omitted ). list id d _t0 _t _d, noobs sep(0) id d _t0 _t _d Paul Lambert Cumulative Incidence Functions UKSUG /32
15 Using stcrprep Competing event: d == 2. stcrprep, events(d) trans(1) noshorten. gen event = d == failcode. stset tstop [iw = weight_c], failure(event) enter(tstart) id(id) (output omitted ). list id d _t0 _t _d weight_c, noobs sep(0) id d _t0 _t _d weight_c Paul Lambert Cumulative Incidence Functions UKSUG /32
16 European Blood and Marrow Transplantation Data 1977 patients from the European Blood and Marrow Transplantation (EBMT) registry who received an allogeneic bone marrow transplantation[6]. Events are death and relapse 836 censored 456 relapse 685 died One covariate of interest, the EBMT risk score, which has been categorized into 3 groups (low, medium and high risk). Paul Lambert Cumulative Incidence Functions UKSUG /32
17 Using stcrprep stcrprep. stset time, failure(status==1,2) scale(365.25) id(patid) (output omitted ). stcrprep, events(status) keep(score) trans(1 2) byg(score). gen event = status == failcode. stset tstop [iw=weight_c], failure(event=1) enter(tstart) noshow (output omitted ) Paul Lambert Cumulative Incidence Functions UKSUG /32
18 Using stcrprep stcrprep. stset time, failure(status==1,2) scale(365.25) id(patid) (output omitted ). stcrprep, events(status) keep(score) trans(1 2) byg(score). gen event = status == failcode. stset tstop [iw=weight_c], failure(event=1) enter(tstart) noshow (output omitted ) We can now estimate the CIF using sts graph. sts graph. sts graph if failcode == 1, by(score) failure // relapse. sts graph if failcode == 2, by(score) failure // death Paul Lambert Cumulative Incidence Functions UKSUG /32
19 Using sts graph to estimate cause-specific CIF 0.5 Kaplan-Meier failure estimates 0.4 Probability of Relapse Low Risk Medium Risk High Risk Years since transplanation Paul Lambert Cumulative Incidence Functions UKSUG /32
20 Testing for difference between cause-specific CIFs Use sts test sts test. sts test score if failcode == 1 Log-rank test for equality of survivor functions Events Events score observed expected Low risk Medium risk High risk Total chi2(2) = Pr>chi2 = Paul Lambert Cumulative Incidence Functions UKSUG /32
21 Testing for difference between cause-specific CIFs Use sts test sts test. sts test score if failcode == 1 Log-rank test for equality of survivor functions Events Events score observed expected Low risk Medium risk High risk Total chi2(2) = Pr>chi2 = Similar to Gray s test [7] since the number at risk is modified when compared to the standard log-rank test. Paul Lambert Cumulative Incidence Functions UKSUG /32
22 Using stcox to fit Fine and Gray Model[9] Use stcrprep without byg() option since Fine and Gray model assumes common censoring distribution.. stcrprep, events(status) keep(score) trans(1 2). stset tstop [iw=weight c], failure(event) enter(tstart) Paul Lambert Cumulative Incidence Functions UKSUG /32
23 Using stcox to fit Fine and Gray Model[9] Use stcrprep without byg() option since Fine and Gray model assumes common censoring distribution. stcox. stcrprep, events(status) keep(score) trans(1 2). stset tstop [iw=weight c], failure(event) enter(tstart). stcox i.score if failcode == 1, nolog Cox regression -- Breslow method for ties No. of subjects = Number of obs = No. of failures = 456 Time at risk = LR chi2(2) = 9.63 Log likelihood = Prob > chi2 = _t Haz. Ratio Std. Err. z P> z [95% Conf. Interval] score Medium risk High risk Paul Lambert Cumulative Incidence Functions UKSUG /32
24 Comparison with stcrreg Comparison of Estimates. estimates table stcrreg stcox*, eq(1) b(%6.5f) se(%6.5f) modelwidth(12) Variable stcrreg stcox stcox_robust score Medium risk High risk legend: b/se Use pweights and vce(cluster id) for robust standard errors. However, Geskus (2011) showed that robust standard errors are less efficient[8]. Paul Lambert Cumulative Incidence Functions UKSUG /32
25 Comparison with stcrreg Comparison of Estimates. estimates table stcrreg stcox*, eq(1) b(%6.5f) se(%6.5f) modelwidth(12) Variable stcrreg stcox stcox_robust score Medium risk High risk legend: b/se Use pweights and vce(cluster id) for robust standard errors. However, Geskus (2011) showed that robust standard errors are less efficient[8]. Perhaps stcrreg should have a norobust option. Paul Lambert Cumulative Incidence Functions UKSUG /32
26 Time Improvements (seconds) EBMT data (1977 subjects) stcrreg stcrprep stcox stcrprep only needs to be run once! Paul Lambert Cumulative Incidence Functions UKSUG /32
27 Time Improvements (seconds) EBMT data (1977 subjects) stcrreg stcrprep stcox stcrprep only needs to be run once! EBMT data 10 (19770 subjects): no ties stcrreg stcrprep stcox - 49 stcrprep only needs to be run once! Paul Lambert Cumulative Incidence Functions UKSUG /32
28 Proportional subhazards (estat phtest) Assess proportional subhazards using Schoenfeld residuals. Paul Lambert Cumulative Incidence Functions UKSUG /32
29 Proportional subhazards (estat phtest) Assess proportional subhazards using Schoenfeld residuals.. estat phtest, Test of proportional-hazards assumption Time: Time chi2 df Prob>chi2 global test Paul Lambert Cumulative Incidence Functions UKSUG /32
30 Proportional subhazards (estat phtest) Assess proportional subhazards using Schoenfeld residuals.. estat phtest, Test of proportional-hazards assumption Time: Time chi2 df Prob>chi2 global test Schoenfeld Residuals for High Risk Group Exponentiated scaled Schoenfeld residual Years since transplanation Paul Lambert Cumulative Incidence Functions UKSUG /32
31 Summary (part 1) Non-parametric estimates of CIF using sts graph. Other exploratory analysis (stphplot, stcoxkm) stcrprep allows fitting of Fine and Gray models with substantial speed improvements. A number of extensions to what is available in stcrreg. Schoenfeld like residuals (estat phtest) [10] Stratified models (strata()) [11]. Stacked models share parameters over different events. Tests need a more in depth study of their properties. Paul Lambert Cumulative Incidence Functions UKSUG /32
32 Parametric approach Previous parametric models of the CIF required modelling of all K causes [12, 13]. After using stcrprep we can fit a parametric equivalent of the Fine and Gray model Paul Lambert Cumulative Incidence Functions UKSUG /32
33 Parametric approach Previous parametric models of the CIF required modelling of all K causes [12, 13]. After using stcrprep we can fit a parametric equivalent of the Fine and Gray model Only need to model cause of interest. Useful for predictions, quantifying differences and non-proportional subhazards. Faster than Fine and Gray model as fewer splits (uses an approximation). Paul Lambert Cumulative Incidence Functions UKSUG /32
34 Parametric approach For those with competing events, allow to be at risk to end of potential follow-up. Split follow-up after competing event into (small) time-intervals. Apply weights to each interval. Likelihood ln L i = d 1i ln [h 1 (t i )] + (1 d 2i ) ln [S(t i )] + d 2i J i j=1 w ij ( ln [S(tij )] ln [ S(t i(j 1) ) ]) Need to specify parametric form of CIF for event of interest, but not for competing events. Also need weighting function. Obtained by modelling censoring distribution. Paul Lambert Cumulative Incidence Functions UKSUG /32
35 Splitting Event 1 Event 2 Censored Time Paul Lambert Cumulative Incidence Functions UKSUG /32
36 Splitting Event 1 Event 2 Censored Time Paul Lambert Cumulative Incidence Functions UKSUG /32
37 Splitting Event 1 Event 2 Censored Time Paul Lambert Cumulative Incidence Functions UKSUG /32
38 Splitting Event 1 Event 2 w 1 w 2 w 3 w 4 w 5 Censored Time Paul Lambert Cumulative Incidence Functions UKSUG /32
39 The censoring distribution Fit a parametric model stpm2, Option to include a variety of covariates. Also to model time-dependent effects. stcrreg assumes common censoring distribution. Need to decide where to evaluate censoring distribution (number of split points) for weighted likelihood. Paul Lambert Cumulative Incidence Functions UKSUG /32
40 Flexible parametric models Possible to use any parametric approach that allows for delayed entry and weights. We use flexible parametric survival models that uses restricted splines to model the baseline using stpm2 in Stata. [14, 15]. g[s(t x i )] = η i = s (ln(t) γ, k 0 ) + x i β where s (ln(t) γ, k 0 ) is a restricted cubic spline function of ln(t) with knots, k 0. g() is a link function. Paul Lambert Cumulative Incidence Functions UKSUG /32
41 Link Functions When using weights with expanded data proportional sub hazards log( log (1 CIF k (t x i ))) = s (ln(t) γ, k 0 ) + x i β proportional odds log relative absolute risk ( CIFk (t x i ) ) 1 CIF k (t x i ) = s (ln(t) γ, k 0 ) + x i β log (CIF k (t x i )) = s (ln(t) γ, k 0 ) + x i β Paul Lambert Cumulative Incidence Functions UKSUG /32
42 Link Functions When using weights with expanded data proportional sub hazards log( log (1 CIF k (t x i ))) = s (ln(t) γ, k 0 ) + x i β proportional odds log relative absolute risk ( CIFk (t x i ) ) 1 CIF k (t x i ) = s (ln(t) γ, k 0 ) + x i β log (CIF k (t x i )) = s (ln(t) γ, k 0 ) + x i β Time-dependent effects can be fitted for any of these link functions. Paul Lambert Cumulative Incidence Functions UKSUG /32
43 Parametric proportional subhazards models 1 stcrprep. stset time, failure(status==1,2) scale(365.25) id(patid) (output omitted ). stcrprep, events(status) keep(score) trans(1 2) censstpm2 every(0.2). gen event = status == failcode. stset tstop [iw=weight_c], failure(event) enter(tstart) noshow failure event: event!= 0 & event <. obs. time interval: (0, tstop] enter on or after: time tstart exit on or before: failure weight: [iweight=weight_c] total observations 0 exclusions observations remaining, representing 1141 failures in single-record/single-failure data total analysis time at risk and under observation at risk from t = 0 earliest observed entry t = 0 last observed exit t = Paul Lambert Cumulative Incidence Functions UKSUG /32
44 Parametric proportional subhazards models 2 stpm2. stpm2 i.score if failcode == 1, scale(hazard) df(4) eform nolog note: delayed entry models are being fitted Log likelihood = Number of obs = exp(b) Std. Err. z P> z [95% Conf. Interval] xb score Medium risk High risk _rcs _rcs _rcs _rcs _cons Paul Lambert Cumulative Incidence Functions UKSUG /32
45 Parametric proportional subhazards models 2 stpm2. stpm2 i.score if failcode == 1, scale(hazard) df(4) eform nolog note: delayed entry models are being fitted Log likelihood = Number of obs = exp(b) Std. Err. z P> z [95% Conf. Interval] xb score Medium risk High risk _rcs _rcs _rcs _rcs _cons Sub-hazard ratios very similar to semi-parametric estimates. Paul Lambert Cumulative Incidence Functions UKSUG /32
46 Predictions of CIF predict cif, failure 0.5 Proportional subhazards 0.5 Non-proportional subhazards Probability of Relapse Probability of Relapse Low Risk Medium Risk Years since transplanation 0.0 High Risk Years since transplanation Paul Lambert Cumulative Incidence Functions UKSUG /32
47 Difference in CIFs. predict CIF diff, sdiff1(score2 0 score3 0) sdiff2(score3 1) ci Difference in Probability of Relapse Years since transplanation Paul Lambert Cumulative Incidence Functions UKSUG /32
48 Difference in CIFs. predict CIF diff, sdiff1(score2 0 score3 0) sdiff2(score3 1) ci Difference in Probability of Relapse Years since transplanation Take reciprocal to estimate Number Needed to Treat (NNT) accounting for competing risks[16] Paul Lambert Cumulative Incidence Functions UKSUG /32
49 Relative absolute risks stpm2. stpm2 i.score if failcode == 1, scale(log) df(4) eform nolog note: delayed entry models are being fitted Log likelihood = Number of obs = exp(b) Std. Err. z P> z [95% Conf. Interval] xb score Medium risk High risk _rcs _rcs _rcs _rcs _cons Paul Lambert Cumulative Incidence Functions UKSUG /32
50 Relative absolute risks stpm2. stpm2 i.score if failcode == 1, scale(log) df(4) eform nolog note: delayed entry models are being fitted Log likelihood = Number of obs = exp(b) Std. Err. z P> z [95% Conf. Interval] xb score Medium risk High risk _rcs _rcs _rcs _rcs _cons Effect sizes are now relative risks rather than subhazard ratios. Assumed constant over time, but this can be relaxed. Paul Lambert Cumulative Incidence Functions UKSUG /32
51 Summary (part 2) Parametric version of Fine and Gray model. Only need to model event of interest to estimate CIF. Models on a variety of scales. Can relax the proportionality assumption. Paul Lambert Cumulative Incidence Functions UKSUG /32
52 Summary (part 2) Parametric version of Fine and Gray model. Only need to model event of interest to estimate CIF. Models on a variety of scales. Can relax the proportionality assumption. Need to choose split times, but can be fairly crude. When modelling competing risks, still useful to model cause-specific hazards. See stpm2cif[5] Paul Lambert Cumulative Incidence Functions UKSUG /32
53 References [1] Andersen PK, Abildstrom SZ, Rosthøj S. Competing risks as a multi-state model. Stat Methods Med Res 2002;11: [2] Coviello V, Boggess M. Cumulative incidence estimation in the presence of competing risks. The Stata Journal 2004;4: [3] Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Statistics in Medicine 2007;26: [4] Hinchliffe SR, Lambert P. Flexible parametric modelling of cause-specific hazards to estimate cumulative incidence functions. BMC Medical Research Methodology 2013;13:13. [5] Hinchliffe SR, Lambert P. Extending the flexible parametric survival model for competing risks. The Stata Journal 2013;13: [6] de Wreede L, Fiocco M, Putter H. mstate: An r package for the analysis of competing risks and multi-state models. Journal of Statistical Software 2011;38. [7] Gray R. A class of k-sample tests for comparing the cumulative incidence of a competing risk. The Annals of Statistics 1988;16: [8] Geskus RB. Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. Biometrics 2011;67: [9] Fine JP, Gray RJ. A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association 1999;446: [10] Zhou B, Fine J, Laird G. Goodness-of-fit test for proportional subdistribution hazards model. Stat Med 2013;. [11] Zhou B, Latouche A, Rocha V, Fine J. Competing risks regression for stratified data. Biometrics 2011;67: [12] Jeong JH, Fine JP. Parametric regression on cumulative incidence function. Biostatistics 2007;8: [13] Jeong JH, Fine JP. Direct parametric inference for the cumulative incidence function. Applied Statistics 2006;55: [14] Lambert PC, Royston P. Further development of flexible parametric models for survival analysis. The Stata Journal 2009;9: [15] Royston P, Lambert PC. Flexible parametric survival analysis in Stata: Beyond the Cox model. Stata Press, [16] Gouskova NA, Kundu S, Imreyb PB, Fine JP. Number needed to treat for time-to-event data with competing risks. Statistics in Medicine 2013;(in press). Paul Lambert Cumulative Incidence Functions UKSUG /32
Competing-risks regression
Competing-risks regression Roberto G. Gutierrez Director of Statistics StataCorp LP Stata Conference Boston 2010 R. Gutierrez (StataCorp) Competing-risks regression July 15-16, 2010 1 / 26 Outline 1. Overview
Introduction. Survival Analysis. Censoring. Plan of Talk
Survival Analysis Mark Lunt Arthritis Research UK Centre for Excellence in Epidemiology University of Manchester 01/12/2015 Survival Analysis is concerned with the length of time before an event occurs.
Relative survival an introduction and recent developments
Relative survival an introduction and recent developments Paul W. Dickman Department of Medical Epidemiology and Biostatistics Karolinska Institutet, Stockholm, Sweden paul.dickman@ki.se 11 December 2008
Topic 3 - Survival Analysis
Topic 3 - Survival Analysis 1. Topics...2 2. Learning objectives...3 3. Grouped survival data - leukemia example...4 3.1 Cohort survival data schematic...5 3.2 Tabulation of events and time at risk...6
SAS and R calculations for cause specific hazard ratios in a competing risks analysis with time dependent covariates
SAS and R calculations for cause specific hazard ratios in a competing risks analysis with time dependent covariates Martin Wolkewitz, Ralf Peter Vonberg, Hajo Grundmann, Jan Beyersmann, Petra Gastmeier,
SUMAN DUVVURU STAT 567 PROJECT REPORT
SUMAN DUVVURU STAT 567 PROJECT REPORT SURVIVAL ANALYSIS OF HEROIN ADDICTS Background and introduction: Current illicit drug use among teens is continuing to increase in many countries around the world.
III. INTRODUCTION TO LOGISTIC REGRESSION. a) Example: APACHE II Score and Mortality in Sepsis
III. INTRODUCTION TO LOGISTIC REGRESSION 1. Simple Logistic Regression a) Example: APACHE II Score and Mortality in Sepsis The following figure shows 30 day mortality in a sample of septic patients as
Missing data and net survival analysis Bernard Rachet
Workshop on Flexible Models for Longitudinal and Survival Data with Applications in Biostatistics Warwick, 27-29 July 2015 Missing data and net survival analysis Bernard Rachet General context Population-based,
Introduction to Event History Analysis DUSTIN BROWN POPULATION RESEARCH CENTER
Introduction to Event History Analysis DUSTIN BROWN POPULATION RESEARCH CENTER Objectives Introduce event history analysis Describe some common survival (hazard) distributions Introduce some useful Stata
Handling missing data in Stata a whirlwind tour
Handling missing data in Stata a whirlwind tour 2012 Italian Stata Users Group Meeting Jonathan Bartlett www.missingdata.org.uk 20th September 2012 1/55 Outline The problem of missing data and a principled
The Cox Proportional Hazards Model
The Cox Proportional Hazards Model Mario Chen, PhD Advanced Biostatistics and RCT Workshop Office of AIDS Research, NIH ICSSC, FHI Goa, India, September 2009 1 The Model h i (t)=h 0 (t)exp(z i ), Z i =
Lecture 2 ESTIMATING THE SURVIVAL FUNCTION. One-sample nonparametric methods
Lecture 2 ESTIMATING THE SURVIVAL FUNCTION One-sample nonparametric methods There are commonly three methods for estimating a survivorship function S(t) = P (T > t) without resorting to parametric models:
The Landmark Approach: An Introduction and Application to Dynamic Prediction in Competing Risks
Landmarking and landmarking Landmarking and competing risks Discussion The Landmark Approach: An Introduction and Application to Dynamic Prediction in Competing Risks Department of Medical Statistics and
Duration Analysis. Econometric Analysis. Dr. Keshab Bhattarai. April 4, 2011. Hull Univ. Business School
Duration Analysis Econometric Analysis Dr. Keshab Bhattarai Hull Univ. Business School April 4, 2011 Dr. Bhattarai (Hull Univ. Business School) Duration April 4, 2011 1 / 27 What is Duration Analysis?
Regression Modeling Strategies
Frank E. Harrell, Jr. Regression Modeling Strategies With Applications to Linear Models, Logistic Regression, and Survival Analysis With 141 Figures Springer Contents Preface Typographical Conventions
Comparing the predictive power of survival models using Harrell s c or Somers D
The Stata Journal (yyyy) vv, Number ii, pp. 1 19 Comparing the predictive power of survival models using Harrell s c or Somers D Roger B. Newson National Heart and Lung Institute, Imperial College London
Module 14: Missing Data Stata Practical
Module 14: Missing Data Stata Practical Jonathan Bartlett & James Carpenter London School of Hygiene & Tropical Medicine www.missingdata.org.uk Supported by ESRC grant RES 189-25-0103 and MRC grant G0900724
Comparison of Survival Curves
Comparison of Survival Curves We spent the last class looking at some nonparametric approaches for estimating the survival function, Ŝ(t), over time for a single sample of individuals. Now we want to compare
How to set the main menu of STATA to default factory settings standards
University of Pretoria Data analysis for evaluation studies Examples in STATA version 11 List of data sets b1.dta (To be created by students in class) fp1.xls (To be provided to students) fp1.txt (To be
especially with continuous
Handling interactions in Stata, especially with continuous predictors Patrick Royston & Willi Sauerbrei German Stata Users meeting, Berlin, 1 June 2012 Interactions general concepts General idea of a (two-way)
Survival analysis methods in Insurance Applications in car insurance contracts
Survival analysis methods in Insurance Applications in car insurance contracts Abder OULIDI 1-2 Jean-Marie MARION 1 Hérvé GANACHAUD 3 1 Institut de Mathématiques Appliquées (IMA) Angers France 2 Institut
Adequacy of Biomath. Models. Empirical Modeling Tools. Bayesian Modeling. Model Uncertainty / Selection
Directions in Statistical Methodology for Multivariable Predictive Modeling Frank E Harrell Jr University of Virginia Seattle WA 19May98 Overview of Modeling Process Model selection Regression shape Diagnostics
Title. Syntax. stata.com. fp Fractional polynomial regression. Estimation
Title stata.com fp Fractional polynomial regression Syntax Menu Description Options for fp Options for fp generate Remarks and examples Stored results Methods and formulas Acknowledgment References Also
Tips for surviving the analysis of survival data. Philip Twumasi-Ankrah, PhD
Tips for surviving the analysis of survival data Philip Twumasi-Ankrah, PhD Big picture In medical research and many other areas of research, we often confront continuous, ordinal or dichotomous outcomes
Dealing with Missing Data
Dealing with Missing Data Roch Giorgi email: roch.giorgi@univ-amu.fr UMR 912 SESSTIM, Aix Marseille Université / INSERM / IRD, Marseille, France BioSTIC, APHM, Hôpital Timone, Marseille, France January
Checking proportionality for Cox s regression model
Checking proportionality for Cox s regression model by Hui Hong Zhang Thesis for the degree of Master of Science (Master i Modellering og dataanalyse) Department of Mathematics Faculty of Mathematics and
Multinomial and Ordinal Logistic Regression
Multinomial and Ordinal Logistic Regression ME104: Linear Regression Analysis Kenneth Benoit August 22, 2012 Regression with categorical dependent variables When the dependent variable is categorical,
The first three steps in a logistic regression analysis with examples in IBM SPSS. Steve Simon P.Mean Consulting www.pmean.com
The first three steps in a logistic regression analysis with examples in IBM SPSS. Steve Simon P.Mean Consulting www.pmean.com 2. Why do I offer this webinar for free? I offer free statistics webinars
Time varying (or time-dependent) covariates
Chapter 9 Time varying (or time-dependent) covariates References: Allison (*) p.138-153 Hosmer & Lemeshow Chapter 7, Section 3 Kalbfleisch & Prentice Section 5.3 Collett Chapter 7 Kleinbaum Chapter 6 Cox
Applied Statistics. J. Blanchet and J. Wadsworth. Institute of Mathematics, Analysis, and Applications EPF Lausanne
Applied Statistics J. Blanchet and J. Wadsworth Institute of Mathematics, Analysis, and Applications EPF Lausanne An MSc Course for Applied Mathematicians, Fall 2012 Outline 1 Model Comparison 2 Model
Advanced Quantitative Methods for Health Care Professionals PUBH 742 Spring 2015
1 Advanced Quantitative Methods for Health Care Professionals PUBH 742 Spring 2015 Instructor: Joanne M. Garrett, PhD e-mail: joanne_garrett@med.unc.edu Class Notes: Copies of the class lecture slides
HURDLE AND SELECTION MODELS Jeff Wooldridge Michigan State University BGSE/IZA Course in Microeconometrics July 2009
HURDLE AND SELECTION MODELS Jeff Wooldridge Michigan State University BGSE/IZA Course in Microeconometrics July 2009 1. Introduction 2. A General Formulation 3. Truncated Normal Hurdle Model 4. Lognormal
Survival Analysis, Software
Survival Analysis, Software As used here, survival analysis refers to the analysis of data where the response variable is the time until the occurrence of some event (e.g. death), where some of the observations
Predicting Customer Default Times using Survival Analysis Methods in SAS
Predicting Customer Default Times using Survival Analysis Methods in SAS Bart Baesens Bart.Baesens@econ.kuleuven.ac.be Overview The credit scoring survival analysis problem Statistical methods for Survival
Survival Analysis of the Patients Diagnosed with Non-Small Cell Lung Cancer Using SAS Enterprise Miner 13.1
Paper 11682-2016 Survival Analysis of the Patients Diagnosed with Non-Small Cell Lung Cancer Using SAS Enterprise Miner 13.1 Raja Rajeswari Veggalam, Akansha Gupta; SAS and OSU Data Mining Certificate
Failure to take the sampling scheme into account can lead to inaccurate point estimates and/or flawed estimates of the standard errors.
Analyzing Complex Survey Data: Some key issues to be aware of Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised January 24, 2015 Rather than repeat material that is
Statistics in Retail Finance. Chapter 6: Behavioural models
Statistics in Retail Finance 1 Overview > So far we have focussed mainly on application scorecards. In this chapter we shall look at behavioural models. We shall cover the following topics:- Behavioural
Statistics 104 Final Project A Culture of Debt: A Study of Credit Card Spending in America TF: Kevin Rader Anonymous Students: LD, MH, IW, MY
Statistics 104 Final Project A Culture of Debt: A Study of Credit Card Spending in America TF: Kevin Rader Anonymous Students: LD, MH, IW, MY ABSTRACT: This project attempted to determine the relationship
Marginal Effects for Continuous Variables Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised February 21, 2015
Marginal Effects for Continuous Variables Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised February 21, 2015 References: Long 1997, Long and Freese 2003 & 2006 & 2014,
Survival Analysis And The Application Of Cox's Proportional Hazards Modeling Using SAS
Paper 244-26 Survival Analysis And The Application Of Cox's Proportional Hazards Modeling Using SAS Tyler Smith, and Besa Smith, Department of Defense Center for Deployment Health Research, Naval Health
An Application of the G-formula to Asbestos and Lung Cancer. Stephen R. Cole. Epidemiology, UNC Chapel Hill. Slides: www.unc.
An Application of the G-formula to Asbestos and Lung Cancer Stephen R. Cole Epidemiology, UNC Chapel Hill Slides: www.unc.edu/~colesr/ 1 Acknowledgements Collaboration with David B. Richardson, Haitao
From this it is not clear what sort of variable that insure is so list the first 10 observations.
MNL in Stata We have data on the type of health insurance available to 616 psychologically depressed subjects in the United States (Tarlov et al. 1989, JAMA; Wells et al. 1989, JAMA). The insurance is
outreg help pages Write formatted regression output to a text file After any estimation command: (Text-related options)
outreg help pages OUTREG HELP PAGES... 1 DESCRIPTION... 2 OPTIONS... 3 1. Text-related options... 3 2. Coefficient options... 4 3. Options for t statistics, standard errors, etc... 5 4. Statistics options...
Complex Survey Design Using Stata
Complex Survey Design Using Stata 2010 This document provides a basic overview of how to handle complex survey design using Stata. Probability weighting and compensating for clustered and stratified samples
Interaction effects and group comparisons Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised February 20, 2015
Interaction effects and group comparisons Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised February 20, 2015 Note: This handout assumes you understand factor variables,
Tests for Two Survival Curves Using Cox s Proportional Hazards Model
Chapter 730 Tests for Two Survival Curves Using Cox s Proportional Hazards Model Introduction A clinical trial is often employed to test the equality of survival distributions of two treatment groups.
xtmixed & denominator degrees of freedom: myth or magic
xtmixed & denominator degrees of freedom: myth or magic 2011 Chicago Stata Conference Phil Ender UCLA Statistical Consulting Group July 2011 Phil Ender xtmixed & denominator degrees of freedom: myth or
Modeling the Claim Duration of Income Protection Insurance Policyholders Using Parametric Mixture Models
Modeling the Claim Duration of Income Protection Insurance Policyholders Using Parametric Mixture Models Abstract This paper considers the modeling of claim durations for existing claimants under income
Multivariable survival analysis S10. Michael Hauptmann Netherlands Cancer Institute Amsterdam, The Netherlands
Multivariable survival analysis S10 Michael Hauptmann Netherlands Cancer Institute Amsterdam, The Netherlands m.hauptmann@nki.nl 1 Confounding A variable correlated with the variable of interest and with
SAS Software to Fit the Generalized Linear Model
SAS Software to Fit the Generalized Linear Model Gordon Johnston, SAS Institute Inc., Cary, NC Abstract In recent years, the class of generalized linear models has gained popularity as a statistical modeling
From the help desk: hurdle models
The Stata Journal (2003) 3, Number 2, pp. 178 184 From the help desk: hurdle models Allen McDowell Stata Corporation Abstract. This article demonstrates that, although there is no command in Stata for
Survival Analysis of Left Truncated Income Protection Insurance Data. [March 29, 2012]
![Survival Analysis of Left Truncated Income Protection Insurance Data. [March 29, 2012]](/thumbs/25/5205543.jpg "Survival Analysis of Left Truncated Income Protection Insurance Data. [March 29, 2012]")
Survival Analysis of Left Truncated Income Protection Insurance Data [March 29, 2012] 1 Qing Liu 2 David Pitt 3 Yan Wang 4 Xueyuan Wu Abstract One of the main characteristics of Income Protection Insurance
Development of the nomolog program and its evolution
Development of the nomolog program and its evolution Towards the implementation of a nomogram generator for the Cox regression Alexander Zlotnik, Telecom.Eng. Víctor Abraira Santos, PhD Ramón y Cajal University
11. Analysis of Case-control Studies Logistic Regression
Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
ECON 142 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE #2
University of California, Berkeley Prof. Ken Chay Department of Economics Fall Semester, 005 ECON 14 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE # Question 1: a. Below are the scatter plots of hourly wages
Interpretation of Somers D under four simple models
Interpretation of Somers D under four simple models Roger B. Newson 03 September, 04 Introduction Somers D is an ordinal measure of association introduced by Somers (96)[9]. It can be defined in terms
Correlation and Regression
Correlation and Regression Scatterplots Correlation Explanatory and response variables Simple linear regression General Principles of Data Analysis First plot the data, then add numerical summaries Look
Life Tables. Marie Diener-West, PhD Sukon Kanchanaraksa, PhD
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
ESTIMATING AVERAGE TREATMENT EFFECTS: IV AND CONTROL FUNCTIONS, II Jeff Wooldridge Michigan State University BGSE/IZA Course in Microeconometrics
ESTIMATING AVERAGE TREATMENT EFFECTS: IV AND CONTROL FUNCTIONS, II Jeff Wooldridge Michigan State University BGSE/IZA Course in Microeconometrics July 2009 1. Quantile Treatment Effects 2. Control Functions
From the help desk: Bootstrapped standard errors
The Stata Journal (2003) 3, Number 1, pp. 71 80 From the help desk: Bootstrapped standard errors Weihua Guan Stata Corporation Abstract. Bootstrapping is a nonparametric approach for evaluating the distribution
Chapter 18. Effect modification and interactions. 18.1 Modeling effect modification
Chapter 18 Effect modification and interactions 18.1 Modeling effect modification weight 40 50 60 70 80 90 100 male female 40 50 60 70 80 90 100 male female 30 40 50 70 dose 30 40 50 70 dose Figure 18.1:
BIOM611 Biological Data Analysis
BIOM611 Biological Data Analysis Spring, 2015 Tentative Syllabus Introduction BIOMED611 is a ½ unit course required for all 1 st year BGS students (except GCB students). It will provide an introduction
Nonlinear Regression Functions. SW Ch 8 1/54/
Nonlinear Regression Functions SW Ch 8 1/54/ The TestScore STR relation looks linear (maybe) SW Ch 8 2/54/ But the TestScore Income relation looks nonlinear... SW Ch 8 3/54/ Nonlinear Regression General
Advanced Statistical Analysis of Mortality. Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc. 160 University Avenue. Westwood, MA 02090
Advanced Statistical Analysis of Mortality Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc 160 University Avenue Westwood, MA 02090 001-(781)-751-6356 fax 001-(781)-329-3379 trhodes@mib.com Abstract
Modelling spousal mortality dependence: evidence of heterogeneities and implications
1/23 Modelling spousal mortality dependence: evidence of heterogeneities and implications Yang Lu Scor and Aix-Marseille School of Economics Lyon, September 2015 2/23 INTRODUCTION 3/23 Motivation It has
Nonlinear relationships Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised February 20, 2015
Nonlinear relationships Richard Williams, University of Notre Dame, http://www.nd.edu/~rwilliam/ Last revised February, 5 Sources: Berry & Feldman s Multiple Regression in Practice 985; Pindyck and Rubinfeld
Please follow the directions once you locate the Stata software in your computer. Room 114 (Business Lab) has computers with Stata software
STATA Tutorial Professor Erdinç Please follow the directions once you locate the Stata software in your computer. Room 114 (Business Lab) has computers with Stata software 1.Wald Test Wald Test is used
Statistics 305: Introduction to Biostatistical Methods for Health Sciences
Statistics 305: Introduction to Biostatistical Methods for Health Sciences Modelling the Log Odds Logistic Regression (Chap 20) Instructor: Liangliang Wang Statistics and Actuarial Science, Simon Fraser
MODEL CHECK AND GOODNESS-OF-FIT FOR NESTED CASE-CONTROL STUDIES
MODEL CHECK AND GOODNESS-OF-FIT FOR NESTED CASE-CONTROL STUDIES by YING ZHANG THESIS for the degree of MASTER OF SCIENCE (Master i Modellering og dataanalyse) Faculty of Mathematics and Natural Sciences
Guide to Biostatistics
MedPage Tools Guide to Biostatistics Study Designs Here is a compilation of important epidemiologic and common biostatistical terms used in medical research. You can use it as a reference guide when reading
Lecture 15 Introduction to Survival Analysis
Lecture 15 Introduction to Survival Analysis BIOST 515 February 26, 2004 BIOST 515, Lecture 15 Background In logistic regression, we were interested in studying how risk factors were associated with presence
Department of Economics Session 2012/2013. EC352 Econometric Methods. Solutions to Exercises from Week 10 + 0.0077 (0.052)
Department of Economics Session 2012/2013 University of Essex Spring Term Dr Gordon Kemp EC352 Econometric Methods Solutions to Exercises from Week 10 1 Problem 13.7 This exercise refers back to Equation
SPSS Notes (SPSS version 15.0)
SPSS Notes (SPSS version 15.0) Annie Herbert Salford Royal Hospitals NHS Trust July 2008 Contents Page Getting Started 1 1 Opening SPSS 1 2 Layout of SPSS 2 2.1 Windows 2 2.2 Saving Files 3 3 Creating
Editor Executive Editor Associate Editors Copyright Statement:
The Stata Journal Editor H. Joseph Newton Department of Statistics Texas A & M University College Station, Texas 77843 979-845-3142 979-845-3144 FAX jnewton@stata-journal.com Associate Editors Christopher
Lab 5 Linear Regression with Within-subject Correlation. Goals: Data: Use the pig data which is in wide format:
Lab 5 Linear Regression with Within-subject Correlation Goals: Data: Fit linear regression models that account for within-subject correlation using Stata. Compare weighted least square, GEE, and random
Using Stata for Categorical Data Analysis
Using Stata for Categorical Data Analysis NOTE: These problems make extensive use of Nick Cox s tab_chi, which is actually a collection of routines, and Adrian Mander s ipf command. From within Stata,
11 Logistic Regression - Interpreting Parameters
11 Logistic Regression - Interpreting Parameters Let us expand on the material in the last section, trying to make sure we understand the logistic regression model and can interpret Stata output. Consider
Missing Data in Longitudinal Studies: To Impute or not to Impute? Robert Platt, PhD McGill University
Missing Data in Longitudinal Studies: To Impute or not to Impute? Robert Platt, PhD McGill University 1 Outline Missing data definitions Longitudinal data specific issues Methods Simple methods Multiple
10 Dichotomous or binary responses
10 Dichotomous or binary responses 10.1 Introduction Dichotomous or binary responses are widespread. Examples include being dead or alive, agreeing or disagreeing with a statement, and succeeding or failing
Methods for Meta-analysis in Medical Research
Methods for Meta-analysis in Medical Research Alex J. Sutton University of Leicester, UK Keith R. Abrams University of Leicester, UK David R. Jones University of Leicester, UK Trevor A. Sheldon University
Confidence Intervals for Exponential Reliability
Chapter 408 Confidence Intervals for Exponential Reliability Introduction This routine calculates the number of events needed to obtain a specified width of a confidence interval for the reliability (proportion
Analysis of Population Cancer Risk Factors in National Information System SVOD
Analysis of Population Cancer Risk Factors in National Information System SVOD Mužík J. 1, Dušek L. 1,2, Pavliš P. 1, Koptíková J. 1, Žaloudík J. 3, Vyzula R. 3 Abstract Human risk assessment requires
Statistics Graduate Courses
Statistics Graduate Courses STAT 7002--Topics in Statistics-Biological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
200609 - ATV - Lifetime Data Analysis
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2015 200 - FME - School of Mathematics and Statistics 715 - EIO - Department of Statistics and Operations Research 1004 - UB - (ENG)Universitat
Generalized Linear Models
Generalized Linear Models We have previously worked with regression models where the response variable is quantitative and normally distributed. Now we turn our attention to two types of models where the
Survival Distributions, Hazard Functions, Cumulative Hazards
Week 1 Survival Distributions, Hazard Functions, Cumulative Hazards 1.1 Definitions: The goals of this unit are to introduce notation, discuss ways of probabilistically describing the distribution of a
Ordinal Regression. Chapter
Ordinal Regression Chapter 4 Many variables of interest are ordinal. That is, you can rank the values, but the real distance between categories is unknown. Diseases are graded on scales from least severe
Statistics in Medicine Research Lecture Series CSMC Fall 2014
Catherine Bresee, MS Senior Biostatistician Biostatistics & Bioinformatics Research Institute Statistics in Medicine Research Lecture Series CSMC Fall 2014 Overview Review concept of statistical power
Quantifying Life expectancy in people with Type 2 diabetes
School of Public Health University of Sydney Quantifying Life expectancy in people with Type 2 diabetes Alison Hayes School of Public Health University of Sydney The evidence Life expectancy reduced by
Randomized trials versus observational studies
Randomized trials versus observational studies The case of postmenopausal hormone therapy and heart disease Miguel Hernán Harvard School of Public Health www.hsph.harvard.edu/causal Joint work with James
Discussion Section 4 ECON 139/239 2010 Summer Term II
Discussion Section 4 ECON 139/239 2010 Summer Term II 1. Let s use the CollegeDistance.csv data again. (a) An education advocacy group argues that, on average, a person s educational attainment would increase
Institut für Soziologie Eberhard Karls Universität Tübingen www.maartenbuis.nl
from Indirect Extracting from Institut für Soziologie Eberhard Karls Universität Tübingen www.maartenbuis.nl from Indirect What is the effect of x on y? Which effect do I choose: average marginal or marginal
Vignette for survrm2 package: Comparing two survival curves using the restricted mean survival time
Vignette for survrm2 package: Comparing two survival curves using the restricted mean survival time Hajime Uno Dana-Farber Cancer Institute March 16, 2015 1 Introduction In a comparative, longitudinal
Comparison of resampling method applied to censored data
International Journal of Advanced Statistics and Probability, 2 (2) (2014) 48-55 c Science Publishing Corporation www.sciencepubco.com/index.php/ijasp doi: 10.14419/ijasp.v2i2.2291 Research Paper Comparison
Nested Logit. Brad Jones 1. April 30, 2008. University of California, Davis. 1 Department of Political Science. POL 213: Research Methods
Nested Logit Brad 1 1 Department of Political Science University of California, Davis April 30, 2008 Nested Logit Interesting model that does not have IIA property. Possible candidate model for structured
13. Poisson Regression Analysis
136 Poisson Regression Analysis 13. Poisson Regression Analysis We have so far considered situations where the outcome variable is numeric and Normally distributed, or binary. In clinical work one often
Sophie ANCELET, IRSN/PRP-HOM/SRBE/LEPID
Quantitative assessment of the childhood leukemia risks related to natural background radiation in France, exploring the impacts of uncertainty in risk models and parameters Sophie ANCELET, IRSN/PRP-HOM/SRBE/LEPID
Modeling Customer Lifetime Value Using Survival Analysis An Application in the Telecommunications Industry
Paper 12028 Modeling Customer Lifetime Value Using Survival Analysis An Application in the Telecommunications Industry Junxiang Lu, Ph.D. Overland Park, Kansas ABSTRACT Increasingly, companies are viewing
Interaction effects between continuous variables (Optional)
Interaction effects between continuous variables (Optional) Richard Williams, University of Notre Dame, http://www.nd.edu/~rwilliam/ Last revised February 0, 05 This is a very brief overview of this somewhat
SPSS TRAINING SESSION 3 ADVANCED TOPICS (PASW STATISTICS 17.0) Sun Li Centre for Academic Computing lsun@smu.edu.sg
SPSS TRAINING SESSION 3 ADVANCED TOPICS (PASW STATISTICS 17.0) Sun Li Centre for Academic Computing lsun@smu.edu.sg IN SPSS SESSION 2, WE HAVE LEARNT: Elementary Data Analysis Group Comparison & One-way