Biostatistical Methods: The Assessment of Relative Risks

by John M. Lachin (The George Washington Univ., Washington, D.C.)

• ISBN13: 9780471369967
• ISBN10: 0471369969
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-05-01
• Publisher: Wiley-Interscience

Summary

Supplemented with numerous graphs, charts, and tables as well as a Web site for larger data sets and exercises, Biostatistical Methods: The Assessment of Relative Risks is an excellent guide for graduate-level students in biostatistics and an invaluable reference for biostatisticians, applied statisticians, and epidemiologists.

Author Biography

<b>JOHN M. LACHIN, ScD</b>, is Professor of Statistics and Biostatistics at the George Washington University in Washington, D.C., and Director of the Biostatistics Center in Rockville, Maryland.

Table of Contents

Preface	xv
Biostatistics and Biomedical Science	1	(12)
Statistics and the Scientific Method	1	(1)
Biostatistics	2	(1)
Natural History of Disease Progression	3	(2)
Types of Biomedical Studies	5	(2)
Studies of Diabetic Nephropathy	7	(6)
Relative Risk Estimates and Tests for Two Independent Groups	13	(48)
Probability As a Measure of Risk	14	(5)
Prevalence and Incidence	14	(1)
Binomial Distribution and Large Sample Approximations	14	(1)
Asymmetric Confidence Limits	15	(4)
Case of Zero Events	19	(1)
Measures of Relative Risk	19	(4)
Large Sample Distribution	23	(5)
Risk Difference	23	(1)
Relative Risk	24	(2)
Odds Ratio	26	(2)
Sampling Models: - Likelihoods	28	(4)
Unconditional Product Binomial Likelihood	28	(1)
Conditional Hypergeometric Likelihood	28	(1)
Maximum Likelihood Estimates	29	(1)
Asymptotically Unbiased Estimates	30	(2)
Exact Inference	32	(4)
Confidence Limits	32	(1)
Fisher-Irwin Exact Test	33	(3)
Large Sample Tests	36	(9)
General Considerations	36	(3)
Unconditional Test	39	(1)
Conditional Mantel-Haenszel Test	40	(1)
Cochran's Test	40	(2)
Likelihood Ratio Test	42	(1)
Test-Based Confidence Limits	43	(1)
Continuity Correction	44	(1)
SAS PROC FREQ	45	(5)
Other Measures of Differential Risk	50	(4)
Attributable Risk Fraction	50	(1)
Population Attributable Risk	50	(3)
Number Needed to Treat	53	(1)
Problems	54	(7)
Sample Size, Power, and Efficiency	61	(26)
Estimation Precision	62	(1)
Power of Z-Tests	63	(5)
Type I and II Errors and Power	63	(4)
Power and Sample Size	67	(1)
Test for Two Proportions	68	(5)
Power of the Z-Test	69	(2)
Relative Risk and Odds Ratio	71	(2)
Power of Chi-Square Tests	73	(2)
Efficiency	75	(8)
Pitman Efficiency	75	(3)
Asymptotic Relative Efficiency	78	(1)
Estimation Efficiency	79	(1)
Stratified Versus Unstratified Analysis of Risk Differences	80	(3)
Problems	83	(4)
Stratified-Adjusted Analysis for Two Independent Groups	87	(82)
Introduction	87	(2)
Mantel-Haenszel Test and Cochran's Test	89	(6)
Conditional Within-Strata Analysis	89	(1)
Marginal Unadjusted Analysis	90	(2)
Mantel-Haenszel Test	92	(1)
Cochran's Test	93	(2)
Stratified-Adjusted Estimators	95	(10)
Mantel-Haenszel Estimates	95	(1)
Test-Based Confidence Limits	96	(1)
Large Sample Variance of Log Odds Ratio	96	(3)
Maximum Likelihood Estiates of the Common Odds Ratio	99	(1)
Minimum Variance Linear Estimators (MVLE)	99	(2)
MVLE versus Mantel Haenszel Estimates	101	(2)
SAS PROC FREQ	103	(2)
Nature of Covariate Adjustment	105	(9)
Confounding and Effect Modification	105	(2)
Stratification Adjustment and Regression Adjustment	107	(1)
When Does Adjustment Matter?	108	(6)
Multivariate Tests of Hypotheses	114	(6)
Multivariate Null Hypothesis	114	(1)
Omnibus Test	115	(2)
Bonferroni Inequality	117	(1)
Partitioning of the Omnibus Alternative Hypothesis	118	(2)
Tests of Homogeneity	120	(6)
Contrast Test of Homogeneity	120	(2)
Cochran's Test of Homogeneity	122	(2)
Zelen's Test	124	(1)
Breslow-Day Test for Odds Ratios	124	(2)
Efficient Tests of No Partial Association	126	(7)
Restricted Alternative Hypothesis of Association	126	(2)
Radhakrishna Family of Efficient Tests of Association	128	(5)
Asymptotic Relative Efficiency of Competing Tests	133	(6)
Family of Tests	133	(2)
Asymptotic Relative Efficiency	135	(4)
Maximin Efficient Robust Tests	139	(6)
Maximin Efficiency	139	(1)
Gastwirth Scale Robust Test	140	(2)
Wei-Lachin Test of Stochastic Ordering	142	(3)
Comparison of Weighted Tests	145	(1)
Random Effects Model	145	(10)
Measurement Error Model	146	(1)
Stratified-Adjusted Estimates from Multiple 2x2 Tables	147	(8)
Power and Sample Size for Tests of Association	155	(4)
Power Function of the Radhakrishna Family	155	(2)
Power and Sample Size for Cochran's Test	157	(2)
Problems	159	(10)
Case-Control and Matched Studies	169	(40)
Unmatched Case-Control (Retrospective) Sampling	169	(6)
Odds Ratio	170	(2)
Relative Risk	172	(1)
Attributable Risk	173	(2)
Matching	175	(4)
Frequency Matching	175	(1)
Matched Pairs Design: Cross-Sectional or Prospective	176	(3)
Tests of Association for Matched Pairs	179	(4)
Exact Test	179	(1)
McNemar's Large Sample Test	180	(2)
SAS PROC FREQ	182	(1)
Measures of Association for Matched Pairs	183	(6)
Conditional Odds Ratio	183	(1)
Confidence Limits for the Odds Ratio	184	(1)
Conditional Large Sample Test and Confidence Limits	185	(1)
Mantel-Haenszel Analysis	186	(1)
Relative Risk for Matched Pairs	187	(1)
Attributable Risk for Matched Pairs	188	(1)
Pair-Matched Retrospective Study	189	(3)
Conditional Odds Ratio	190	(1)
Relative Risks from Matched Retrospective Studies	191	(1)
Power Function of McNemar's Test	192	(3)
Unconditional Power Function	192	(1)
Conditional Power Function	192	(2)
Other Approaches	194	(1)
Matching Efficiency	195	(1)
Stratified Analysis of Pair-Matched Tables	195	(6)
Pair and Member Stratification	196	(1)
Stratified Mantel-Haenszel Analysis	197	(1)
MVLE	197	(1)
Tests of Homogeneity and Association	198	(3)
Random Effects Model Analysis	201	(1)
Problems	201	(8)
Applications of Maximum Likelihood and Efficient Scores	209	(38)
Binomial	209	(2)
2x2 Table: Product Binomial (Unconditionally)	211	(8)
MLEs And Their Asymptotic Distribution	211	(1)
Logit Model	212	(5)
Tests of Significance	217	(2)
2 x 2 Table, Conditionally	219	(1)
Score-Based Estimate	220	(2)
Stratified Score Analysis of Independent 2x2 Tables	222	(4)
Conditional Mantel-Haenszel Test and the Score Estimate	223	(1)
Unconditional Cochran Test as a C(α) Test	224	(2)
Matched Pairs	226	(5)
Unconditional Logit Model	226	(2)
Conditional Logit Model	228	(2)
Conditional Likelihood Ratio Test	230	(1)
Conditional Score Test	230	(1)
Matched Case-Control Study	231	(1)
Iterative Maximum Likelihood	231	(7)
Newton-Raphson (or Newton's Method)	232	(1)
Fisher Scoring (Method of Scoring)	233	(5)
Problems	238	(9)
Logistic Regression Models	247	(70)
Unconditional Logistic Regression Model	247	(12)
General Logistic Regression Model	247	(3)
Logistic Regression and Binomial Logit Regression	250	(3)
SAS PROCEDURES	253	(2)
Stratified 2 x 2 Tables	255	(2)
Family of Binomial Regression Models	257	(2)
Interpretation of the Logistic Regression Model	259	(13)
Model Coefficients and Odds Ratios	259	(4)
Partial Regression Coefficients	263	(4)
Model Building: Stepwise Procedures	267	(3)
Disproportionate Sampling	270	(1)
Unmatched Case Control Study	271	(1)
Tests of Significance	272	(13)
Likelihood Ratio Tests	272	(1)
Efficient Scores Test	273	(2)
Wald Tests	275	(2)
Type III Tests in SAS PROC GENMOD	277	(1)
Robust Inferences	278	(5)
Power and Sample Size	283	(2)
Interactions	285	(7)
Qualitative-Qualitative Covariate Interaction	286	(4)
Interactions with a Quantitative Covariate	290	(2)
Measures of the Strength of Association	292	(4)
Squared Error Loss	292	(1)
Entropy Loss	293	(3)
Conditional Logistic Regression Model for Matched Studies	296	(9)
Conditional Logistic Model	296	(4)
Special Case: 1:1 Matching	300	(1)
Matched Retrospective Study	300	(1)
Fitting the General Conditional Logistic Regression Model: The Conditional PH Model	301	(2)
Robust Inference	303	(1)
Explained Variation	303	(2)
Problems	305	(12)
Analysis of Count Data	317	(36)
Event Rates and the Homogeneous Poisson Model	317	(6)
Poisson Process	317	(1)
Doubly Homogeneous Poisson Model	318	(2)
Relative Risks	320	(3)
Violations of the Homogeneous Poisson Assumptions	323	(1)
Over-Dispersed Poisson Model	323	(7)
Two-Stage Random Effects Model	324	(3)
Relative Risks	327	(2)
Stratified-Adjusted Analyses	329	(1)
Poisson Regression Model	330	(8)
Homogeneous Poisson Regression Model	330	(7)
Explained Variation	337	(1)
Applications of Poisson Regression	338	(1)
Over-Dispersed and Robust Poisson Regression	338	(5)
Quasi-Likelihood Over-Dispersed Poisson Regression	338	(2)
Robust Inference Using the Information Sandwich	340	(3)
Power and Sample Size for Poisson Models	343	(1)
Conditional Poisson Regression for Matched Sets	344	(1)
Problems	345	(8)
Analysis of Event-Time Data	353	(96)
Introduction to Survival Analysis	354	(14)
Hazard and Survival Function	354	(1)
Censoring at Random	355	(1)
Kaplan-Meier Estimator	356	(3)
Estimation of the Hazard Function	359	(2)
Comparison of Survival Probabilities for Two Groups	361	(7)
Lifetable Construction	368	(9)
Discrete Distributions: Actuarial Lifetable	368	(1)
Modified Kaplan-Meier Estimator	369	(1)
Competing Risks	370	(5)
SAS PROC LIFETEST: Survival Estimation	375	(2)
Family of Weighted Mantel-Haenszel Tests	377	(7)
Weighted Mantel-Haenszel Test	377	(1)
Mantel-logrank Test	378	(1)
Modified Wilcoxon Test	379	(1)
Gp Family of Tests	380	(1)
Measures of Association	381	(2)
SAS PROC LIFETEST: Tests of Significance	383	(1)
Proportional Hazards Models	384	(25)
Cox's Proportional Hazards Models	385	(3)
Stratified Models	388	(1)
Time-Dependent Covariates	389	(1)
Fitting the Model	390	(1)
Robust Inference	391	(2)
Adjustments for Tied Observations	393	(4)
Model Assumptions	397	(2)
Explained Variation	399	(2)
SAS PROC PHREG	401	(8)
Evaluation of Sample Size and Power	409	(5)
Exponential Survival	409	(3)
Cox's Proportional Hazards Model	412	(2)
Analysis of Recurrent Events: The Multiplicative Intensity Model	414	(12)
Counting Process Formulation	415	(2)
Nelson-Aalen Estimator	417	(2)
Aalen-Gill Test Statistics	419	(3)
Multiplicative Intensity Model	422	(4)
Problems	426	(23)
Appendix Statistical Theory	449	(56)
A.1 Introduction	449	(2)
A.1.1 Notation	449	(1)
A.1.2 Matrices	450	(1)
A.1.3 Partition of Variation	451	(1)
A.2 Central Limit Theorem and the Law of Large Numbers	451	(4)
A.2.1 Univariate Case	451	(2)
A.2.2 Multivariate Case	453	(2)
A.3 Delta Method	455	(2)
A.3.1 Univariate Case	455	(1)
A.3.2 Multivariate Case	456	(1)
A.4 Slutsky's Convergence Theorem	457	(3)
A.4.1 Convergence in Distribution	457	(1)
A.4.2 Convergence in Probability	458	(1)
A.4.3 Convergence in Distribution of Transformations	458	(2)
A.5 Least Squares Estimation	460	(5)
A.5.1 Ordinary Least Squares (OLS)	460	(2)
A.5.2 Gauss-Markov Theorem	462	(1)
A.5.3 Weighted Least Squares (WLS)	463	(2)
A.5.4 Iteratively Reweighted Least Squares (IRLS)	465	(1)
A.6 Maximum Likelihood Estimation and Efficient Scores	465	(11)
A.6.1 Estimating Equation	465	(1)
A.6.2 Efficient Score	466	(1)
A.6.3 Fisher's Information Function	467	(3)
A.6.4 Cramer-Rao Inequality: Efficient Estimators	470	(1)
A.6.5 Asymptotic Distribution of the Efficient Score and the MLE	471	(1)
A.6.6 Consistency and Asymptotic Efficiency of the MLE	472	(1)
A.6.7 Estimated Information	472	(1)
A.6.8 Invariance Under Transformations	473	(1)
A.6.9 Independent But Not Identically Distributed Observations	474	(2)
A.7 Likelihood Based Tests of Significance	476	(7)
A.7.1 Wald Tests	476	(2)
A.7.2 Likelihood Ratio Tests	478	(1)
A.7.3 Efficient Scores Test	479	(4)
A.8 Explained Variation	483	(5)
A.8.1 Squared Error Loss	484	(2)
A.8.2 Residual Variation	486	(1)
A.8.3 Negative Log-Likelihood Loss	487	(1)
A.8.4 Madalla's R2LR	487	(1)
A.9 Robust Inference	488	(6)
A.9.1 Information Sandwich	488	(5)
A.9.2 Robust Confidence Limits and Tests	493	(1)
A.10 Generalized Linear Models and Quasi-Likelihood	494	(11)
A.10.1 Generalized Linear Models	494	(1)
A.10.2 Exponential Family of Models	495	(3)
A.10.3 Deviance and the Chi-Square Goodness of Fit	498	(2)
A.10.4 Quasi-Likelihood	500	(2)
A.10.5 Conditional GLMs	502	(1)
A.10.6 Generalized Estimating Equations (GEE)	503	(2)
References	505	(20)
Author Index	525	(6)
Index	531