Statistical Methods for Health Sciences

Mohamed M. Shoukri, C. A. Pause9780849310959, 0-8493-1095-4

Building upon material presented in the first edition, this second edition continues to address the analytical issues related to the modeling and analysis of cluster data, both physical clustering – sampling of communities, families, or herds – and overtime clustering – longitudinal, repeated measures, or time series data.

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Table of contents :
1095_pdf_toc.pdf……Page 1
Statistical Methods for Health Sciences……Page 2
THE AUTHORS……Page 4
PREFACE TO THE FIRST EDITION……Page 5
PREFACE TO THE SECOND EDITION……Page 7
TABLE OF CONTENTS……Page 8
A. NON-NORMALITY……Page 12
Table of Contents……Page 0
1. Bartlett’s Test……Page 20
3. Welch’s Statistic (1951) for Testing Equality of Group Means:……Page 21
4. Brown and Forsythe Statistic (1974b) for Testing Equality of Group Means:……Page 22
5. Cochran’s (1937) Method of Weighting for Testing Equality of Group Means:……Page 23
C. NON-INDEPENDENCE……Page 26
I. INTRODUCTION……Page 30
A. CASE 1: THE ONE-WAY RANDOM EFFECTS MODEL……Page 31
B. CASE 2: THE TWO-WAY RANDOM EFFECTS MODEL……Page 33
C. CASE 3: THE TWO-WAY MIXED EFFECTS MODEL……Page 35
D. COVARIATE ADJUSTMENT IN THE ONE-WAY RANDOM EFFECTS MODEL……Page 39
III. COMPARING THE PRECISIONS OF TWO METHODS (GRUBBS, 1948 and SHUKLA, 1973)……Page 41
IV. CONCORDANCE CORRELATION AS A MEASURE OF REPRODUCIBILITY……Page 46
V. ASSESSING REPRODUCIBILITY USING THE COEFFICIENT OF VARIATION……Page 52
II. MEASURES OF ASSOCIATION IN 2X2 TABLES……Page 54
A. CROSS SECTIONAL SAMPLING……Page 55
B. COHORT AND CASE-CONTROL STUDIES……Page 58
III. STATISTICAL INFERENCE ON ODDS RATIO……Page 59
A. SIGNIFICANCE TESTS……Page 61
Example 3.1……Page 62
B. INTERVAL ESTIMATION……Page 63
C. ANALYSIS OF SEVERAL 2×2 CONTINGENCY TABLES……Page 64
Example 3.2……Page 65
1. Test of Homogeneity……Page 66
Example 3.3……Page 67
2. Significance Test of Common Odds Ratio……Page 68
3. Confidence Interval on the Common Odds Ratio……Page 69
A. ESTIMATING THE ODDS RATIO……Page 71
B. TESTING THE EQUALITY OF MARGINAL DISTRIBUTIONS……Page 74
V. STATISTICAL ANALYSIS OF CLUSTERED BINARY DATA……Page 76
A. TESTING HOMOGENEITY……Page 78
1. Donner’s Adjustment……Page 80
2. Rao and Scott’s Adjustment……Page 82
Example 3.6 “Hypothetical Drug Trial”……Page 84
B. INFERENCE ON THE COMMON ODDS RATIO……Page 87
1. Donald and Donner’s Adjustment……Page 88
2. Rao and Scott’s Adjustment……Page 90
Example 3.7……Page 91
VI. MEASURE OF INTERCLINICIAN AGREEMENT FOR CATEGORICAL DATA……Page 96
Example 3.8……Page 97
1. PROBABILISTIC MODELS……Page 99
B. CONFIDENCE INTERVAL ON KAPPA IN 2X2 TABLE……Page 102
Example 3.9……Page 105
C. AGREEMENT BETWEEN TWO RATERS WITH MULTIPLE CATEGORIES……Page 106
1. Weighted Kappa……Page 107
Remarks……Page 108
Example 3.10……Page 110
D. MORE THAN TWO CLINICIANS……Page 111
Example 3.11……Page 112
Remarks……Page 113
b. Reliability Kappa……Page 114
2. Case II. Multiple Categories and Multiple Raters……Page 117
Example 3.12 “CVM Data”……Page 119
A. INTRODUCTION……Page 123
B. ESTIMATING PREVALENCE……Page 124
C. ESTIMATING PREDICTIVE VALUE POSITIVE AND PREDICTIVE VALUE NEGATIVE……Page 126
D. ESTIMATION IN DOUBLE SAMPLING……Page 128
Example 3.13……Page 134
VIII. DEPENDENT SCREENING TESTS (MULTIPLE READINGS)……Page 135
A. ESTIMATION OF PARAMETERS……Page 138
1. Estimating Prevalence by Group Testing……Page 142
B. EVALUATING THE PERFORMANCE OF MEDICAL SCREENING TESTS IN THE ABSENCE OF A GOLD STANDARD (Latent class models)……Page 145
1. Estimation of Error Rates Under the Assumption of Conditional Independence……Page 146
2. The Effect of Conditional Dependence (Vacek 1985)……Page 149
I. INTRODUCTION……Page 152
II. THE LOGISTIC TRANSFORMATION……Page 154
III. CODING CATEGORICAL EXPLANATORY VARIABLES AND INTERPRETATION OF COEFFICIENTS……Page 158
Example 4.1……Page 159
IV. INTERACTION AND CONFOUNDING……Page 160
Example 4.2……Page 162
A. PEARSON’S X2 – STATISTIC……Page 166
B. THE LIKELIHOOD RATIO CRITERION (Deviance)……Page 167
Example 4.3……Page 170
General Comments:……Page 173
B. INTRACLUSTER EFFECTS……Page 174
1. Modelling Sources of Variation……Page 175
2. Correlated Binary Responses……Page 177
Example 4.4 Shell’s data……Page 178
3. Test for Trend in the 2 x I Table……Page 180
Example 4.5……Page 181
1. Random Effects Models……Page 183
2. Bahadur’s Model……Page 187
3. Models with More Than One Random Effect : “Hierarchical or Multilevel Modelling of Binary Data”……Page 190
E. ESTIMATING EQUATIONS APPROACH……Page 195
Example 4.7……Page 201
Example 4.8……Page 203
A. COHORT VERSUS CASE-CONTROL MODELS……Page 204
B. MATCHED ANALYSIS……Page 207
C. CONDITIONAL LIKELIHOOD……Page 208
D. FITTING MATCHED CASE-CONTROL STUDY DATA IN SAS……Page 211
Example 4.9 “Hypothetical Data”……Page 212
Remark……Page 214
I. INTRODUCTION……Page 215
A. SIMPLE DESCRIPTIVE METHODS……Page 217
Example 5.2……Page 218
2. Additive Seasonal Variation Model……Page 225
Example 5.3……Page 226
3. Detection of Seasonality : Nonparametric Test……Page 228
4. Autoregressive Errors: Detection and Estimation……Page 230
Example 5.1……Page 216
5. Modelling Seasonality and Trend Using Polynomial and Trigonometric Functions……Page 232
Example 5.5……Page 233
A. STOCHASTIC PROCESSES……Page 235
B. STATIONARY SERIES……Page 236
C. THE AUTOCOVARIANCE AND AUTOCORRELATION FUNCTIONS……Page 237
III. MODELS FOR STATIONARY TIME SERIES……Page 240
1. The AR(1) Model……Page 241
2. AR(2) Model (Yule’s Process)……Page 244
4. First Order Moving Average Process MA(1)……Page 246
5. The Second Order Moving Average Process MA(2)……Page 247
6. The Mixed Autoregressive Moving Average Processes……Page 248
1. Deterministic Trend Models……Page 251
Example 5.6……Page 252
B. DIFFERENCING……Page 254
C. ARIMA MODELS……Page 255
D. NONSTATIONARITY IN THE VARIANCE……Page 256
A. Specification……Page 258
a. The Method of Moments……Page 262
b. Maximum Likelihood Method……Page 264
Remark……Page 267
VI. FORECASTING……Page 270
VII. MODELING SEASONALITY WITH ARIMA: The condemnation rates series revisited…….Page 275
B. ONE-WAY ANOVA WITH CORRELATED ERRORS……Page 280
C. TWO-WAY ANOVA WITH CORRELATED ERRORS……Page 282
Example 5.9……Page 286
A. “EFFECT OF MYCOBACTERIUM INOCULATION ON WEIGHT”……Page 288
B. VARIATION IN TEENAGE PREGNANCY RATES (TAPR) IN CANADA……Page 289
A. BASIC MODELS……Page 290
B. HYPOTHESIS TESTING……Page 292
1. Adjustment in the Two-way ANOVA……Page 293
C. RECOMMENDED ANALYSIS FOR EXAMPLE A……Page 295
Remark……Page 296
Remarks……Page 297
D. RECOMMENDED ANALYSIS FOR EXAMPLE B……Page 301
1. Age 15-17……Page 302
2. Age 18-19……Page 303
IV. MISSING OBSERVATIONS……Page 304
Example 6.1……Page 305
A. FORMULATION OF THE MODELS……Page 314
(i) Model (1) for fixed effects:……Page 316
(ii) Model (2) for fixed effects :……Page 317
2. Compound Symmetry (CS model):……Page 318
4. Autoregressive Covariance Structure (AR)……Page 319
B. MAXIMUMLIKELIHOOD (ML) AND RESTRICTED MAXIMUM LIKELIHOOD (REML) ESTIMATION……Page 320
C. MODEL SELECTION……Page 321
VI. THE GENERALIZED ESTIMATING EQUATIONS APPROACH……Page 325
Example 6.5……Page 332
Comments……Page 334
I. INTRODUCTION……Page 335
A. VENTILATING TUBE DATA……Page 338
B. CYSTIC OVARY DATA……Page 340
C. BREAST CANCER DATA……Page 341
1. Methods for Non-censored Data……Page 343
2. Methods for Censored Data……Page 344
1. The Log-Rank Test for Comparisons Between Two Groups……Page 350
2. The Log-Rank Test for Comparisons Between Several Groups……Page 353
2. The Weibull Model for Survival Analysis……Page 355
a) Exponential Model……Page 356
Graphical Assessment of Model Adequacy……Page 357
1. The Cox Proportional Hazards Model……Page 361
ii) Cox’s Method for Tied Failure Times……Page 363
3. Time Dependent Covariates in the Cox Proportional Hazards Model……Page 366
IV. CORRELATED SURVIVAL DATA……Page 367
i) The GEE Approach……Page 368
ii) The GJE Approach……Page 371
The GJE portion of the SAS output for the correlated ear data is as shown:……Page 373
B. FRAILTY MODELS……Page 374
REFERENCES……Page 377
Average Milk Production per Month (kg) for 10 Ontario Farms……Page 390