## Applied Longitudinal Data Analysis for Epidemiology: A Practical GuideIn this book the most important techniques available for longitudinal data analysis are discussed. This discussion includes simple techniques such as the paired t-test and summary statistics, but also more sophisticated techniques such as generalised estimating equations and random coefficient analysis. A distinction is made between longitudinal analysis with continuous, dichotomous, and categorical outcome variables. It should be stressed that the emphasis of the discussion lies on the interpretation of the different techniques and on the comparison of the results of different techniques. Furthermore, special chapters will deal with the analysis of two measurements, experimental studies and the problem of missing data in longitudinal studies. Finally, an extensive overview of (and a comparison between) different software packages is provided. It is important to realise that this book is a practical guide and especially suitable for non-statisticians. |

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Intro

Study Design 7

Continous outcome variables15Continous outcome variables 55

GEE 62

Random Coeff Analysis 77

Dichotomous Outcome 120

Long with 2 outcome 167

Missing Data

Tracking

Software

p.3 data set has 4 predictors x1 continuous time indepen, x2 cont time dep, x3 dichot time-dep, x4 dichot time-ind

p.6 long and broad data structures

most clinical trials cannot distinguish between age (DOB-Measurement) , period (measurement time) & birth (cohort-birth year) effects

Ex period effect of hot summer on age v activity

Ex cohort effect on height v age

(p.9)

### Contents

Introduction | 1 |

12 General approach | 2 |

14 Example | 3 |

15 Software | 5 |

Study design | 7 |

22 Observational longitudinal studies | 9 |

222 Other confounding effects | 13 |

223 Example | 14 |

7754 Example | 153 |

72 Count outcome variables | 156 |

721 Example | 157 |

7212 GEE analysis | 158 |

7213 Random coefficient analysis | 163 |

722 Comparison between GEE analysis and random coefficient analysis | 165 |

Longitudinal studies with two measurements the definition and analysis of change | 167 |

821 A numerical example | 171 |

23 Experimental longitudinal studies | 15 |

Continuous outcome variables | 18 |

311 Example | 20 |

32 Nonparametric equivalent of the paired ttest | 21 |

321 Example | 22 |

33 More than two measurements | 23 |

a numerical example | 26 |

332 The shape of the relationship between an outcome variable and time | 29 |

333 A numerical example | 30 |

334 Example | 32 |

34 The univariate or the multivariate approach? | 37 |

35 Comparing groups | 38 |

a numerical example | 39 |

352 Example | 41 |

36 Comments | 45 |

37 Posthoc procedures | 46 |

371 Example | 47 |

38 Different contrasts | 48 |

381 Example | 49 |

39 Nonparametric equivalent of MANOVA for repeated measurements | 52 |

391 Example | 53 |

Continuous outcome variables relationships with other variables | 55 |

43 Example | 57 |

44 Longitudinal methods | 60 |

45 Generalized estimating equations | 62 |

453 Interpretation of the regression coefficients derived from GEE analysis | 66 |

454 Example | 68 |

4542 Results of a GEE analysis | 69 |

4543 Different correlation structures | 72 |

4544 Unequally spaced time intervals | 75 |

46 Random coefficient analysis | 77 |

463 Example | 80 |

4632 Unequally spaced time intervals | 88 |

47 Comparison between GEE analysis and random coefficient analysis | 91 |

471 Extensions of random coefficient analysis | 92 |

4721 A numerical example | 93 |

474 Comments | 95 |

481 Example | 98 |

Other possibilities for modelling longitudinal data | 102 |

522 Modelling of changes | 105 |

523 Autoregressive model | 107 |

524 Overview | 108 |

5252 Data structure for alternative models | 109 |

5254 Random coefficient analysis | 112 |

53 Comments | 114 |

54 Another example | 118 |

Dichotomous outcome variables | 120 |

612 More than two measurements | 122 |

614 Example | 123 |

6143 Comparing groups | 126 |

62 Relationships with other variables | 128 |

623 Sophisticated methods | 129 |

624 Example | 131 |

6242 Random coefficient analysis | 137 |

625 Comparison between GEE analysis and random coefficient analysis | 140 |

626 Alternative models | 143 |

627 Comments | 144 |

Categorical and count outcome variables | 145 |

712 More than two measurements | 146 |

713 Comparing groups | 147 |

715 Relationships with other variables | 151 |

7153 Sophisticated methods | 152 |

822 Example | 173 |

83 Dichotomous and categorical outcome variables | 175 |

84 Comments | 177 |

85 Sophisticated analyses | 178 |

Analysis of experimental studies | 179 |

92 Example with a continuous outcome variable | 181 |

922 Simple analysis | 182 |

923 Summary statistics | 184 |

924 MANOVA for repeated measurements | 185 |

9241 MANOVA for repeated measurements corrected for the baseline value | 186 |

925 Sophisticated analysis | 188 |

93 Example with a dichotomous outcome variable | 195 |

933 Sophisticated analysis | 196 |

94 Comments | 200 |

Missing data in longitudinal studies | 202 |

102 Ignorable or informative missing data? | 204 |

103 Example | 205 |

1032 Analysis of determinants for missing data | 206 |

104 Analysis performed on datasets with missing data | 207 |

1041 Example | 208 |

105 Comments | 212 |

106 Imputation methods | 213 |

10613 Multiple imputation method | 214 |

1062 Dichotomous and categorical outcome variables | 216 |

70632 Dichotomous outcome variables | 219 |

1064 Comments | 221 |

107 Alternative approaches | 223 |

Tracking | 225 |

113 Dichotomous and categorical outcome variables | 230 |

114 Example | 234 |

1141 Two measurements | 235 |

1142 More than two measurements | 237 |

115 Comments | 238 |

1152 Risk factors for chronic diseases | 239 |

116 Conclusions | 240 |

Software for longitudinal data analysis | 241 |

1222 SAS | 243 |

1223 SPLUS | 244 |

1224 Overview | 246 |

123 GEE analysis with dichotomous outcome variables | 247 |

1232 SAS | 248 |

1233 SPLUS | 249 |

1234 Overview | 250 |

1242 SAS | 251 |

1243 SPLUS | 255 |

1244 SPSS | 257 |

1245 MLwiN | 259 |

1246 Overview | 262 |

125 Random coefficient analysis with dichotomous outcome variables | 263 |

1252 STATA | 264 |

1253 SAS | 265 |

1254 MLwiN | 269 |

1255 Overview | 270 |

126 Categorical and count outcome variables | 271 |

127 Alternative approach using covariance structures | 272 |

1271 Example | 274 |

Sample size calculations | 280 |

132 Example | 283 |

286 | |

295 | |