Multivariable Analysis: A Practical Guide for Clinicians and Public Health Researchers

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 15
1.1 Why should I do multivariable analysis?......Page 19
1.2 What are confounders and how does multivariable analysis help me to deal with them?......Page 24
1.3 What are suppressers and how does multivariable analysis help me to deal with them?......Page 27
1.4 What are interactions and how does multivariable analysis help me to deal with them?......Page 29
2.2 How is multivariable analysis used in observational studies of etiology?......Page 32
2.3 How is multivariable analysis used in intervention studies (randomized and nonrandomized)?......Page 34
2.4 How is multivariable analysis used in studies of diagnosis?......Page 39
2.5 How is multivariable analysis used in studies of prognosis?......Page 41
3.1 How does the nature of the outcome variable influence the choice of which type of multivariable analysis to do?......Page 43
3.2 What type of multivariable analysis should I use with an interval outcome?......Page 44
3.2.A Multiple linear regression......Page 45
3.2.B Analysis of variance (ANOVA)......Page 46
3.2.C Underlying assumptions of multiple linear regression and ANOVA......Page 50
3.2.D Choosing between multiple linear regression and ANOVA......Page 53
3.3 What type of multivariable analysis should I use with a dichotomous outcome?......Page 54
3.4 What type of multivariable analysis should I use with an ordinal variable?......Page 57
3.5 What type of multivariable analysis should I use with a nominal outcome?......Page 60
3.6 What type of multivariable analysis should I use with a time-to-outcome variable?......Page 62
3.7.A Loss to follow-up......Page 68
3.7.B Alternative outcome......Page 69
3.7.C Withdrawal......Page 70
3.7.D Varying time of enrollment......Page 72
3.8 How can I test the validity of the censoring assumption for my data?......Page 73
3.9 What is the proportionality assumption of proportional hazards analysis?......Page 76
3.10 What type of multivariable analysis should I use with counts?......Page 78
3.10.A Poisson regression......Page 79
3.10.B Negative binomial models......Page 81
3.11 What type of multivariable analysis should I use with an incidence rate?......Page 82
3.12.A. Dichotomizing an interval variable......Page 84
3.12.B. Changing time-to-outcome to a dichotomous outcome (yes/no)......Page 87
3.12.C. Dichotomizing ordinal variables or treating them as nominal variables......Page 89
3.12.D. Converting a count to time to outcome or to a dichotomous outcome......Page 90
3.12.E. General advice for changing the coding of outcome variables......Page 91
4.2 How do I incorporate nominal independent variables into a multivariable analysis?......Page 92
4.3 How do I incorporate interval-independent variables into a multivariable model?......Page 94
4.3.A Mathematical transformations......Page 98
4.3.B Splines......Page 100
4.3.C Multiple dichotomous variables......Page 102
4.5 How do I incorporate ordinal independent variables into a multivariable model?......Page 104
5.1 Does it matter if my independent variables are related to each other?......Page 106
5.2 How do I assess whether my variables are multicollinear?......Page 107
5.3 What should I do with multicollinear variables?......Page 109
6.2 How do I decide what confounders to include in my model?......Page 111
6.3 What independent variables should I exclude from my multivariable model?......Page 112
6.4 How many subjects do I need to do multivariable analysis?......Page 115
6.5 What if I have too many independent variables given my sample size?......Page 120
6.5.A Exclude variables that are not empirically operating as confounders......Page 121
6.5.B Choose one variable to represent two or more related variables......Page 122
6.5.C.2 Scores......Page 123
6.5.C.3 Multi-item scales......Page 124
6.5.C.4 Factor analysis......Page 125
6.6 What should I do about missing data on my independent variables?......Page 126
6.7 What should I do about missing data on my outcome variable?......Page 133
7.1 What numbers should I assign for dichotomous or ordinal variables in my analysis?......Page 136
7.2 Does it matter what I choose as my reference category for multiple dichotomous (“dummied”) variables?......Page 138
7.3 How do I enter interaction terms into my analysis?......Page 140
7.4 How do I enter time into my proportional hazards or other survival analysis?......Page 142
7.5 What about subjects who experience their outcome on their start date?......Page 147
7.6 What about subjects who have a survival time shorter than physiologically possible?......Page 149
7.7 How do I incorporate time into my Poisson analysis?......Page 151
7.8 What are variable selection techniques?......Page 152
7.9 My model won’t converge. What should I do?......Page 157
8.2.A  Multiple linear regression......Page 158
8.2.B  Multiple logistic regression......Page 160
8.2.D Multinomial logistic regression......Page 165
8.2.F  Poisson regression and negative binomial regression......Page 166
8.3.A Coefficients in multiple linear regression......Page 167
8.3.B Coefficient in multiple (binary) logistic regression......Page 169
8.3.C Coefficients in proportional odds regression......Page 174
8.3.D Coefficients in multinomial logistic regression......Page 175
8.3.F Coefficients in Poisson regression and negative binomial regression......Page 176
8.5 Do I have to adjust my multivariable regression coefficients for multiple comparisons?......Page 177
9.2 What are residuals? How are they used to assess the fit of models?......Page 180
9.3 How do I test the normal distribution and equal variance assumptions of a multiple linear regression model?......Page 183
9.4 How do I test the linearity assumption of a multivariable model?......Page 184
9.5 What are outliers and how do I detect them in a multivariable model?......Page 185
9.6 What should I do when I detect outliers?......Page 188
9.7 What is the additive assumption and how do I assess whether my multiple independent variables fit this assumption?......Page 189
9.9 How do I test the proportionality assumption?......Page 192
9.9.A log-minus-log survival plot......Page 193
9.9.D. Time-dependent covariates......Page 194
9.10 What if the proportionality assumption does not hold for my data?......Page 195
10.1 What are propensity scores? Why are they used?......Page 198
11.1 What circumstances lead to correlated observations?......Page 203
11.2 Should I avoid study designs that lead to correlated observations?......Page 205
11.3 How do I analyze correlated observations?......Page 207
11.3.A Transform repeated observations into a single measure......Page 209
11.3.B Generalized estimating equations......Page 211
11.3.C Mixed-effects model......Page 215
11.3.D Repeated measures analysis of variance/repeated measures analysis of covariance......Page 218
11.3.E Conditional logistic regression......Page 222
11.3.F Anderson–Gill formation of the proportional hazards model......Page 223
11.3.G Marginal approach for proportional hazards analysis......Page 224
11.4 How do I calculate the needed sample size for studies with correlated observations?......Page 225
12.1 How can I validate my models?......Page 226
13.2 What are the advantages and disadvantages of time-dependent covariates?......Page 231
13.3 What are classification and regression trees (CART) and should I use them?......Page 234
13.5 How do I choose which software package to use?......Page 237
14.1 How much information about how I constructed my multivariable models should I include in the Methods section?......Page 239
14.2 Do I need to cite a statistical reference for my choice of method of multivariable analysis?......Page 241
14.3 Which parts of my multivariable analysis should I report in the Results section?......Page 242
15 Summary: Steps for constructing a multivariable model......Page 245
Index......Page 247