The margin of error and number of predictors that can be estimated given a sample size of 1100 participants, based on four sample size requirements outlined by Riley et al46
| Step 1: To produce a precise estimate (margin of error <0.05) | ||||||
| Outcome proportion† | 0.1 | 0.2 | ||||
| Margin of error | 0.018 | 0.024 | ||||
| Step 2: To produce predicted values with a small mean error across all individuals (mean absolute prediction error=0.05) | ||||||
| Outcome proportion† | 0.1 | 0.2 | ||||
| Number of parameters | 44 | 31 | ||||
| Step 3: To produce a small required shrinkage of predictor effects (shrinkage=0.1) | ||||||
| R2Nagelkerke* | 0.1 | 0.2 | 0.5 | 0.1 | 0.2 | 0.5 |
| Outcome proportion† | 0.1 | 0.1 | 0.1 | 0.2 | 0.2 | 0.2 |
| Number of parameters | 6 | 12 | 33 | 8 | 16 | 47 |
| Step 4: To produce a small optimism in apparent model fit (optimism=0.05) | ||||||
| R2Nagelkerke* | 0.1 | 0.2 | 0.5 | 0.1 | 0.2 | 0.5 |
| Outcome proportion† | 0.1 | 0.1 | 0.1 | 0.2 | 0.2 | 0.2 |
| Number of parameters | 27 | 28 | 30 | 36 | 37 | 42 |
*In absence of existing studies for a similar target population, Riley et al46 suggest an R2Nagelkerke value between 0.1 and 0.2 for prediction models of health-related outcomes. When direct or mechanistic measurements are included, the R2Nagelkerke may be closer to 0.5.
†Based on existing research that examines healthcare use among homeless adults, we expect the outcome proportion will be greater than in the general population.2