The therapeutic index (TI) compares the effective dose of a drug to the toxic dose, with a higher TI indicating a safer drug. It is calculated as the ratio of the dose that causes toxicity (TD50) to the dose needed for a therapeutic effect (ED50). The dose-response relationship shows how effects change with dose levels. Knowledge of lethal doses, effective doses, and the dose-response curve allows evaluation of a drug's causality, threshold effects, and safety based on the TI.