Relative Risk Calculator
The Relative Risk Calculator computes the ratio of event probabilities between exposed and unexposed groups in cohort studies. Determine relative risk (RR), absolute risk reduction (ARR), and number needed to treat (NNT) from your study data.
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What is Relative Risk?
Relative risk (RR) compares the probability of an event in the exposed group to the probability in the unexposed group. An RR of 2.0 means exposed individuals are twice as likely to experience the outcome. An RR of 0.5 means exposure halves the risk (50% risk reduction).
Relative risk is the standard measure of association in cohort studies and randomized controlled trials. It's more intuitive than odds ratio because it directly represents probability ratios. RR = 1.0 means no difference between groups.
使用される計算公式・方程式
この計算ツールは5つの主要な公式を使用しています：
1 Relative Risk ▼
Risk in exposed = a/(a+b). Risk in unexposed = c/(c+d). RR is their ratio.
2 Absolute Risk Reduction ▼
If control risk = 20% and treatment risk = 12%: ARR = 20% - 12% = 8 percentage points.
3 Number Needed to Treat ▼
ARR of 8%: NNT = 1/0.08 = 12.5. You need to treat 13 patients to prevent 1 event.
比率計算ツールの使い方
この比率計算ツールは、以下の3ステップで簡単にご利用いただけます：
数値を入力
入力欄に既知の比率の値を入力します。求めたい未知数の入力欄は空欄のままにしておきます。
モードを選択
比率モード（解く、簡素化、スケーリング）を選択します。各モードで異なる計算式が適用されます。
結果を確認
計算するボタンを押します。結果画面に答えと、視覚的な比率バー、円グラフ、詳細なステップバイステップの解決プロセスが表示されます。
実例問題と段階的な解説
本比率計算ツールを使って、以下の3つの例題をステップバイステップで解決するプロセスです：
入力 1 Drug trial: treated group vs placebo
入力 2 Smoking and heart disease (cohort study)
入力 3 Calculate NNT for a vaccine
よくある質問 (FAQ)
What does a relative risk of 1.0 mean? ▼
RR = 1.0 means the event is equally likely in both groups — no association between exposure and outcome. RR > 1 indicates increased risk; RR < 1 indicates decreased risk (protection).
How is relative risk different from odds ratio? ▼
RR uses probabilities (events/total), while OR uses odds (events/non-events). For rare outcomes (<10%), they're nearly equal. For common outcomes, OR overstates the association compared to RR.
What is a clinically significant relative risk? ▼
This depends on context. In cancer screening, RR = 0.80 (20% risk reduction) may be significant. In vaccine trials, RR = 0.05 (95% efficacy) is transformative. Always consider both RR and ARR.
Can relative risk be used in case-control studies? ▼
No. Case-control studies sample by outcome, not exposure, so you can't calculate true incidence rates. Use odds ratio instead. RR is only valid in cohort studies and RCTs where you follow groups over time.
What is the number needed to treat (NNT)? ▼
NNT is the inverse of absolute risk reduction. It tells you how many patients must receive treatment to prevent one adverse event. Lower NNT = more effective treatment. NNT of 10 means treat 10 patients to prevent 1 event.