# How to calculate patient-specific estimates of benefit and harm from a RCT

One of the more challenging concepts for students is how to apply information from a study to an individual patient. Students have been taught how to calculate a number needed to treat (NNT) but that isn’t often very useful for the current patient they are seeing. Usually our patients are sicker or healthier than those in the study we are reading. Studies include a range of patients so the effect we see in the results is the average effect for all patients in the study.

Imagine you are seeing Mr. Fick, a 70 yo M with ischemic cardiomyopathy (EF 20%) and refractory anemia (baseline Hg 7-10 mg/dl). He reports stable CHF symptoms of dyspnea walking around the house after about 30 ft. He reports other signs and symptoms of CHF are stable. Medications include lisinopril 20mg bid, aspirin daily, furosemide 80 mg daily, and iron tablets daily. He is not taking a beta blocker due to bradycardia and can’t take a statin due to myopathy. He has refused an ICD in the past. BP is 95/62 mm Hg, pulse is 50 bpm, weight is stable at 200 lbs. Labs done one week earlier show a stable Na 0f 125 mmol/l, K 3.8 mmol/l, Hg 8 g/dl, platelets 162 k, WBC is normal with 22% lymphs on differential, cholesterol is 220 mg/dl, and uric acid is 6.2.  Since he has severe CHF you are considering adding spironolactone to his regimen. he is concerned because he has a hard time tolerating medications. He wants to know how much it will help him. What do you tell him?

This figure is from the RALES trial, a study of spironolactone in patients with advanced CHF. Use the figure below to figure out Mr. Fick’s individual estimated risk of death if he agrees to take spironolactone.

There are 4 methods I will demonstrate to calculate a patient-specific estimate of effect from an RCT. First, think about what information you will need to estimate Mr. Fick’s specific benefits of spironolactone. You will need the NNT from the RALES trial and Mr. Fick’s estimated risk of death (we call this the PEER or the patient expected event rate). Where do we get the PEER of death for Mr. Fick? You use a validated prediction rule. I use Calculate by QxMD. Look in the Cardiology folder under heart failure and open the Seattle Heart Failure Model. Plug in Mr. Fick’s data and you get his 1 year expected risk of death (56%).

Method 1: Calculate patient-specific NNT using PEER: the formula for this is 1 / (PEER x RRR) where RRR is the relative risk reduction from the RALES trial (30%. To calculate that: 1-RR is the RRR). So plugging that in, Mr. Fick’s NNT is 1 / (0.56 x 0.3) = 6 (the NNT from the RALES trial is 9).

Method 2: Estimate patient-specific NNT using f: F is what I call the fudge factor. It is your guesstimation of how much higher or lower Mr. Fick’s risk of death is than that of the average patient in the study. If you say he is 2 times more likely to die then f is 2. If you think he is half as likely then f is 0.5. The way to use f is to divide the study NNT by f. This gives an estimate of Mr. Fick’s NNT. So lets just say Mr. Fick is twice as likely to die than those in the study. The NNT of the study is 9.  So 9/2 is 4.5 which I would round up to 5.

NNTs are nice but its hard to use them directly with a patient. The next 2 calculations are more useful for patients.

Method 3: use the RR  to calculate Mr. Fick’s actual risk of death: the RR of death in the RALES trial is 0.70. You multiply this by his estimated death rate and you get his expected death risk if he were on spironolactone instead of nothing. His risk of death is 56%. So 0.70 x 0.56 = 39%. So if Mr. Fick takes spironolactone I expect his risk of death to go from 56% down to 39%. That’s useful information to tell the patient.

Method 4: use the RRR to calculate Mr. Fick’s actual risk of death: This is similar to the concept above except that you have to remember that the RRR (relative risk reduction) is relative. So first you calculate how much risk is reduced by the treatment. The RRR is 30% (1-RR is RRR). Then I multiply this by the patient’s risk of death. 0.30 x 0.56 is 0.168. This 16.8% represents how much risk I have removed from the baseline risk. Now I have to subtract it from the baseline risk and I get his final risk. So 0.56-0.168=0.39 or 39%. Same number as method 3 and it has to give the same number because its just a different way of calculating the exact same thing.

I hope this is useful and now you can give patients some real numbers instead of just saying your risk is decreased by x%.

Remember you need: patients risk of the event without treatment (usually from a prediction rule or maybe the placebo event rate of the study or placebo rate of a subgroup) and event rates from the study. Then you can make all the calculations from there.