**(This is a draft and truncated version - for final and full version, see**

Concise Encyclopedia of Biostatistics for Medical Professionals)

Concise Encyclopedia of Biostatistics for Medical Professionals)

**half-life of medications**

When a drug is ingested, it may reach its peak concentration in the system gradually but then starts to decay quickly, or may reach the peak quickly and starts decaying slowly. Half-life is the time taken to go from the peak concentration to half that concentration. Figure H.1 shows half-life for a drug that reaches its peak gradually but decays quickly. Half-life is utilized to measure the duration that a drug remains in the system and may form the basis for prescribing the periodicity (once-a-day, twice-a-day, etc.) of intake. For example, Schulze-Bonhage and Hintz [1] suggested that the anti-epileptic drug perampenal can be prescribed once daily because of its long half-life.

If half-life of a drug is 3 hours, it reduces to one-half of its peak concentration in 3 hours. It does not mean it will vanish in the next 3 hours. After 6 hours, the drug concentration will be one-half of what it was at 3 hours, i.e., one-fourth of the peak concentration; and after 9 hours it will be one-eighth of its peak concentration. It takes more than 4 half-lives to reduce the concentration to less than 5% of its peak concentration. After this, the concentration will not vanish but tends to stabilize. A rule-of-thumb says that it takes about four times the half-life of the drug for the concentration of that drug in the system to reach a steady state irrespective of the half-life. So if you administer a drug with a half-life of 12 hours, the steady state will be achieved after 48 hours. Drugs with short half-life reach to a steady state relatively quickly compared with those with long half-life. An example of the statistical use of half-life is in the field of

**crossover trials**. For a usual crossover experiment to be successful there must be no

**carryover effect**. The time required for the carryover effect to vanish is called the

**washout period**. This should generally be at least four times the half-life of the substance to be confident there is only negligible amount of the substance in the system.

Half-life is obtained by fitting a

**regression**of concentration on time and locating the time point where concentration is one-half of the peak. In most pharmacologic applications, concentration decline is fast in the beginning and increasingly slow later on, which suggests that a log-scale is appropriate. Hence a linear regression of log(concentration) vs. time is generally used. If the slope of this line is

*b*,

Half-life:

*T*½ = . ... ...

**For final and full version, see**

Concise Encyclopedia of Biostatistics for Medical Professionals

Concise Encyclopedia of Biostatistics for Medical Professionals