The rates are represented as “per person-time” to provide more accurate comparisons among groups when follow-up time (i.e., patient exposure time) is not the same in all groups. Theoretically, we can express a rate of events per patient year, but the rate would be typically be a fraction or too small. In practice, the rate can be expressed as per 100, 1000, 100,000, 1 million patient-years or patient-years at risk.

“Patient-year at risk” means that the denominator of the rate calculation is ascertained by adding exposure times of all patients, where each patient’s exposure time is defined as days spent in a pre-determined time period (i.e., a year), censored only by events such as death or disenrollment, or the end of the time period. Divide the total number of days by 365 or 365.25 to get the actual year value.

“Patient-year” means that the denominator of the rate calculation is ascertained by counting all patients who are in the pre-determined time period for at least one day.

The expressions “per 100,000 patient-years at risk” and “per million patient-years” are just different ways of normalizing the rates to better present them. Thus, a hospitalization rate of 0.0000015 per patient-year, can also be expressed as 1.5 per million patient-years.

CTSpedia.org provided pretty detail explanation about the person-time (person year is just a special case of the person-time). An example of calculating death rate using patient year is illustrated from Organ Donor website.

The rate expressed in 'patient year' has been used in many different scenarios. For example, the following paragraph from a website have used 'The number of exacerbations per patient year'; 'the number of exacerbation days per patient year',...

"Additionally, tiotropium significantly reduced the number of exacerbations (0.853 vs 1.051 exacerbations per patient-year; p=0.003) (1) and number of exacerbation days (mean: 12.61 vs 15.96 days per patient year; p is less than 0.001). Similarly, tiotropium significantly reduced the frequency of exacerbation related hospitalizations (0.177 vs 0.253 means hospitalizations per patient year, p=0.013)(1) and the number of hospitalization days (1.433 vs. 1.702, mean days per patient year, p=0.001) compared to placebo. In addition, a reduction in the number of treatment days (antibiotic or steroids) (p is less than 0.001) and unscheduled visits to health care providers for exacerbations (p = 0.017) were also significantly reduced with tiotropium compared to placebo."

In FDA guidance "Efficacy, Safety, and Pharmacokinetic Studies to Support Marketing of Immune Globulin Intravenous (Human) as Replacement Therapy for Primary Humoral Immunodeficiency", the rate of SBI (serious bacterial infection) is per person-year.

"The protocol should prospectively define the study analyses. We expect that the data analyses presented in the BLA will be consistent with the analytical plan submitted to the IND. Based on our examination of historical data, we believe that a statistical demonstration of a

**serious infection rate per person-year**less than 1.0 is adequate to provide substantial evidence of efficacy. You may test the null hypothesis that the serious infection rate is greater than or equal to 1.0 per person-year at the 0.01 level of significance or, equivalently, the upper one-sided 99% confidence limit would be less than 1.0. "

"We recommend that you provide in the BLA descriptive statistics for the number of serious infection episodes per person-year during the period of study observation."

## 15 comments:

Dear Dr Deng,

If it is possible I want to ask about person-years calculation.

// Between 2005-2009 (5 years)11,261,600 mg simvastatin were consumed by patients.

Since Defined Daily Dose of simvastatin is 30 mg, patient exposure is calculated as 1,028.46 patient-year.

The calculation is true or not?

Please inform me

Best regards,

Hande Sipahi,Pharm.Msc.,

Nobel İlaç Sanayii ve Ticaret A.Ş.

İnkılap Mahallesi, Küçüksu Caddesi,

Akçakoca Sokak, No:10

34768 Ümraniye-İSTANBUL

Tel: +90 216 633 64 81

Faks: +90 216 633 64 94

e-mail: fv3@nobel.com.tr

Dear Dr Deng,

I have to estimate aproximately how many patients were exposed to a certain drug in 13 months. The numerator is quantity of drug sold in mg( 7.873.450 mg). The DDD is 10 mg (according WHO). To express the result in patient year

Patient year = 7.873.450 / (10 x 365) = 2157.

Is this calculus correct?

What is the meaning of this result?

Fernando Pereira

fecepe@gmail.com

Dr. Deng,

Would you be able to provide guidance on a question related to the calculation of the CI for a rate per person years? I have used the poisson distribution initially to calculate the Standard error to construct the confidence interval. However I have a request from a regulator to adjust for possible overdispersion. Does that make any sense here? The rate is question is a death rate (so only occurs once per subject). When I run poisson regression the deviance indicates it is under-dispersed and the pearson's chi-square that is is over-dispersed. Any thoughts?

Thanks!

We also use the poisson regression in obtaining the confidence interval. We use SAS procedure GENMOD with # of events as dependent variable and person year as offset variable.

Regarding the over-dispersion issue, you may refer to another blog article at

http://onbiostatistics.blogspot.com/2009/07/poisson-regression-and-zero-inflated.html

you may try the PROC Countreg to adjust for the overdispersion

Dr. Deng - Hello and thank you for this very informative discussion. I have a question about patient year risk from the perspective of forecasting long term outcome. If a clinical study of a patient group with a fixed risk rate over time has documented 1 event per 100 patient years, what is the probability that a new patient with similar circumstances will have an event after 1 year? Is it 1%? How about after 10 years? Is it 10% or actually lower? I'm trying to compare to something more tangible like flipping a coin, where the probability is not 100% after two tosses, but does increase over time, but I'm not knowledgeable enough of the math behind this type of forecasting.

I would appreciate any knowledge you could share. This type of forecasting is often used by doctors to inform patients of their long term risk, and I don't believe it's very well understood.

Thanks so much.

If we have the person years at risk calculated in the data file, but defined for a cell, how can we use the pyr measure in formulation of risk??

If we have the person years at risk calculated in the data file, but defined for a cell, how can we use the pyr measure in formulation of risk?? Thank you.

I am not sure about your question. I am assuming you can always use the data manipulation tools to read the data into the organized format and then perform the analyses.

It's an awesome post in support of all the web visitors; they

will obtain advantage from it I am sure.

Thank you for this helpful information.

I have a question about incidence rate.

If the number of patients during a longitudinal study changes drastically, the incidence rate becomes way higher due to the fact that we divide the number of cases or events by a smaller number of patient-years. Can I solve this problem by dividing this by the total number of patients remaining in the cohort study?

Thank you in advance!

Dear Dr. Deng,

I have a similar question as the one posted earlier by a colleague from Istambul: If the period of exposure is bigger than 1 year (for example 5 years), do we still use 365 or 365.25 as denominator to calculate the patient-year at risk? it doesn't matter the number of years (in this example 5 years)?

I've seen a calculation in a Risk Management Plan where the author used as denominator the total number of days during the exposure period (for example 4140 days). Is this also correct?

Thank you very much in advance for your response.

Liliana Di Stabile, MD.

Email: ldistabile@yahoo.ca

Yes, I think that it is good enough to calculate the person-year by (total # of days) / 365.25.

In terms of the analyses, 'person-year' is just a concept and one of the ways to measure exposure. if the unit of time is small, you can use # of days, # of weeks as the denominator for analyses.

Thank you so much Dr. Deng for your prompt response. Best regards. Liliana

Dear Dr Deng,

I have a questions about patient-years, incidence of complications, and comparing two groups which I hope you can help with:

Background: I am comparing frail patients vs non frail patients. They have a number of procedures during follow-up for cancer. Some of them get complications from these procedures (30-day post-procedure complications). The hypothesis is that frail patients get more of these. The follow-up period is variable so I think it's best expressed as person-years. Some patients will get multiple complications and some will have none.

What is the best way of calculating if there is a statistical difference between these groups?

I have tried a T test which looks at complication rates or individual patient but I wonder whether this is correct?

Many thanks in advance

YZ

If I have 1 per 1000 person years

Does it mean this: IF we observe 1000 people for one year we would expect one person to be a new case during the year of observation?

Also, if I have 504 per 10,000 person years

Does it mean this: IF we observe 10,000 people for one year we would expect 504 people to be new cases during the year of observation?

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