Excel spreadsheet to calculate the p-value for Fisher Exact test

A colleague of mine wants to have a small program to calculate the p-values during the course of the study for a randomized, open label study. For those who don't want to use any statistical software such as SAS, an excel spreadsheet can serve the purpose.

                 Calculating p-value for Fisher exact test

However, this is not a good practice and should be discouraged or prehibited. Even though this is a randomized, open label study, the study team should be restrained from continuously performing the testing based on the cumulative data.

Age Group in Pediatric, Perinatal or Preterm, and Geriatric Subjects

In a previous blog article, I discussed the “Pediatric use and geriatric use of drug and biological products”:

For Pediatric population: according to ICH guidance E11 "Clinical Investigation of Medicinal Products in the Pediatric Population", the pediatric population contains several sub-categories:

• preterm newborn infants

• term newborn infants (0 to 27 days)

• infants and toddlers (28 days to 23 months)

• children (2 to 11 years)

• adolescents (12 to 16-18 years (dependent on region))

Notice that in FDA's guidance "General Considerations for Pediatric Pharmacokinetic Studies
for Drugs and Biological Products for Drugs and Biological Products", the age classification is a little bit different. I am assuming that the ICH guidance E11 should be the correct reference.
Geriatric population:
Geriatric population is defined as persons 65 years of age and older. There is no upper limit of age defined.

Recently, I run into several studies where the age group needs to be further split.

Pediatric population can be further divided into 2-5 years old, 6-11 years old, and 12-16 years old.

This grouping of the pediatric population was used in a pharmacokinetic study in primary immunodeficiency patients in child. Per FDA’s request, the pediatric patients are further divided into groups 2-5, 6-11, and 12-16 years old. FDA asked that the study should contain subjects in each of the sub-groups so that the assessment can be made to see if the pharmacokinetics are consistent across different pediatric sub-groups (or at least there should be no obvious difference among these sub-groups).

“An Open-label, Single-sequence, Crossover Study to Evaluate the Pharmacokinetics, Safety and Tolerability of Subcutaneous GAMUNEX®-C in Pediatric Subjects With Primary Immunodeficiency”

The age definition in perinatal period is much trickier. In a policy statement by Committee on Fetus and Newborn “Age Terminology Duringthe Perinatal Period”, various definitions of age are described:

• Gestational age (or “menstrual age”) is the time elapsed between the first day of the last normal
• menstrual period and the day of delivery
• “Chronological age” (or “postnatal” age) is the time elapsed after birth
• Postmenstrual age (PMA) is the time elapsed between the first day of the last menstrual period and birth (gestational age) plus the time elapsed after birth (chronological age). Postmenstrual age is usually described in number of weeks and is most frequently applied during the perinatal period beginning after the day of birth.

In clinical trials with pre-term babies, the study endpoints are usually defined based on the post-menstrual age (PMA). For example, in an article by Bassler et al “Early inhaled budesonide for the prevention ofbronchopulmonary dysplasia”, the primary outcome was a composite of death

or bronchopulmonary dysplasia at 36 weeks of postmenstrual age. While the study treatment will not be given until after the birth, 36 weeks of postmenstrual age is counted from the first day of the last menstrual period. For different babies, the chronological age or observation period (when the death or BPD event is observed) will be different depending on the actual gestational age.  

It can be illustrated in the following diagram.

• Gestational age = birth date – the first day of the last normal menstrual period
• Chronological age = assessment date or event date – birth date
• Postmenstrual age = assessment date or event date – the first day of the last menstrual period
• Postmenstrual age = gestational age + chronological age

Geriatric population can be further divided: 

In a study with Interstitial Lung Diseases (ILDs) in elderly patients, there are substantial number of patients with age >= 80 years old. The traditional definition of geriatric population using 65 years old as a cut point will not be sufficient. We end up further dividing the geriatric population into 65 - < 80 years old and >= 80 years old. We think this will provide more meaningful sub-grouping to assess the impact of the age group in ILD indication. 

(Bayes) Success Run Theorem for Sample Size Estimation in Medical Device Trial

In a recent discussion about the sample size requirement for a clinical trial in a medical device field, one of my colleagues recommended an approach of using “success run theorem” to estimate the sample size. ‘Success run theorem’ may also be called ‘Bayes success run theorem’. In process validation field, it is a typical method based on a binomial distribution that leads to a defined sample size.  

Application of success run theorem depends on the reliability of the new process (or new device). In medical device trials, the reliability is the probability that an item (i.e. the device) will carry out its function satisfactorily for the stated period when used according to the specified conditions. A reliability of 95% means that a medical device will be functional without problem for 95% of times.

With the success run theorem, we will calculate the sample size so that we have 95% confidence interval to run the device without failure (reliability). Usually, people use 95% confidence interval to achieve 95% reliability. With ‘success run theorem’, the sample size can be calculated as:

                                 N = ln(1-C)/ln( R)

Where N is the sample size needed, C is the confidence interval, and R is the reliability.

With typical 95% confidence interval to achieve 95% reliability, a sample size of 57 will be needed. 

The website below contains the explanation how the success run theorem formula is derived. With C = 1 – R^(n+1), we would have N = [ln(1-C)/ln(R)] – 1, slightly different from the formula above.

 How do you derive the Success-Run Theorem from the traditional form of Bayes Theorem?

This derivation above is based on uniform prior for reliability (a conservative assumption) which assumes no information from predicate devices and the same weight to every reliability value to fall anywhere between 0 to 1.

In medical device field, devices evolve and they are constantly being improved. When we evaluate a new device or next generation device, there is usually some prior information that can be based on. Therefore, instead of uniform prior for reliability, Bayesian technique with mixture of beta priors for reliability can be applied. Using mixtures of beta priors for reliability, we will be able to incorporate historical information from predicate device to decrease the sample size requirement.

We have seen this application in the field of automotive electronics attribute testing, but have not seen any application in FDA regulatory medical device testing.

References:  

• Mark Durivage (2017) How To Establish The Number Of Runs Required For Process Validation
• Mark Durivage (2016)
• Risk-Based Approaches To Establishing Sample Sizes For Process Validation
• Mark Durivage (2014) Sample Sizes: How Many Do I Need?
• Howdo you derive the Success-Run Theorem from the traditional form of BayesTheorem?
• Kleyner, S Bhagath, M. Gasparini, and J. Robinson (1997) Bayesian Techniques to Reduce the Sample Size in Automotive Electronics Attribute Testing