Time to Event Data: What to Present? Hazard Ratio, Median Time, Survival Rate?

One of the common endpoints in clinical trials is time to event as calculated as the duration from the time of randomization to the time of occurrence of the specific event (either the good or bad event). In oncology studies, the time to event variable can be overall survival (OS) as calculated from the time of randomization to the time of death or progression-free survival (PFS) as calculated from the time of randomization to the time of disease progression or death (whichever occurs first). In non-oncology studies, the time to event variable is everywhere:

• Time to first exacerbation in COPD, bronchiectasis 
• Time to first clinical worsening event in pulmonary hypertension
• Time to clinical recovery in COVID-19 therapeutical trials
• Time to healing of all non-aborted genital herpes lesions in recurrent genital herpes infection treatment studies 

While time to event may not be related to the death (survival), the time to event analysis is still commonly called 'survival analysis'. 

The statistical analyses for time to event variable include mainly the Kaplan-Meier estimate along with the log-rank test for different survival curves and Cox proportional hazard regression model (or Cox regression in short). 

The statistics can include survival rate (or rate of subjects without an event), median survival time (median time to event), hazard ratio, and their 95% confidence intervals. 

Survival rate (or rate of subjects without an event) is the percentage of subjects in a study or treatment group who are still alive for a certain period of time after they were randomized and started treatment for a disease, such as cancer. It may be called a milestone survival rate. A five-year survival rate will be the percentage of people in a study or treatment group who are alive five years after their randomization or the start of treatment. For clinical trials with short durations, usually, a short survival rate (for example, 6-month survival rate, 1-year survival rate, 3-year survival rate) will be more commonly used.  

Median survival is a statistic that refers to how long subjects survive with a disease in general or after the randomization or initiation of the treatment. It is the time — expressed in weeks, months, or years — when half the subjects are expected to be alive. It means that the chance of surviving beyond that time is 50 percent. similarly, median time to event is a statistic that refers to how long subjects have no specific event after the randomization or initiation of the treatment. It is the time — expressed in weeks, months or years — when half the subjects are expected to be event free. It means that the chance of having an event beyond that time is 50 percent.

Hazard ratio is the ratio of hazards and equals to the hazard rate in the treatment group ÷ the hazard rate in the control group. Hazard rate represents the instantaneous event rate, which means the probability that an individual would experience an event at a particular given point in time after the intervention. 

To present the analysis results for time to event variable, all different statistics can be displayed in the same table. The summary table can be designed as the following: 

Table 14.2.x 

Summary and Analysis of Time to XXX Event

ITT Analysis Set

	Test Drug (N=xx)	Control (N=xx)	p-value
Number of Subjects with Event (n, %)	xx (xx.x)	xx (xx.x)	0.xxx [1]
Number of Subjects Censored (n, %)	xx (xx.x)	xx (xx.x)
Time to XXX Event (time unit)
Kaplan-Meier Estimate			0.xxx [2]
25th Quartile (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
Median (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
75th Quartile (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
Rate (%) of Subjects without an    Event for at Least
1 time unit (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
2 time unit (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
3 time unit (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
4 time unit (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
Etc.
Hazard Ratio (95% CI) (Test Drug     vs Control) [3]	x.xx (x.xx, x.xx)		0.xxx [3]

[1] p-value is calculated with Fisher’s exact test.
[2] p-value is calculated with Logrank test stratified by strata1 and strata2.
[3] Hazard ratio, 95% CI, and p-value are calculated with Cox proportional hazard model with treatment, strata1, strata2 as explanatory variables.

Notice that all three statistics are included: median time to event (or median survival time), rate of subjects without an event (or survival rate), and hazard ratio. Three p-values are calculated: a p-value from Fisher's exact test (or Chi-square test) to compare the event rates between two groups - time was not factored in the calculation; a p-value from log-rank test to compare two survival curves; and p-value from Cox regression model.   

Survival rate is mostly used in oncology studies and rate of subjects with no event is not very commonly used in non-oncology studies. We still see some publications in oncology area where only survival rate is reported and neither the median time nor the hazard ratio is reported - seems to be a little bit obsolete practice. For example, almost all studies from the Children's Oncology Group would only report the survival rate, not the median survival time, not the hazard ratio. 

Median survival time is a good measure if there are enough events that occurred during the study period. If not too many events are observed in the treatment group during the study, the median survival time can not be calculated. 

Hazard ratio is a good measure for the treatment effect when comparing two treatment groups or two sub-groups. see a previous post "Interpreting Hazard Ratio: Can we say "percent reduction in risk"?"

Blinding and Masking Issue in Covid-19 Vaccine Clinical Trials

Clinical trials for Covid-19 vaccine development are moving into the critical late phase stage. The front runners right now are Moderna (in collaboration with NIAIH), Oxford University (in collaboration with AstraZeneca), and BioNTech (in collaboration with Pfizer). All three had published the positive results from their phase 1/2 studies to demonstrate that the Covid-19 vaccines can generate utilizing antibodies against SARS-COV-2 virus and vaccines are tolerable and generally safe in healthy volunteers. 

• Moderna Phase 1 results: Jackson et al (2020) An mRNA Vaccine against SARS-CoV-2 — Preliminary Report NEJM 
• Oxford/AstraZeneca Phase 1/2 results:  Folegatti et al (2020) Safety and immunogenicity of the ChAdOx1 nCoV-19 vaccine against SARS-CoV-2: a preliminary report of a phase 1/2, single-blind, randomised controlled trial. Lancet
• BioNTech/Pfizer Phase 1/2 results: Mulligan et al (2020) Phase 1/2 Study to Describe the Safety and Immunogenicity of a COVID-19 RNA Vaccine Candidate (BNT162b1) in Adults 18 to 55 Years of Age: Interim Report. medRxiV

The confirmatory studies are about to begin to demonstrate the efficacy and safety of the Covid-19 vaccines. The requirements for study design, efficacy endpoint, and safety endpoints are laid out in FDA's guidance "Development and Licensure of Vaccines to Prevent COVID-19"

Moderna is supposed to announce the start of phase 3 study next week. The other two will follow. The phase 3 studies from these three companies have already been registered in clinicaltrials.gov. The table below lists key parameters from these three studies. BioNTch/Pfizer had phase 1/2/3 studies combined in the same study protocol where the results from the phase 1 portion of the study have been published (see above Mulligan et al) 

	Moderna/NIAIH	Oxford/AstraZeneca	BioNTech/Pfizer
Protocol Title	A Phase 3, Randomized, Stratified, Observer-Blind, Placebo-Controlled Study to Evaluate the Efficacy, Safety, and Immunogenicity of mRNA-1273 SARS-CoV-2 Vaccine in Adults Aged 18 Years and Older	A Phase 2/3 Study to Determine the Efficacy, Safety and Immunogenicity of the Candidate Coronavirus Disease (COVID-19) Vaccine ChAdOx1 nCoV-19	A Phase 1/2/3, Placebo-Controlled, Randomized, Observer-Blind, Dose-Finding Study to Evaluate the Safety, Tolerability, Immunogenicity, and Efficacy of SARS-COV-2 RNA Vaccine Candidates Against COVID-19 in Healthy Adults
Phase	Phase 3	Phase 2/3	Phase 1/2/3
Sample Size	30,000	10,260	32,000
Treatment Groups	mRNA-1273 Placebo	ChAdOx1 nCoV-19 (Abs 260) MenACWY vaccine ChAdOx1 nCoV-19 (Abs 260) + 2.2x10^10vp (qPCR) boost Two dose MenACWY vaccine ChAdox1 n-CoV-19 (Abs 260) vaccine low dose ChAdOx1 nCoV-19 (qPCR) ChAdOx1 nCoV-19 plus 5x10^10vp boost (qPCR)	BNT162b1 BNT162b2 BNT162b3 Placebo
Age Groups	18 years and older	18 years or older 18-55 years 70 years and older 5-12 years inclusive	18-55 years of age 65-85 years of age 18-85 years of age
Number of Doses	100 microgram 2 doses (on day 1 and day 29)	1 or 2 doses	Low, low-mid, mid, or high doses 1 or 2 doses
Randomization	Randomized	Randomized	Randomized
Control Group	Placebo [0.9% sodium chloride (normal saline) injection]	MenACWY vaccine (also named Menveo or Nimenrix)	Placebo [a sterile saline solution for injection (0.9% sodium chloride injection, in a 0.5-mL dose)]
Blinding/Masking	Quadruple (Participant, Care Provider, Investigator, Outcome Assessor)	Single (Participant)	Triple (Participant, Care Provider, Investigator)

With the side-by-side comparison, we can see the clear difference in selecting the control group and how the blinding/masking is handled. In studies by Moderna and BioNTech, the control group is a placebo consisting of only the normal saline. But the quadruple and the triple masking (beyond the double-blind) are used to prevent the potential unblinding. 

 In the study by Oxford, the control group is another vaccine, MenACWY vaccine that is approved for protecting against meningococcal disease (meningitis and blood poisoning (septicaemia)) caused by serogroups A, C, W, and Y. The single blinding is used and the participants (volunteers) will not know whether they receive Covid-19 vaccine or MenACWY vaccine. 

In order to prevent potential unblinding - the participants become knowing which treatment they have received, using an active vaccine such as MenACWY that have been approved to be safe seems to be better and more adequate. In the publication of their phase 1 study results, they explained why it's necessary to use MenACWT vaccine as control. 

"MenACWY was used as a comparator vaccine to maintain blinding of participants who experienced local or systemic reactions, since these reactions are a known association with viral vector vaccinations. Use of saline as a placebo would risk unblinding participants as those who had notable reactions would know they were in the ChAdOx1 nCoV-19 vaccine group."

Placebo with saline as the control group is acceptable to FDA. In FDA's guidance "Development and Licensure of Vaccines to Prevent COVID-19", it says "Later phase trials, including efficacy trials, should be randomized, double-blinded, and placebo controlled" even though there is no mention about the requirement for the component of the placebo. 

With placebo (saline) as the control group, no matter whether the triple or quadruple blinding is used, there is still a potential unblinding by the participants because the participants can guess which treatment (Covid-19 vaccine or placebo) they have received based on the adverse events they may experience.

The published early phase results indicate that participants receiving Covid-19 vaccine experience more frequent adverse events in local injection site reactions and systemic reactions. BioNTech/Pfizer study says: 

"pain at the injection site was the most frequent prompted local reaction, reported after Dose 1 by 58.3% (7/12) in the 10 μg, 100.0% (12/12 each) in the 30 μg and 100 μg BNT162b1 groups, and by 22.2% (2/9) of placebo recipients. After Dose 2, pain was reported by 83.3% and 100.0% of BNT162b1 recipients at the 10 μg and 30 μg dose levels, respectively, and by 16.7 % of placebo recipients."

"Reports of fatigue and headache were more common in the BNT162b1 groups compared to placebo. Additionally, chills, muscle pain, and joint pain were reported among BNT162b1 recipients and not in placebo recipients."

After vaccination, participants may be able to guess they have received Covid-19 if they experience adverse events such as local injection site pain and systemic side effects such as fatigue, headache, chills, muscle pain,... They will be able to guess (pretty accurately) that they have received Placebo (saline) if they don't experience any local reactions or systemic side effects. 

If participants become aware of the treatment they have received, will it have an impact on their behavior? Will participants knowing to receive Covid-19 vaccine feel they have some protection, therefore maybe let loose their guard against Covid-19? I hope this will not be the case, otherwise, the biases induced by the behavior change because of the potential unblinding will have an impact on the efficacy results (most likely toward the null hypothesis of no difference).

Waterfall plot(s) to display the results in oncology and non-oncology clinical trials

The waterfall plot(s) started as a visualization tool in oncology studies to display the results of tumor burden, tumor size (or change in tumor size), the tumor responses have gained popularity and appeared in many publications. The application of the waterfall plot has gone beyond the oncology clinical trials. 

According to a paper by Gillespie (2012) Understanding Waterfall Plots,

Waterfall plots are graphic illustrations of data that can vary from audio frequencies to clinical trial patient information and results. In oncology, for example, a waterfall plot may be used to present each individual patient’s response to a particular drug based on a parameter, such as tumor burden. The horizontal (x) axis across the plot may serve as a baseline measure; vertical bars are drawn for each patient, either above or below the baseline. The vertical (y) axis may be used to measure maximum percent change from baseline, e.g., percent growth or reduction of the tumor by radiologic measurement. Those vertical bars that are above the line represent nonresponders or progressive disease. Vertical bars below the baseline (x) axis are drawn for each patient that has achieved some degree of tumor reduction, often depicted as negative percent.

In general, waterfall plots go from the worst value, such as greatest progression of disease, on the left side of the plot, to the best value, i.e., most reduction of tumor, on the right side of the plot; this can also be shown by shifting the graph to a similar presentation, moving from the worst outcomes on the bottom to the best outcomes on the top. The length of each vertical bar hanging below the horizontal axis increases as the plot moves to the right side of the graph, thus resembling a waterfall and giving the graph its name. Thus, the data are not presented randomly, or in order of when a patient first enrolled in a trial, but are organized in order to provide a clear picture of the study population’s results: from worst to best, based on the parameters included. 

The waterfall plot(s) has the following features: 

• It’s basically a bar graph, where each bar typically represents a patient; they are usually ordered from worst results to best.
• The horizontal axis is generally chosen to be a baseline measure, and the bars may go either above or below the baseline. 
• The x-axis is generally the subject number. If the x-axis is not labeled, it defaults to be the subject number. The subjects are listed according to the rank from worst results (on the left) to best results (on the right)
• The y-axis is generally used to quantify response to treatment; for instance, it might represent the percent of growth or reduction in a tumor while a patient is undergoing radiology. Negative bars would show reduction; positive bars would be patients whose cancer is still progressing or non-responders.
• For a study with multiple arms, each arm will have its own waterfall plot. For a study with three treatment arms, there will be three waterfall plots. The difference can be seen by comparing the patterns from different waterfall plots. 

In Advani (2018) CD47 Blockade by Hu5F9-G4 and Rituximab in Non-Hodgkin’s Lymphoma, a waterfall plot was used to display the change in tumor-lesion size with treatments of 5F9 and Rituximab. The waterfall plot showed the best overall change in the size of tumor target lesions among patients with diffuse large B-cell lymphoma (DLBCL; indicated by an asterisk) or follicular lymphoma, according to the maintenance dose received. The y-axis is the percentage changes in the tumor burden of target lesions and the x-axis is the patient number.

In Kopetz et al (2019) Encorafenib, Binimetinib, and Cetuximabin BRAF V600E–Mutated Colorectal Cancer, three waterfall plots were used to display the differences in patterns in best percentage change in the size of target lesions among three treatment groups (triple-therapy, double-therapy, and control groups). Notice that each treatment group has its own waterfall plot. Y-axis is the best percentage change from baseline in tumor size of target lesion. The X-axis is the subject number (even though it is not labeled). 

Waterfall plot(s) has been used in studies beyond the oncology studies. Here are some examples:

In Vichinsky et al (2019) A Phase 3 Randomized Trial of Voxelotor in Sickle Cell Disease, three waterfall plots were used to display the treatment effect in change in hemoglobin level of Vexelotor comparing to Placebo. The y-axis is the change in hemoglobin level from baseline to week 24 (g/dL) and the x-axis is the subject number for each treatment group (even though it is not labeled). 

In Nathan et al (2020) Efficacy of Pirfenidone in the Context of Multiple Disease Progression Events in Patients With Idiopathic Pulmonary Fibrosis, two colorful waterfall plots (one for pirfenidone group and one for the placebo group) were used to display the pattern and distribution of frequency and type of adverse outcome (or disease progression) events including the decline in 6MWD, the decline in %FVC, respiratory-related hospitalization, death, and combination of them. The y-axis is the number of events and the x-axis is the patient number for each treatment group. 

In a retrospective pretest-posttest study with no controls by Sanchez et al (2019) Multiple lifestyle interventions reverses hypertension, two waterfall plots (one for SBP and one for DBP) were used to display the pre-post change in systolic and diastolic blood pressure to indicate the NEWSTART Lifestyle intervention was an effective and rapid means to decrease SBP and DBP.

While waterfall plots can visually show the treatment effects either change from baseline or between treatment groups, there are drawbacks as well. 

According to Kim et al (2019) Assessment of Accuracy of Waterfall Plot Representations of Response Rates in Cancer Treatment Published in Medical Journals, the article assessed 126 studies published in 6 journals where waterfall plots were used to show visual response rates. The author concludes that that waterfall plots are used more frequently over time and exaggerate the visual estimate of the response rate.

In a paper by Shao et al Use and Misuse of Waterfall Plots, the authors concluded that "there was substantial variability in criteria used to generate published waterfall plots. Waterfall plots are subject to substantial variability in criteria used to define them and are influenced by measurement errors; they should be generated by trained radiologists. Caution should be exercised when interpreting the results of waterfall plots in the context of clinical trials."

Waterfall plots can be generated in SAS. There are quite some papers discussing the tips and tricks in generating waterfall plots: 

• Create a waterfall plot in SAS
• Waterfall plot: two different approaches, one beautiful graph 
• Graphical Results in Clinical Oncology Studies
• Useful SAS techniques in Efficacy Analysis for Oncology studies
• Plotting Against Cancer: Creating Oncology Plots Using SAS®

FDA Guidance "Development and Licensure of Vaccines to Prevent COVID-19" - sample size situation for phase 3 studies

Last week, FDA issued its guidance for industry "Development and Licensure of Vaccines to Prevent COVID-19". Unlike the usual FDA guidance where FDA issues the draft guidance with a comment period, this guidance is immediately effective as the final version upon its issuance.

The guidance sets its expectations for the development and licensure of vaccines to prevent coronavirus disease (COVID-19), including considerations for manufacturing, nonclinical and clinical studies, and post-licensure requirements. Also, Dr. Peter Marks, director of the Center for Biologics Evaluation and Research, shed light on the reasoning behind the agency’s 50% efficacy threshold and where the agency stands on challenge trials and emergency use authorizations (EUAs). See the article "Marks on COVID-19 vaccine efficacy, EUAs and challenge trials"

The guidance provided details about the pivotal (phase 3) efficacy and safety study. For phase 3 study, the primary efficacy endpoint should be "the incidence of laboratory-confirmed symptomatic COVID-19" specified in the guidance as the following: 

Section E of the guidance 'Statistical Considerations' provided the specific requirements for the statistical success criteria (i.e., point estimate of vaccine efficacy at least 50% and the lower bound of the alpha-adjusted confidence interval at least 30%). 

What does the vaccine efficacy of 50% mean?

Vaccine Efficacy (VE) = [(COVID-19 attack rate in the unvaccinated group - COVID-19 attack rate in the vaccinated group) / COVID-19 attack rate in the unvaccinated group] * 100%

where the attack rate is equivalent to the incidence rate. 

Using the relative risk (RR) or risk ratio [= (incidence of COVID-19 cases in the vaccinated group) / (incidence of COVID-19 cases in the unvaccinated group)], VE = 1 - RR.

Suppose after 3-6 months observation period post-vaccination, there are 100 cases of laboratory-confirmed symptomatic COVID-19 patients in the unvaccinated group and 50 cases in the vaccinated group, assuming the total follow-up time (person-time) are similar between the unvaccinated and vaccinated groups, the VE will be calculated as (100-50)/100 *100%= 50%.

In practice, the person time (PT) in the vaccinated group and unvaccinated group will be included in the calculation of attack rate or incidence rate where the attack rate = the number of cases observed in the vaccination group or unvaccinated group / Person Time (PT) in the vaccination or vaccination group. If the Poisson regression method is used, the person time will be used in the model as an offset variable. Person time (PT) is the same concept as person-year or patient-year and can be calculated in the same way as the person year with a perhaps different unit. 

VE at least 50% is a point estimate - not dependent on the sample size. For a much smaller trial, if we have 5 cases in the vaccination group and 10 cases in the vaccination group, the VE will still be 50%.

For sample size calculation, we will also need to know the confidence interval. As indicated in the FDA's guidance,  the lower bound of the appropriately alpha-adjusted confidence interval around the primary efficacy endpoint point estimate needs to be greater than 30%.

How to calculate the sample size? Which parameters do we need to calculate the sample size? 

The commercial software (such as EAST, SAS Proc Power, PASS, NQuery Advisor) can all be used to calculate the sample size. In a hypothetic example in the previous post, the sample size was calculated using EAST module for Ratio of Poisson Rates. 

Matthew M. Loiacono had a thesis on "Sample Size Estimation and Power Calculations for Vaccine Efficacy Trials for Exceedingly Rare Diseases" where two SAS macros were developed to estimate the sample sizes: one based on the Exact Conditional Test and one based on the Z Test Normal Approximation.

The sample size calculation will need the following five parameters:

• Incidence of laboratory-confirmed symptomatic COVID-19 cases in the unvaccinated group 
• True efficacy of test vaccine under the alternative hypothesis (according to FDA guidance, this is 50%) 
• Minimum efficacy of test vaccine, under the null hypothesis (according to FDA guidance, this is 30%)
• Power: pre-specified statistical power desired to achieve (usually 80% or 90%) 
• Alpha: pre-specified maximum one-sided level of the test (usually 0.05 for experimental level)

The most critical parameter is the incidence of laboratory-confirmed symptomatic COVID-19 cases - it is difficult to predict; it shifts with geographic location and time; it is impacted by the COVID-19 prevention strategies and policies. In general, the lower the incidence of COVID-19 cases, the larger the sample size is needed for phase 3 study to demonstrate the vaccine efficacy. 

Assuming the incidence of COVID-19 is 0.01 in unvaccinated (placebo) group, with 80% statistical power and alpha = 0.05, using the SAS macro based on Exact Conditional Test method, 33868 volunteers need to be randomized (estimated 254 COVID-19 cases observed) to detect the vaccine efficacy with point estimate at least 50% and lower bound of 95% confidence interval greater than 30%. 

Sample Size for COVID-19 Vaccine Phase 3 Study

Vaccine development for COVID-19 is at historic speed. Several companies have already had vaccines in the early phase of clinical trials. Leading the pack are AstraZeneca / Oxford University and Moderna / NIH who are targeting July for starting the late-stage phase 3 studies. Phase 3 study is pivotal in demonstrating that the vaccine is safe and effective in the general population including those at high risk of contracting COVID-19 and those with underly diseases.

There are quite some discussions about the sample size of the phase 3 study - the sample size for phase 3 study should be adequate to provide sufficient statistical power to demonstrate the vaccine's efficacy in preventing the COVID-19 infection and also adequate for regulatory agencies to assess the safety of the vaccine - sample size should be big enough so that the rare event (if any) can be observed. The sample size is being proposed to be at least 30,000 volunteers.

• FDA Shouldn't Authorize Coronavirus Vaccines Unless They're Tested on at Least 30,000 People: Experts
• Vaccine experts want the FDA to commit to 30,000 people in Covid-19 vaccine trials
• Lawmakers ask FDA to outline COVID-19 vaccine approval process
• Opinion: Here’s why the FDA may approve a Covid-19 vaccine before the November elections, according to Jefferies’ biotech-research team

For pivotal clinical trials, the sample sizes depend on the study design and the primary efficacy endpoint; and estimated based on assumptions.

The study design will be traditionally randomized, double-blinded, placebo- or active-controlled, parallel-group design (not human challenge design even though it has been pushed by some people) - see a previous post "Human Challenge Study Design for Covid-19 Vaccine Clinical Trials?".

• Human challenge trials with live coronavirus aren’t the answer to a Covid-19 vaccine
• Human Challenge Study Design for Covid-19 Vaccine Clinical Trials?

The primary efficacy endpoint is the incidence of symptomatic COVID-19. Moderna has finalized the study design for its phase 3 study and it says that the study will include 30,000 volunteers and the primary and secondary efficacy endpoints as the following:

"The primary objective of the trial, which is set to start in July, is to assess the ability of mRNA-1273 to prevent symptomatic COVID-19 disease. Secondary endpoints will assess the ability of mRNA-1273 to prevent hospitalization and infection with SARS-CoV-2."

•  Fauci: Moderna’s Phase 3 Covid-19 Vaccine Trial Of 30,000 Individuals Will Begin In July
• Moderna finalizes design of phase 3 COVID-19 vaccine trial ahead of July start
• Exclusive: U.S. plans massive coronavirus vaccine testing effort to meet year-end deadline

AstraZeneca/Oxford's COVID-19 vaccine enters phase 2/3 clinical trial. Their proposed sample size is much smaller than 30,000 subjects mentioned by US experts. We can also notice that they propose to use the vaccine against meningococcal bacteria as the control (instead of placebo). 

"Researchers at the University of Oxford have begun enrolling subjects in a phase 2/3 clinical trial of AstraZeneca-partnered COVID-19 vaccine AZD1222. The next stage of the program, which follows a 1,000-subject phase 1, is set to enroll 10,260 people in the U.K. to generate results to support the first shipments to customers in September."

"Once the vaccine moves into phase 3, the researchers will limit enrollment to people age 18 years and older. Adult participants in the phase 2 and 3 trials will be randomized to receive one or two doses of AZD1222 or a vaccine against meningococcal bacteria that will serve as the control.

The use of an active vaccine as a control is intended to ensure participants are unable to tell whether they received AZD1222 based on side effects such as soreness at the injection site. In the absence of such effects across both groups, participants could determine whether they had received the vaccine and make behavioral changes that skew the results of the study. "

Baseline on the study registration on clinicaltrials.gov "A Phase 2/3 Study to Determine the Efficacy, Safety and Immunogenicity of the Candidate Coronavirus Disease (COVID-19) Vaccine ChAdOx1 nCoV-19", we can see the following:

• The study consisted of different sub-groups (different age groups and different duration of the follow-up period).
• The primary efficacy endpoint is the number of biologically confirmed (PCR positive) symptomatic cases of COVID-19
• The primary safety endpoint is the occurrence of serious adverse events (SAEs) throughout the study duration.

It is not clear what the assumptions are used for estimating the sample size (30,000 subjects for Moderna's phase 3 study or 10,260 subjects for AstraZeneca/Oxford's phase 3 study). Perhaps the sample size is more based on the experiences rather than the calculation based on the solid assumptions.
In order to estimate the sample size, we will need to know the incidence rate of symptomatic COVID-19 in the control group (subjects who receive a placebo or a none anti-COVID-19 vaccine) and then the effect size (how much reduction in the incidence rate of symptomatic COVID-19 in the vaccine group (subjects who receive COVID-19 vaccination) - both of these are difficult to obtain.

• Estimating COVID-19 Prevalence in Symptomatic Americans
• COVID-19 Cases in U.S.

The incidence rate of symptomatic COVID-19 can vary significantly depending on the timing, the location, and the prevention and COVID-19 control strategies (i.e., stay-at-home, quarantine, social distance).

Back in January and February, the incidence rate of symptomatic COVID-19 would be very high. But now the COVID-19 situation in China has been under control. It is no longer feasible to test the efficacy of the COVID-19 vaccine in China. There are reports that COVID-19 vaccine researchers in China are looking for foreign sites to recruit the volunteers to test the efficacy of their vaccine candidate.

In the US, the incidence rate of symptomatic COVID-19 would be very high in New York and New Jersey in March/April time, now the states with high incidence rates have shifted to the southern states such as Texas, Arizona, North Carolina.

For phase 3 study to demonstrate the efficacy against the COVID-19, a sufficient number of subjects need to be included in the study so that (hopefully) a sufficient number of symptomatic COVID-19 cases can be observed (more in the control group and less in COVID-19 vaccine group). If subjects are recruited in areas with a high incidence rate, it will be quicker to accrue the number of symptomatic COVID-19 cases. Ironically, with strict COVID-19 prevention/control strategies, by the time the phase 3 studies start, the situation may be under the control and the incidence rate may be too low to accrue enough symptomatic COVID-19 cases. In the article below, a drop in coronavirus cases was listed as one of the biggest risks for Moderna's phase 3 study.

Here Are the 3 Biggest Risks for Moderna Right Now

"3. A drop in coronavirus cases

Of course, a drop in coronavirus cases is great news for everyone. But in order for Moderna and other vaccine makers to test their investigational products, the virus must be actively circulating. In an outbreak situation, the vaccine or placebo is administered to a group of healthy volunteers. If a high number of placebo participants get sick and those who received the vaccine don't, it's likely the vaccine is working. But if the virus is hardly present, it would be impossible to draw such a conclusion.

In the U.S., coronavirus cases recorded by the Centers for Disease Control and Prevention are cumulative, so they will continue to grow. And some states are still seeing spikes. But nationally, the number of people seeking medical attention for symptoms has been on the decline. If the trend continues, it may present difficulties for Moderna and rivals conducting trials in the U.S. to prove vaccine efficacy.

That doesn't mean the vaccine is doomed, but testing it could become more complicated. If virus circulation drops considerably, researchers may conduct a "challenge" trial. That means healthy volunteers are immunized, then exposed to the virus. There also is the possibility of conducting trials in other areas where the virus is on the rise. At this point, Moderna hasn't said it would turn to either of these alternatives."

The primary efficacy endpoint of "biologically confirmed symptomatic cases of COVID-19" belongs to the count data. Given the incidence rate is very low among the general population, the data can be assumed to follow a Poisson distribution or negative binomial distribution. The sample size calculation will then need to be based on Poisson rates or negative binomial rates. 

Hypothetically, the statements about the sample size for phase 3 COVID-19 vaccine studies can be something like this assuming 50% reduction in symptomatic CIVID-19 cases in the vaccine group:

Assuming that the incidence rate (Poisson mean) of subjects with symptomatic COVID-19 case is 0.003 (0.3%) in control group and 0.0015 (0.15%) in COVID-19 vaccination group, 32,673 subjects needs to be randomized to have 80% statistical power to detect the treatment difference."

In the US, we saw the rise in coronavirus cases - it is bad, really bad, but ironically it is good for vaccine clinical trials - it is easier and quicker to accrue a sufficient number of symptomatic COVID-19 cases and it requires less sample size for phase 3 studies to demonstrate the difference between vaccinated and control groups. As Dr. John Skerritt from the Department of Health, Australia said about the COVID-19 pandemic: "Do not waste a good crisis". 

Neutralizing Antibodies: Active Immunization and Passive Immunization Against Covid-19

Generally speaking, a person achieves immunity to disease through the presence of neutralizing antibodies, or proteins produced by the body that can neutralize or even destroy toxins or other disease carriers.  Active immunization is the process of vaccination to prevent an infectious disease by activating the body’s production of antibodies that can fight off invading bacteria or viruses.

The neutralizing antibodies (so-called because they stop the virus from being able to infect cells) can also be obtained from outside the body and can be given the recipients as a therapy for the prevention or treatment of a disease. Passive immunization is the process of administering the antibodies against a particular infectious agent.

An easy example is the antibodies against the rabies. In order to get immunity against rabies virus, we can receive rabies vaccine. Usually 2-3 weeks after the administration of the rabies vaccine (usually several courses), the neutralizing antibodies against rabies will develop in recipient’s body – this is called vaccine-induced active immunity. However, rabies antibodies can also be obtained from the human plasma donated by people in plasma collection centers scattered throughout the United States. The pooled plasma can be fractionated, and rabies antibodies can be obtained – these products are called RIG (Rabies Immune Globulin or hyperimmune globulin against rabies). The RIG can be given to the people to obtain so called ‘passive immunity’. If someone had potential exposure to rabies (for example, bite by wild animals) and had no record of rabies vaccination, the RIG should be immediately given to achieve the passive immunity for short period protection.

The same process of active immunity and passive immunity applies to the Covid-19 situation. Below is a table to compare the active immunity vs. passive immunity in Covid-19 situation:

Active Immunity	Passive Immunity
Relies on neutralizing antibodies against SARS-CoV-2 (the virus causing Covid-19)
active immunity results when exposure to a disease organism triggers the immune system to produce antibodies to SARS-CoV-2	passive immunity results when receiving a therapy containing neutralizing antibodies against SARS-CoV-2
Neutralizing antibodies are generated by our own immune system	Neutralizing antibodies are manufactured or obtained outside the body and then given to the recipients
Active Immunity can be obtained in two ways: Natural Immunity: obtaining immunity because of infection with Covid-19 (whether it is symptomatic or asymptomatic) Vaccine-Induced Immunity: obtaining immunity by receiving the vaccine (vaccination) that won’t make someone sick, but will trigger the body to make neutralizing antibodies), which is known as vaccine-induced immunity	passive immunity is provided when a person is given neutralizing antibodies. Antibody-containing blood products: convalescent plasma obtained from Covid-19 recovered patients Hyperimmune products (containing concentrated neutralizing antibodies) Manufactured antibody products
It will take a while for the body to generate neutralizing antibodies	Off-the-shelf, ready to use
Immunity (once obtained) will be longer	Immunity will be shorter
Companies who are working on vaccines: see previous post “Coronavirus Vaccine Tracker - Developing Vaccines Against Covid-19 “	Key players in the field (examples only): Convalescent plasma – Mayo Clinic Hyperimmune globulin – Grifols Neutralizing antibodies cocktail - Regeneron, Eli Lilly, Sorrento Therapeutics
Clinical trials in ‘healthy’ volunteers	Clinical trials in Covid-19 patients
Clinical trials to demonstrate the effect in prevention (prevent from symptomatic Covid-19)	Clinical trials to demonstrate the effect in treatment (speed up the recovery of the symptomatic Covid-19 patients and decrease the mortality)
The development process is longer	The development process is shorter
Larger sample size for clinical trials required for demonstrating the efficacy in prevention of Covid-19	Smaller sample size for clinical trials required for demonstrating the efficacy in the treatment of Covid-19

References:

• What to Know About Active Vs. Passive Immunity—And Why Both Matter With COVID-19
• Explainer: What are antibody therapies and who is developing them for COVID-19?
• A coronavirus vaccine is still months away, but an antibody treatment could be closer
• Coronavirus Antibody Therapies Raise Hopes—and Skepticism
• "Immunity passports" in the context of COVID-19
• CDC: Immunity Types
• CDC: Rabies 
• China begins phase 1 clinical trials of neutralizing antibody treatment for COVID-19

Coronavirus Vaccine Tracker - Developing Vaccines Against Covid-19

Ultimately, to win the battle against the Covid-19, we will rely on a safe and effective available in very large quantities. Pharmaceutical companies (large or small), biotech companies, academic, and governmental agencies have all rushed into the vaccine development field to fight the Covid-19. We hope that some vaccines will eventually become the winners.

The New York Times has a website for "Coronavirus Vaccine Tracker". The tracker grouped the vaccines into four categories:

• Genetic Vaccines developed by Moderna, BioNTech/Pfizer, Inovio, ...
• Viral Vector Vaccines developed by Oxford/Astrazeneca, CanSinoBIO, Johnson and Johnson,...
• Protein-Based Vaccines developed by Novavax, GSK, Baylor College of Medicine,...
• Whole-Virus Vaccines developed by Sinovac, Sinopharm,...

So far, some vaccines have gone beyond the pre-clinical stage and progressed into the clinical trial stage. Below is a timeline for those vaccines already in human trials: 

Also, this map shows where coronavirus vaccines are being tested around the world.

However, vaccine development is a lengthy process consisting of phase 1 -> phase 2 -> phase 3 clinical trials before the vaccine can be approved for use. In phase 3 study, the candidate vaccine must be demonstrated to be safe in the general public (with different age groups including the population with underly conditions)

With so many clinical trials initiated or to be indicated, there may be a shortage of volunteers for these studies. The extreme measures to control the Covid-19 (guarantee, stay-at-home, face-masks,...) are necessary to prevent the virus spread, however, it will lower the incidence rate of Covid-19 - consequently, the phase 3 studies for vaccines will require larger sample size with more participants in order to have the adequate statistical power and accumulate a sufficient number of Covid-19 infection cases to establish the efficacy of the candidate vaccine. The phase 2 study will include around 1000 volunteers and the phase 3 study will be even bigger with tens of thousands of volunteers. For those vaccines already in the clinical trial stage: the University of Oxford's phase 1/2 trial had a sample size of 1,090 participants. Moderna's vaccine candidate is being tested in phase 2 study with 600 participants. Its phase 3 study is planned to start this July and will include 30,000 participants to test if the vaccine is safe in general population and if the vaccine is effective in preventing symptomatic Covid-19.


Can we really expect to have a safe and effective Covid-19 vaccine available in a year? It is unlikely, but some people are cautiously optimistic. Read the panel discussions below:

Can a Vaccine for Covid-19 Be Developed in Record Time?

A discussion moderated by Siddhartha Mukherjee

Should Drug Safety (or Pharmacovigilence) Group be Provided with the Randomization Schedule for Blinded Studies?

To avoid the conscious and unconscious bias in safety and efficacy assessment, clinical trials are usually designed as double-blinded studies whenever the blinding is feasible. Double-blind indicates that the treatment assignments are concealed to the investigator and the study participants. The blinding is usually extended to the entire study team including the sponsor, CRO, and vendors. If too many study participants are unblinded during the study, the study integrity will be compromised.

However, not everybody is blinded to the treatment assignment. On the Sponsor side, the clinical trial material (CTM) management group is usually unblinded and has full access to the treatment assignments - because they need to make sure that the correct drugs (active or control) are packaged, labeled, shipped, and dispensed. CTM group will track the inventory at the study sites to make sure the study materials are available at all open sites.

The drug safety group or pharmacovigilance group (PVG) may also request for full access to the treatment assignment and they claim the full access to the treatment assignment is needed for serious adverse event reporting.

It is true that the regulations require the drug safety group to report the 'serious and unexpected suspected adverse reaction (SUSAR)' to regulatory agencies, investigators, and IRBs/ECs.

• 21CFR 312.32 IND safety reporting
• Directive 2001/20/EC of the European Parliament and of the Council
• Breaking the Blind in Clinical Trials & Reporting to Health Authorities, Investigators & IRBs/Ethics Committees
• Clinical Safety Data Management: Definitions and Standards for Expedited Reporting
• Safety assessment in Clinical Trials and Beyond

Code of Federal Regulation regarding IND Safety Reporting says:

"(i) Serious and unexpected suspected adverse reaction. The sponsor must report any suspected adverse reaction that is both serious and unexpected. The sponsor must report an adverse event as a suspected adverse reaction only if there is evidence to suggest a causal relationship between the drug and the adverse event, such as:

(A) A single occurrence of an event that is uncommon and known to be strongly associated with drug exposure (e.g., angioedema, hepatic injury, Stevens-Johnson Syndrome);

(B) One or more occurrences of an event that is not commonly associated with drug exposure, but is otherwise uncommon in the population exposed to the drug (e.g., tendon rupture);

(C) An aggregate analysis of specific events observed in a clinical trial (such as known consequences of the underlying disease or condition under investigation or other events that commonly occur in the study population independent of drug therapy) that indicates those events occur more frequently in the drug treatment group than in a concurrent or historical control group."

EU has similar regulations. According to EU directive "on the approximation of the laws, regulations and administrative provisions of the Member States relating to the implementation of good clinical practice in the conduct of clinical trials on medicinal products for human use"

Article 17 Notification of serious adverse reactions 1. (a) The sponsor shall ensure that all relevant information about suspected serious unexpected adverse reactions that are fatal or life-threatening is recorded and reported as soon as possible to the competent authorities in all the Member States concerned, and to the Ethics Committee, and in any case no later than seven days after knowledge by the sponsor of such a case, and that relevant follow-up information is subsequently communicated within an additional eight days. (b) All other suspected serious unexpected adverse reactions shall be reported to the competent authorities concerned and to the Ethics Committee concerned as soon as possible but within a maximum of fifteen days of first knowledge by the sponsor. (c) Each Member State shall ensure that all suspected unexpected serious adverse reactions to an investigational medicinal product which are brought to its attention are recorded. (d) The sponsor shall also inform all investigators.

It is true that the drug safety group needs the treatment assignment information to assess the causal relationship of a SUSAR event to the study drug. If a SUSAR occurs in a placebo group, the event will then not be required to be reported.

Unlike the STM group, the drug safety group only needs the treatment assignment for individual subjects at the time when a SUSAR is reported. It is concerning that the drug safety group is given full access to the treatment assignment for all subjects. Drug safety group personnel sometimes can accidentally communicate the treatment assignment information outside the drug safety group (to the investigator and to the blinded study team) and causing the accidental unblinding of the subject.

I just read the FDA’s review document for a Merck product and noticed the review comments mentioning that drug safety staff should be blinded during the study. Given the potential accidental unblinding caused by drug safety staff, it is prudent to restrict drug safety staff’s access to the randomization codes for ongoing blinded studies.  

https://www.accessdata.fda.gov/drugsatfda_docs/nda/2014/204886Orig1s000MedR.pdf

However, the drug safety group should be given emergency access to the randomization codes. In the situation a SUSAR is reported, drug safety personnel who are handling the SUSAR reporting can log into the interactive response technology (IRT) including interactive web response (IWR) and interactive voice response system (IVR) systems, and obtain the randomization information and treatment assignment for the individual subject with SUSAR reported. 

In summary, the drug safety group or PVG should not be given full access to all randomization codes, but should be provided in a controlled way the access to treatment information for individual subjects who have SUSAR reported.