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COVID-19 Phase 2, Phase 3 Continuous Endpoint NCT04315298

Evaluation of the Efficacy and Safety of Sarilumab in Hospitalized Patients With COVID-19: Complete Statistical Analysis

This analysis examines the Phase 2 primary CRP endpoint and selected secondary outcomes from the randomized, placebo-controlled sarilumab study in hospitalized patients with COVID-19. It explains the reported estimates, their uncertainty, and the limits of what the registry record establishes.

Trial start: 2020-03-18  ·  Enrollment: 1912  ·  Sponsor: Regeneron Pharmaceuticals
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for Evaluation of the Efficacy and Safety of Sarilumab in Hospitalized Patients With COVID-19 (NCT04315298), a randomized phase 2, phase 3 study. The primary outcome is Percent Change From Baseline in CRP Levels at Day 4 in Participants With Serum IL-6 Level Greater Than the ULN (Phase 2).

1912
Enrollment
Phase 2, Phase 3
3
Arms
In the primary outcome
-0.57
Mean difference
Phase 2: Sarilumab 200mg IV
-0.72–-0.42
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT04315298
PhasePhase 2, Phase 3
ConditionCOVID-19
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment1912
Arms in the primary outcome3
Lead sponsorRegeneron Pharmaceuticals
Results postedYes

2. Clinical Question

Population

The primary endpoint concerns the Phase 2 modified intention-to-treat population: hospitalized participants with COVID-19 who were randomized, received at least one dose of study drug, and had high baseline IL-6 levels. The endpoint analysis is specifically restricted to participants with serum IL-6 greater than the upper limit of normal. The registry record also describes broader Phase 2 objectives and Phase 3 cohorts, but the primary result is not an estimate across every enrolled participant.

Intervention

The Phase 2 intervention groups received sarilumab 200mg IV or sarilumab 400mg IV. The record also lists sarilumab 800mg IV in Phase 3 cohorts. The primary comparison is between each of the two Phase 2 sarilumab groups and Phase 2 placebo.

Comparator

The comparator for the primary endpoint is Phase 2 placebo. The study is described as randomized and placebo-controlled. The registry record does not report details of the allocation procedure beyond randomized allocation.

Primary question

Among the Phase 2 mITT participants with high baseline IL-6, what percent change from baseline in CRP was estimated at Day 4 in each treatment group, and how did the sarilumab groups compare with placebo? CRP is the measured endpoint; the registry describes negative percent-change values as indicating improvement in CRP. This endpoint is a laboratory measure at a specified time, not by itself a direct measure of recovery, survival, or a broader clinical outcome.

3. Trial Design

The registry record describes an adaptive Phase 2/3, randomized, double-blind, placebo-controlled study of sarilumab in hospitalized patients with COVID-19. The design is parallel-group, with quadruple masking recorded. The sponsor is Regeneron Pharmaceuticals. The record lists an enrollment of 1912 and a completed status. The listed study start is 2020-03-18, and primary completion is 2020-07-24.

The study included Phase 2 and Phase 3 components. Its brief summary describes a Phase 2 objective of evaluating clinical efficacy in hospitalized adults regardless of disease-severity strata. Phase 3 Cohort 1 is described in relation to participants receiving mechanical ventilation at baseline, with separate references to critical and severe groups in the adverse-event listings. Phase 3 Cohort 2 is also described in relation to mechanical ventilation at baseline. The arm descriptions additionally list Phase 3 Cohort 3. The specific design rationale and operational details for these cohorts are not reported in the registry record.

The Phase 2 primary endpoint is narrower than the broad study objective: it is percent change from baseline in CRP at Day 4 among participants whose serum IL-6 level was greater than the upper limit of normal. Phase 2 placebo is compared separately with sarilumab 200mg IV and sarilumab 400mg IV. The primary analysis population is defined as randomized participants who received at least one dose and had high baseline IL-6 levels.

The record lists 74 outcome measures and 152 analyses. It does not report the original sample-size justification or the trial’s detailed statistical analysis plan. In particular, the word adaptive in the official title does not establish which adaptations were planned or implemented; those details are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: Of 1946 participants screened, 1912 were randomized and 1861 were treated. 51 randomized participants were never treated: 26 withdrew consent, 14 investigator decision, 9 deaths, and 3 other.

Only the first 6 of 19 groups are shown.

Overall Study

StagePhase 2: PlaceboPhase 2: Sarilumab 200mg IVPhase 2: Sarilumab 400mg IVPhase 3 Cohort 1: Placebo - CriticalPhase 3 Cohort 1: Sarilumab 200mg IV - CriticalPhase 3 Cohort 1: Sarilumab 400mg IV - Critical
STARTED90187180170242338
COMPLETED61117125101157209
NOT COMPLETED2970556985129

Reasons for not completing this period:

ReasonPhase 2: PlaceboPhase 2: Sarilumab 200mg IVPhase 2: Sarilumab 400mg IVPhase 3 Cohort 1: Placebo - CriticalPhase 3 Cohort 1: Sarilumab 200mg IV - CriticalPhase 3 Cohort 1: Sarilumab 400mg IV - Critical
Withdrawal by Subject000222
Physician Decision000010
Lost to Follow-up510681213
Death2460495970114

Analysis population for the primary outcome, as defined in the registry: Phase 2 mITT population: The modified intention-to-treat (mITT) population includes all randomized participants who received at least one dose of the study drug and have high baseline IL-6 levels.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Only the first 6 of 20 groups are shown.

CharacteristicUnitPhase 2: PlaceboPhase 2: Sarilumab 200mg IVPhase 2: Sarilumab 400mg IVPhase 3 Cohort 1: Placebo - CriticalPhase 3 Cohort 1: Sarilumab 200mg IV - CriticalPhase 3 Cohort 1: Sarilumab 400mg IV - Critical
Participants analysed90187180170242338
Age, ContinuousYears60.3 (SD 13.4)57.1 (SD 14.6)56.3 (SD 14.7)60.1 (SD 15.0)58.5 (SD 13.7)61.8 (SD 14.2)
Sex: Female, Male: FemaleParticipants2163425967111
Sex: Female, Male: MaleParticipants69124138111175227
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants1654405977115
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants599810587119163
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants153535244660
Race (NIH/OMB): American Indian or Alaska NativeParticipants000111
Race (NIH/OMB): AsianParticipants9202113108
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants001010
Race (NIH/OMB): Black or African AmericanParticipants153231233965
Race (NIH/OMB): WhiteParticipants3970647489127
Race (NIH/OMB): More than one raceParticipants000000
Race (NIH/OMB): Unknown or Not ReportedParticipants27656359102137
CRP levelsmilligrams per Liter (mg/L)192.537 (SD 122.295)191.997 (SD 124.583)195.037 (SD 119.274)167.476 (SD 115.020)187.573 (SD 108.085)179.085 (SD 103.837)

6. Primary Endpoint

The registry lists the primary outcome as Percent Change From Baseline in CRP Levels at Day 4 in Participants With Serum IL-6 Level Greater Than the ULN (Phase 2), measured over Baseline and Day 4.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
UnitPercent Change
Endpoint classificationContinuous Endpoint

The primary endpoint is percent change from baseline in C-reactive protein (CRP) at Day 4, assessed in Phase 2 participants with serum interleukin 6 (IL-6) above the upper limit of normal. The registry describes the group estimates as least-squares means from an analysis of covariance model. The calculation is based on the log of the Day 4-to-baseline CRP ratio and then transformed back to the raw scale. The record specifies that negative values imply improvement in CRP.

CRP is a laboratory measure, so this endpoint provides a quantified comparison of a biological measurement at a defined time. The Day 4 measure allows the study to compare early change from baseline between randomized groups. An analysis of covariance can estimate group differences while accounting for model terms, although the specific covariates used are not reported in the registry record.

The endpoint should be interpreted within its stated population and timeframe. It does not directly report how participants felt or functioned, how long they remained hospitalized, or whether they survived. The registry lists clinical status, fever, and oxygenation outcomes among secondary measures, but those are distinct endpoints and should not be substituted for the primary CRP result. A change in a laboratory value is therefore evidence about the laboratory endpoint, not by itself proof of a corresponding change in broader clinical outcomes.

7. Results Posted in the Registry

Mean difference: Phase 2: Sarilumab 200mg IV

-0.57

95% CI: -0.72 to -0.42

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-0.9-0.7-0.5-0.3-0.20.0Phase 2: Placebo (n=80)Phase 2: Sarilumab 200mg IV (n=152)Phase 2: Sarilumab 400mg IV (n=153)Percent Change (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Phase 2: Sarilumab 200mg IVPhase 2: Sarilumab 400mg IV-0.79-0.62-0.45-0.28-0.110.06mean difference vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Time to Improvement (2 Points) in Clinical Status Assessment in Severe or Critical Patients With Serum IL-6 Levels Greater Than the Upper Limit of Normal (Phase 2)Time-to-Event AnalysisHazard ratio1.12 (0.76 to 1.66)2,445 events
Time to Improvement (2 Points) in Clinical Status Assessment in Severe or Critical Patients With All Serum IL-6 Levels (Phase 2)Time-to-Event AnalysisHazard ratio1.18 (0.83 to 1.70)1,147 events
Time to Resolution of Fever for at Least 48 Hours Without Antipyretics or Until Discharge, Whichever is Sooner, in Patients With Documented Fever at Baseline (Phase 2)Time-to-Event AnalysisHazard ratio1.29 (0.83 to 2.02)485 events

Time to Improvement (2 Points) in Clinical Status Assessment in Severe or Critical Patients With Serum IL-6 Levels Greater Than the Upper Limit of Normal (Phase 2)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Phase 2: Placebo vs Phase 2: …Phase 2: Placebo vs Phase 2: …0.690.841.011.221.471.77hazard ratio (as reported) vs control (95% CI)

Time to Improvement (2 Points) in Clinical Status Assessment in Severe or Critical Patients With All Serum IL-6 Levels (Phase 2)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Phase 2: Placebo vs Phase 2: …Phase 2: Placebo vs Phase 2: …0.740.891.061.271.511.81hazard ratio (as reported) vs control (95% CI)

Time to Resolution of Fever for at Least 48 Hours Without Antipyretics or Until Discharge, Whichever is Sooner, in Patients With Documented Fever at Baseline (Phase 2)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Phase 2: Placebo vs Phase 2: …Phase 2: Placebo vs Phase 2: …0.680.861.091.371.732.19hazard ratio (as reported) vs control (95% CI)

The listed secondary outcomes cover clinical-status improvement, fever resolution, and oxygenation-related measures, with some analyses restricted by severity or baseline IL-6. The posted time-to-event results for selected Phase 2 outcomes show broadly similar median times across placebo and sarilumab groups. Across the displayed comparisons, the hazard-ratio confidence intervals include 1, and the reported p-values do not provide clear evidence of a difference under those tests. These measures address clinical events over follow-up, whereas the primary endpoint addresses a Day 4 laboratory change in a defined Phase 2 population.

The secondary findings therefore provide a different kind of evidence from the primary CRP analysis. They do not directly confirm or refute a laboratory result: a biomarker may change without a matching measured difference in clinical outcomes, and the endpoints may differ in population, timing, event frequency, and precision. The registry lists many outcome measures and analyses, but only a subset of the secondary results is described in the posted material underlying this interpretation. A complete evaluation across all secondary measures cannot be inferred from the selected outcomes alone.

Secondary results generally carry less weight when their testing was not protected by a prespecified hierarchy or multiplicity adjustment, because repeated testing can increase the chance of chance findings. Whether such a strategy was used is not reported in the registry record. Secondary analyses can still help describe patterns and generate questions, but their p-values should not automatically be treated as independent confirmatory tests. Nor should the presence of several outcomes be used to select only the most favorable result. The strongest reading keeps the primary endpoint, selected secondary outcomes, and uncertainty about multiplicity distinct.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary endpoint, the posted Phase 2 least-squares mean percent change in CRP was -0.2 for placebo, -0.77 for sarilumab 200mg IV, and -0.78 for sarilumab 400mg IV. The endpoint description states that negative values imply improvement in CRP. Thus, the reported group estimates are negative, with the sarilumab group estimates more negative than the placebo estimate. These are estimates for the specified high-baseline-IL-6 population at Day 4, rather than results for the entire enrolled study population.

The registry’s own ANCOVA analyses report a 95% confidence interval for the log-scale least-squares mean contrast of -1.456 to -1.035 for placebo versus sarilumab 200mg IV, with p < 0.001. For placebo versus sarilumab 400mg IV, the corresponding interval is -1.511 to -1.090, with p < 0.001. The analyses are labelled superiority in the registry. These are sponsor-reported model-based results on the log scale; their scale should not be confused with the raw-scale percent-change estimates described for the treatment groups.

Separate simple, unadjusted recalculations from the posted group summaries give mean differences of -0.57 for sarilumab 200mg IV versus placebo, with a 95% interval from -0.725 to -0.415, and -0.58 for sarilumab 400mg IV versus placebo, with a 95% interval from -0.735 to -0.425. The recalculated p-values are each < 0.001. These calculations use the posted summary values and approximate pooled standard deviations; they are not replacements for the ANCOVA analyses reported by the sponsor. The registry’s analysis takes precedence for interpreting the trial’s own modeled comparison. No discrepancy is flagged between the recalculation and the posted analysis.

The secondary results include time-to-event comparisons for clinical-status improvement and fever resolution. In the reported comparisons, the confidence intervals for the hazard ratios include 1, and the listed p-values do not indicate a clear separation between the compared groups under conventional testing. The recorded medians are broadly similar across groups in these outcomes. These results do not erase or change the primary laboratory result: they measure different outcomes, populations, and time courses. Nor does the primary endpoint establish a corresponding clinical benefit.

Overall, the primary registry analysis indicates a statistically distinguishable difference in the modeled Day 4 CRP endpoint for both sarilumab dose comparisons with placebo in the specified Phase 2 population. The size and precision of that difference must be read in light of the model scale, selected population, single time point, and uncertainty intervals. The registry record alone does not establish the implications of the biomarker comparison for other outcomes.

10. Statistical Methods Explained

The study is recorded as randomized, double-blind, placebo-controlled, parallel-group, and quadruple-masked. Randomization is intended in general to support fair comparisons by distributing measured and unmeasured baseline factors across assigned groups, while masking can reduce the influence of treatment knowledge on care or outcome assessment. These are general statistical principles; the registry record does not provide enough detail to assess how allocation was implemented or how masking was maintained.

What does the primary ANCOVA estimate?

Analysis of covariance (ANCOVA) is a regression-based method for comparing groups while accounting for specified covariates. In general, adjustment can improve precision when covariates are prognostic and can address planned baseline differences. The registry reports ANCOVA and least-squares means for the primary endpoint, but the covariates, model diagnostics, handling of departures from model assumptions, and any sensitivity analyses are not reported in the registry record. The reported primary contrast is on the log scale. The group-level endpoint description also gives transformed estimates on the raw percent-change scale. These scales answer related but not identical presentation questions, so a log-scale estimate should not be read as though it were a raw percentage-point difference.

What is the role of the unadjusted recalculation?

The recalculated comparisons use the posted group means and standard errors to form simple, unadjusted differences and approximate pooled variability. This is a summary-statistics check, not a reproduction of the trial’s ANCOVA. The group sizes differ, and the recalculation does not account for any covariates in the sponsor’s model. The standard deviations used in the calculation are described as approximate. A simple calculation can help readers understand the direction and scale of the posted group summaries, but it cannot recover the original model specification or replace its inference. The sponsor’s analysis is the primary analysis for interpreting the registry result.

How should the p-values be read?

A p-value measures how compatible the observed data are with a specified null hypothesis under the assumptions of the analysis. In general, a small p-value is not the probability that the null hypothesis is true, nor is it a measure of clinical importance. The registry reports p < 0.001 for each primary ANCOVA comparison, while the simple recalculations report p < 0.001. Because those values come from different analyses and scales, they should be kept distinct. The registry record does not report whether the primary comparisons were adjusted for multiplicity.

The secondary time-to-event analyses use the Log Rank method and report hazard ratios, confidence intervals, and p-values. In general, a hazard ratio summarizes the relative rate of an event over follow-up under the analysis assumptions; it is not a ratio of medians. For an outcome defined as time to improvement or resolution, the event is the specified improvement or resolution. The precise interpretation depends on the event definition and coding. The registry labels the analyses but does not report further detail about proportional-hazards checks, censoring rules, or model diagnostics.

Why do confidence intervals matter?

A confidence interval expresses uncertainty in an estimate under the model and sampling assumptions. In general, a 95% confidence procedure would cover the target parameter in 95% of repeated samples if its assumptions held. It does not mean that there is a 95% probability that a fixed parameter lies within the particular interval. For the primary contrasts, the posted intervals are separated from zero on the reported log-scale comparison. For the secondary hazard ratios, the reported intervals span 1. That distinction describes the statistical uncertainty; it does not establish the clinical importance of either result.

What can be said about analysis populations?

The primary population is defined as the Phase 2 modified intention-to-treat population: randomized participants who received at least one dose and had high baseline IL-6 levels. This definition excludes randomized participants who did not receive study drug and does not cover all enrolled participants by definition. The registry record does not report a full accounting of participants excluded from each endpoint analysis, the approach to missing Day 4 CRP values, or sensitivity analyses for missing data. Such details matter because an analysis based on available measurements can be affected if missingness is related to outcome or group.

The total registry record contains many outcomes and analyses. In general, testing many hypotheses increases the chance of at least one apparently notable result if no multiplicity strategy is used. Whether and how the trial controlled that risk, including any hierarchy or adjustment across phases, cohorts, endpoints, and treatment comparisons, is not reported in the registry record. Consequently, individual p-values should be read as the results of the reported comparisons, without assuming that they represent multiplicity-adjusted confirmatory evidence.

11. Confidence Intervals and Precision

The primary registry analysis reports confidence intervals around its model-based contrasts. For placebo compared with sarilumab 200mg IV, the 95% confidence interval for the reported log-scale estimate runs from -1.456 to -1.035. For placebo compared with sarilumab 400mg IV, it runs from -1.511 to -1.090. Both intervals lie on the negative side of zero. These intervals describe the range of values compatible with the analysis at the stated confidence level, subject to the model and sampling assumptions. Their log-scale estimates should not be interpreted as raw percent-change differences.

The simple recalculations from posted summary statistics report intervals of -0.725 to -0.415 for the 200mg comparison and -0.735 to -0.425 for the 400mg comparison. These are unadjusted mean-difference intervals, using approximate pooled variability. They are narrower in meaning than a complete assessment of uncertainty: they do not account for the sponsor’s ANCOVA model, unreported covariate choices, or uncertainty related to missing-data handling. The recalculated intervals are therefore useful as descriptive checks, not as the trial’s definitive inferential results.

Confidence intervals are more informative than a point estimate alone because they show the range of estimates consistent with the data under the analysis. Their width reflects statistical precision, but precision does not resolve questions about bias, endpoint relevance, or generalizability. A narrow interval can still apply only to a restricted population and measure. Likewise, an interval excluding the null value does not by itself show that the estimated difference is important to patients.

The registry’s secondary time-to-event intervals are wider in relation to their estimates and include 1 in each listed comparison. This indicates that the observed data are compatible with a range of hazard ratios, including the null value, under those analyses. The record does not provide enough information to evaluate the precision of every other listed outcome or the robustness of these estimates to alternate modeling choices.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect1013
75% of the observed effect1723
50% of the observed effect3851
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect10205010040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: Phase 2: Sarilumab 200mg IV.

The sample-size calculations are planning illustrations based on the observed effect, not the trial’s original sample-size plan. For the continuous primary endpoint, the figures are participants per arm. For the time-to-event endpoint, the figures are total events across the comparison, not participants per arm. These are different quantities and should not be compared as if they were interchangeable.

The stated illustration assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario uses an effect set to the stated fraction of the observed effect. The planning entries for 80% power and 90% power describe the number of participants per arm, or total events for time-to-event outcomes, that would be needed under those assumptions to have the corresponding probability of detecting the specified effect if it were present. The 90% power target requires more information than the 80% target under the same assumptions.

Scenarios that plan for 75% or 50% of the observed effect represent smaller effects than the full observed estimate. Smaller effects are harder to distinguish from random variation, so they require more participants or more events to achieve the same target power. The figures are conditional on the observed effect being an appropriate basis for planning and on the stated assumptions holding. They are not estimates of the power the completed trial actually had; this is not observed power.

The registry record does not report the original design’s sample-size justification or its original assumptions. The planning illustrations should therefore be used to understand how sample requirements change with effect size and target power, not to infer what the investigators planned or whether the trial was adequately powered for every endpoint, cohort, or comparison.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

  1. Observed difference Δ = -0.570; pooled standard deviation σ = 0.442.
  2. n = 2 × (1.96 + 0.842)2 × 0.4422 / -0.5702 = 9.4, rounded up to 10 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -0.57                      # observed difference in means
sigma <- 0.441872143616621                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(4315298)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 10 (80% power), 13 (90% power)
 75% of observed effect: n per arm = 17 (80% power), 23 (90% power)
 50% of observed effect: n per arm = 38 (80% power), 51 (90% power)
power.t.test: 10.5 
Simulated power at n = 10 per arm: 0.776 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

Very small required sample. The formula gives a very small requirement because the observed effect is very large relative to the variability. Normal-approximation formulas are unreliable at such sizes, and the simulation above shows the power actually achieved. An exact or simulation-based design would be needed in practice.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
ANCOVALS Mean (log scale) -1.25-1.456 to -1.035< 0.001
ANCOVALS Mean (log scale) -1.30-1.511 to -1.090< 0.001

The sponsor-reported primary analyses are ANCOVA comparisons of least-squares means on the log scale. They report a value of -1.25 for placebo versus sarilumab 200mg IV, with a 95% confidence interval from -1.456 to -1.035 and p < 0.001. For placebo versus sarilumab 400mg IV, the reported value is -1.30, with a 95% confidence interval from -1.511 to -1.090 and p < 0.001.

The recalculations use the posted group summaries to estimate simple unadjusted mean differences on the raw percent-change scale. They are not intended to reconstruct the ANCOVA model, and the two types of estimates should not be treated as numerically identical or placed on the same scale without transformation. The record does not flag a discrepancy between the recalculation and sponsor analysis. Nevertheless, the sponsor’s own analysis takes precedence because it is the trial’s reported model-based analysis. The recalculation is supplementary context about the posted summaries, not a substitute analysis or a reason to revise the sponsor’s result.

15. Multiplicity, Missing Data and Analysis Populations

The registry record lists 74 outcome measures and 152 analyses. When several outcomes, comparisons, populations, and time points are assessed, there are multiple opportunities to observe a small p-value by chance. General statistical approaches to this issue include prespecifying a hierarchy of hypotheses or adjusting significance thresholds across a family of tests. Whether either approach was used for this study, and which analyses were included in any testing family, is not reported in the registry record.

The primary results include two sarilumab-versus-placebo comparisons. The posted analyses are labelled superiority, but that label alone does not establish that the two comparisons were adjusted for multiplicity or that a formal testing sequence was used. The registry record also does not describe how Phase 2 and Phase 3 analyses, cohorts, secondary outcomes, or repeated assessments were handled in an overall error-control strategy. The reported p-values should therefore be understood as the values attached to the specific posted analyses, without assuming that they are adjusted across all tests.

Missing-data handling is also not reported in sufficient detail. The primary population requires a Day 4 CRP assessment for the endpoint estimate, but the record does not explain how missing measurements were addressed, how many values were missing, or whether sensitivity analyses were conducted. The same limitation applies to the detailed censoring and missing-outcome rules for the secondary time-to-event analyses. In general, missing data can affect estimates if the probability of a missing measurement is related to treatment or outcome. Without the analysis details, the extent and direction of any effect cannot be assessed.

The primary mITT definition is reported: randomized participants who received at least one dose and had high baseline IL-6 levels. The registry record does not report a full flow of participants into each analysis population or explain whether additional exclusions were made. These omissions limit independent assessment of selection, missingness, and multiplicity, even though the endpoint estimates and sponsor analyses are posted.

16. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Phase 2: Placebo399043.3%
Phase 2: Sarilumab 200mg IV9018748.1%
Phase 2: Sarilumab 400mg IV8418046.7%
Phase 3 Cohort 1: Placebo - Critical8917052.4%
Phase 3 Cohort 1: Sarilumab 200mg IV - Critical11924249.2%
Phase 3 Cohort 1: Sarilumab 400mg IV - Critical18333854.1%
Phase 3 Cohort 1: Placebo - Severe117015.7%
Phase 3 Cohort 1: Sarilumab 200mg IV - Severe2314016.4%
Phase 3 Cohort 1: Sarilumab 400mg IV - Severe3013721.9%
Phase 3 Cohort 1: Placebo - MSOD274658.7%
Phase 3 Cohort 1: Sarilumab 200 mg IV - MSOD679570.5%
Phase 3 Cohort 1: Sarilumab 400 mg IV - MSOD589263.0%
Phase 3 Cohort 1: Placebo - Immunocompromised3837.5%
Phase 3 Cohort 1: Sarilumab 200 mg IV - Immunocompromised61250.0%
Phase 3 Cohort 1: Sarilumab 400 mg IV - Immunocompromised91560.0%
Phase 3 Cohort 2: Placebo101566.7%
Phase 3 Cohort 2: Sarilumab 800 mg IV51631.2%
Phase 3 Cohort 3: Placebo1616.7%
Phase 3 Cohort 3: Sarilumab 800 mg IV1250.0%
Participants with at least one serious adverse event
Serious adverse events by armPhase 2: Placebo43.3%Phase 2: Sarilumab 200mg IV48.1%Phase 2: Sarilumab 400mg IV46.7%Phase 3 Cohort 1: Placebo - C…52.4%Phase 3 Cohort 1: Sarilumab 2…49.2%Phase 3 Cohort 1: Sarilumab 4…54.1%Phase 3 Cohort 1: Placebo - S…15.7%Phase 3 Cohort 1: Sarilumab 2…16.4%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Phase 2: Placebo24 of 90
Phase 2: Sarilumab 200mg IV60 of 187
Phase 2: Sarilumab 400mg IV49 of 180
Phase 3 Cohort 1: Placebo - Critical59 of 170
Phase 3 Cohort 1: Sarilumab 200mg IV - Critical70 of 242
Phase 3 Cohort 1: Sarilumab 400mg IV - Critical114 of 338

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Phase 2: Placebo20 of 90
Phase 2: Sarilumab 200mg IV48 of 187
Phase 2: Sarilumab 400mg IV44 of 180
Phase 3 Cohort 1: Placebo - Critical24 of 170
Phase 3 Cohort 1: Sarilumab 200mg IV - Critical57 of 242
Phase 3 Cohort 1: Sarilumab 400mg IV - Critical83 of 338

Most frequent serious adverse event terms

Event termOrgan systemPhase 2: PlaceboPhase 2: Sarilumab 200mg IVPhase 2: Sarilumab 400mg IVPhase 3 Cohort 1: Placebo - CriticalPhase 3 Cohort 1: Sarilumab 200mg IV - CriticalPhase 3 Cohort 1: Sarilumab 400mg IV - Critical
Respiratory failureRespiratory, thoracic and mediastinal disorders6 of 9015 of 18712 of 18015 of 17023 of 24222 of 338
COVID-19Infections and infestations3 of 9013 of 1875 of 18015 of 17019 of 24223 of 338
Cardiac arrestCardiac disorders3 of 909 of 18716 of 1807 of 1707 of 24225 of 338
Acute kidney injuryRenal and urinary disorders5 of 909 of 1879 of 18010 of 17012 of 24210 of 338
Acute respiratory failureRespiratory, thoracic and mediastinal disorders7 of 908 of 1874 of 18010 of 1706 of 24217 of 338
Deep vein thrombosisVascular disorders1 of 904 of 1879 of 1804 of 1708 of 24212 of 338
Septic shockInfections and infestations1 of 904 of 1872 of 1809 of 1706 of 24212 of 338
HypoxiaRespiratory, thoracic and mediastinal disorders4 of 903 of 1875 of 1804 of 1705 of 24211 of 338
Cardio-respiratory arrestCardiac disorders6 of 9011 of 1878 of 1801 of 1703 of 2422 of 338
HypotensionVascular disorders0 of 904 of 1873 of 1806 of 1706 of 24210 of 338

Most frequent non-serious adverse event terms

Event termOrgan systemPhase 2: PlaceboPhase 2: Sarilumab 200mg IVPhase 2: Sarilumab 400mg IVPhase 3 Cohort 1: Placebo - CriticalPhase 3 Cohort 1: Sarilumab 200mg IV - CriticalPhase 3 Cohort 1: Sarilumab 400mg IV - Critical
Alanine aminotransferase increasedInvestigations13 of 9038 of 18730 of 18019 of 17042 of 24251 of 338
Aspartate aminotransferase increasedInvestigations15 of 9030 of 18730 of 18016 of 17036 of 24236 of 338
Transaminases increasedInvestigations0 of 900 of 1870 of 1800 of 1700 of 24224 of 338
Hepatic enzyme increasedInvestigations0 of 900 of 1870 of 1800 of 1700 of 2420 of 338
Liver function test increasedInvestigations0 of 900 of 1870 of 1800 of 1700 of 2420 of 338
NeutropeniaBlood and lymphatic system disorders0 of 900 of 1870 of 1800 of 1700 of 2420 of 338
CholangitisHepatobiliary disorders0 of 900 of 1870 of 1800 of 1700 of 2420 of 338
Acinetobacter infectionInfections and infestations0 of 900 of 1870 of 1800 of 1700 of 2420 of 338
BacteraemiaInfections and infestations0 of 900 of 1870 of 1800 of 1700 of 2420 of 338
Clostridium difficile colitisInfections and infestations0 of 900 of 1870 of 1800 of 1700 of 2420 of 338

Serious events with the highest arm-level rate: acute respiratory failure (50.0%), anaemia (20.0%), covid-19 (16.7%), septic shock (16.7%), atrial fibrillation (16.7%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry’s adverse-event listings give, for each listed group, the number at risk and the number affected by serious adverse events, other adverse events, and deaths. These counts are reported separately by phase, cohort, treatment, and in some cases severity or clinical category. They are descriptive safety data, and the group denominators vary. They should be read within the specific group labels rather than combined across groups or treated as direct comparative rates.

For example, the Phase 2 placebo listing reports 39 participants affected by serious adverse events among 90 at risk, while the Phase 2 sarilumab 200mg IV listing reports 90 among 187 at risk and the 400mg IV listing reports 84 among 180 at risk. The corresponding death counts in these listings are 24, 60, and 49. These are counts, not adjusted comparisons. No risk differences, relative risks, or statistical tests for these safety comparisons are reported in the record excerpt.

The serious-event terms listed most prominently include acute respiratory failure, anaemia, COVID-19, septic shock, atrial fibrillation, and pulseless electrical activity, with the record giving percentages for these terms. The underlying denominator and precise meaning of those term percentages are not specified in the available listing, so they should not be interpreted as incidence rates for an entire treatment group. The reported safety counts are not, by themselves, evidence of causation or a complete benefit-risk assessment.

17. What the Result Does, and Does Not, Mean

The primary analysis shows that the sponsor’s model estimated different Day 4 CRP results for each sarilumab dose comparison with placebo in the Phase 2 population with high baseline IL-6. The reported ANCOVA confidence intervals lie below zero on the log scale, and both comparisons have p < 0.001. The group estimates on the raw percent-change scale are negative, which the registry defines as improvement in CRP. These statements describe the measured endpoint and the reported statistical analyses.

The result does not establish that a particular CRP difference is important to participants, nor does it by itself establish an effect on clinical status, oxygenation, fever, hospitalization, or survival. Those outcomes require their own estimates and uncertainty assessment. The selected secondary time-to-event results have intervals that include the null value; they should be read as separate analyses rather than as translations of the CRP result.

The finding also does not automatically apply to every hospitalized patient with COVID-19. The primary population is restricted to Phase 2 participants with high baseline IL-6 who were randomized and received at least one dose. The study included other phases and cohorts, but the primary endpoint result is not an all-cohort estimate. The registry’s summaries do not establish how results vary in groups outside the primary analysis population.

Finally, a statistically distinguishable estimate is not the same as certainty. Confidence intervals, model assumptions, missing-data methods, and multiplicity procedures all affect interpretation. Some of those methodological details are not reported in the registry record. The most defensible conclusion is therefore limited: the reported Phase 2 analysis found a difference in its specified Day 4 CRP endpoint, while the clinical meaning and broader implications cannot be determined from that endpoint alone.

18. Why This Trial Matters Statistically

This trial is statistically interesting because it has a broad Phase 2/3 structure but a primary result tied to a narrower Phase 2 population and a laboratory endpoint. Recognizing the distinction between the overall study and the analysis population is essential: an enrollment figure for the full study does not describe the population contributing to every outcome. The primary result is specifically about high baseline IL-6 participants and Day 4 CRP.

It also illustrates why the analysis scale matters. The registry gives transformed raw-scale percent-change estimates for each treatment group, while the sponsor’s comparisons are reported as ANCOVA least-squares mean contrasts on the log scale. A separate simple calculation from group summaries produces unadjusted mean differences. These estimates are related, but they are not interchangeable. Reading them without checking their scale and model could lead to mistaken conclusions about what was estimated.

The study also demonstrates the value of separating statistical evidence from clinical interpretation. The primary model-based comparisons have small p-values and confidence intervals that do not include the null value on the reported scale. Yet the outcome is a biomarker measurement, and selected clinical secondary outcomes have their own uncertainty. Statistical evidence for one endpoint does not answer every clinical question.

Finally, a large registry record with many outcomes makes multiplicity and transparent reporting important. The listed outcome and analysis counts indicate a substantial set of evaluations, while the record does not specify the full error-control strategy or missing-data approach. Those limitations do not invalidate the posted estimates; they define what can be concluded from the registry record and what requires fuller methodological documentation.

19. Limitations

The primary endpoint is restricted to the Phase 2 mITT population with high baseline IL-6 and measures CRP at Day 4. The result should not be generalized automatically to the other Phase 2 participants, Phase 3 cohorts, or all hospitalized patients in the study. The posted endpoint is a laboratory measure, and the registry record does not establish how its changes map onto patient-important outcomes.

The sponsor’s detailed ANCOVA specification is not reported. The covariates, model diagnostics, and sensitivity analyses are therefore unavailable for independent review in the registry record. The unadjusted recalculations rely on approximate pooled variability and posted summaries; they cannot reproduce the sponsor’s model. The sponsor analysis remains the appropriate reported analysis for the primary result.

The record does not give the original sample-size justification, detailed multiplicity strategy, or missing-data methods. It also does not provide a complete participant flow for each endpoint analysis in the information used. These gaps limit assessment of whether the planned testing strategy, missing observations, and analysis-population selection could affect interpretation.

The selected secondary outcomes do not provide a complete account of all listed outcomes, and their results should not be treated as a single coherent confirmatory test without knowing the testing plan. Adverse-event counts are reported across differing group definitions and denominators; the listed counts alone do not support adjusted comparative safety conclusions. The serious-event term percentages also lack a stated denominator in the listing. These are limitations on interpretation, not grounds for inferring unreported results.

20. Related Tutorials

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23. Record Summary

The registry record describes a completed, randomized, double-blind, placebo-controlled, parallel-group Phase 2/3 study of sarilumab in hospitalized patients with COVID-19. It lists quadruple masking, Regeneron Pharmaceuticals as sponsor, enrollment of 1912, a start date of 2020-03-18, and primary completion on 2020-07-24.

The primary endpoint is percent change from baseline in CRP at Day 4 among Phase 2 mITT participants with serum IL-6 above the upper limit of normal. The sponsor-reported ANCOVA comparisons of both sarilumab doses with placebo have 95% confidence intervals below zero on the log scale and p < 0.001. Selected secondary time-to-event comparisons are less conclusive, with reported confidence intervals including 1.

The registry record does not report the original sample-size justification, detailed multiplicity procedures, or sufficient information about missing-data handling and model specification. The primary result is evidence about the specified CRP endpoint and population; its broader clinical meaning cannot be established from that result alone.

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