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Secondary Hyperparathyroidism Phase 3 Time-to-Event Analysis NCT00345839

E.V.O.L.V.E. Trial™: EValuation Of Cinacalcet Hydrochloride (HCl) Therapy to Lower CardioVascular Events: Complete Statistical Analysis

The E.V.O.L.V.E. trial compared cinacalcet with placebo for time to a primary cardiovascular composite endpoint in people with chronic kidney disease and secondary hyperparathyroidism receiving dialysis. The posted results include a Cox hazard ratio, a log-rank test, and selected secondary and safety information.

Trial start: 2006-08-22  ·  Enrollment: 3883  ·  Sponsor: Amgen
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 E.V.O.L.V.E. Trial™: EValuation Of Cinacalcet Hydrochloride (HCl) Therapy to Lower CardioVascular Events (NCT00345839), a randomized phase 3 study. The primary outcome is Time to Primary Composite Endpoint (All-cause Mortality, Myocardial Infarction, Hospitalization for Unstable Angina, Heart Failure or Peripheral Vascular Event).

3883
Enrollment
Phase 3
2
Arms
In the primary outcome
0.93
Hazard ratio
Cinacalcet vs Placebo
0.85–1.02
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00345839
PhasePhase 3
ConditionSecondary Hyperparathyroidism, Chronic Kidney Disease
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment3883
Arms in the primary outcome2
Lead sponsorAmgen
Results postedYes

2. Clinical Question

Population

The registry describes people with chronic kidney disease and secondary hyperparathyroidism who were receiving dialysis. The primary analysis used the Efficacy Analysis Set, which included all randomized participants; participants were analyzed in the group to which they were assigned under the intent-to-treat method. The registry reports an enrollment of 3883.

Intervention

Cinacalcet, also described in the registry as cinacalcet HCl, was the active treatment. The registry identifies the study as phase 3 and reports random allocation and double masking. Specific dosing, treatment duration, and adherence information are not reported in the registry record.

Comparator

The comparator was placebo. The study used a parallel-group design. The arm descriptions do not provide further details about treatment procedures, and those details are not reported in the registry record.

Primary question

The primary question was whether time from randomization to the first confirmed event in a composite of all-cause mortality, myocardial infarction, hospitalization for unstable angina, heart failure, or a peripheral vascular event differed between the cinacalcet and placebo groups. The registry reports a Cox hazard ratio and a log-rank p-value for this comparison. These statistics describe the posted time-to-event comparison; they do not, by themselves, establish a causal explanation for any observed difference.

The endpoint combines several serious outcomes into one time-to-first-event measure. This can capture a broad range of events relevant to cardiovascular health, while also meaning that the composite result does not identify which component drives the overall comparison. The registry lists additional outcomes, including all-cause mortality, myocardial infarction, hospitalization for unstable angina, heart failure, peripheral vascular events, cardiovascular mortality, stroke, and bone fracture. The listed components are not interchangeable: their clinical meaning and frequency may differ. The primary result therefore addresses the composite question specified in the registry, rather than answering every question about each component separately.

3. Trial Design

The E.V.O.L.V.E. trial was a phase 3, randomized, double-masked, parallel-group comparison of cinacalcet and placebo. The registry gives an enrollment of 3883 and identifies chronic kidney disease and secondary hyperparathyroidism as the conditions under study. Its brief description concerns patients receiving dialysis. The study is marked completed, and the registry records its start and primary completion dates.

Random allocation is intended, in general, to make treatment groups comparable on average at the start of a trial. Masking can reduce the influence of treatment knowledge on participant experience, clinical decisions, and outcome assessment. Those are general design principles; the registry does not report the exact randomization procedure, the masking procedures for each role, or details of allocation concealment. The arm descriptions do not add treatment-procedure information.

The primary analysis description states that it used the Efficacy Analysis Set, including all randomized participants, and that participants were analyzed according to their randomized treatment group using the intent-to-treat method. This means the stated analysis retains the randomized-group comparison rather than reclassifying participants according to treatment received. The primary endpoint was time from randomization to the first confirmed event in the composite, assessed up to 5.4 years. The registry also describes the primary comparison as stratified by history of diabetes and country.

The registry lists ten outcome measures and twenty analyses. It identifies secondary outcomes that include mortality and several cardiovascular events, as well as bone fracture. The displayed secondary information is incomplete across those outcomes: comparative results for outcomes without posted estimates are not reported in the registry record. The protocol, detailed follow-up procedures, original sample-size justification, planned interim analyses, and full statistical analysis plan 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: Participants were screened over a 30 day period.

Overall Study

StageCinacalcetPlacebo
STARTED19481935
COMPLETED17991776
NOT COMPLETED149159

Reasons for not completing this period:

ReasonCinacalcetPlacebo
Withdrawal by Subject9198
Lost to Follow-up5861

Analysis population for the primary outcome, as defined in the registry: Utilizes the Efficacy Analysis Set which includes all randomized participants. Participants were analyzed in the treatment group as randomized using the Intent-to-treat (ITT) method.

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.

CharacteristicUnitCinacalcetPlaceboTotal
Participants analysed194819353883
Age, ContinuousYears54.8 (SD 14.5)54.0 (SD 14.2)54.4 (SD 14.4)
Sex: Female, Male: FemaleParticipants8097691578
Sex: Female, Male: MaleParticipants113911662305
Race/Ethnicity, Customized: White or CaucasianParticipants112411162240
Race/Ethnicity, Customized: Black or African AmericanParticipants409428837
Race/Ethnicity, Customized: Hispanic or LatinoParticipants317310627
Race/Ethnicity, Customized: AsianParticipants473885
Race/Ethnicity, Customized: JapaneseParticipants415
Race/Ethnicity, Customized: American Indian or Alaska NativeParticipants5712
Race/Ethnicity, Customized: Native Hawaiian or Other Pacific IslanderParticipants12921
Race/Ethnicity, Customized: AborigineParticipants145
Race/Ethnicity, Customized: OtherParticipants292251
History of Diabetes Stratification Factor: DiabetesParticipants6196141233
History of Diabetes Stratification Factor: No DiabetesParticipants132913212650
Country stratification factor: ArgentinaParticipants171170341
Country stratification factor: AustraliaParticipants7475149
Country stratification factor: AustriaParticipants312960
Country stratification factor: BelgiumParticipants5050100
Country stratification factor: BrazilParticipants151150301
Country stratification factor: CanadaParticipants7373146
Country stratification factor: DenmarkParticipants81119
Country stratification factor: FranceParticipants404080
Country stratification factor: GermanyParticipants8181162
Country stratification factor: HungaryParticipants6667133

6. Primary Endpoint

The registry lists the primary outcome as Time to Primary Composite Endpoint (All-cause Mortality, Myocardial Infarction, Hospitalization for Unstable Angina, Heart Failure or Peripheral Vascular Event), measured over From date of randomization until date of first confirmed primary composite endpoint event, assessed up to 5.4 years.

ElementRegistry entry
Result typeMedian
Measure of spreadInter-Quartile Range
UnitMonths
Endpoint classificationTime-to-Event Analysis

The primary endpoint measures the time from randomization until the first confirmed occurrence of any event in a composite: all-cause mortality, myocardial infarction, hospitalization for unstable angina, heart failure, or a peripheral vascular event. The registry says this outcome was assessed up to 5.4 years. Because it is a time-to-event endpoint, the analysis uses not only whether an event occurred but also when the first qualifying event was observed. Participants without a recorded event by the end of their available follow-up can contribute information up to that point, subject to the analysis methods and censoring rules.

In general, a composite endpoint can be useful when several clinically important events are relevant to the research question. It can capture the first occurrence of a range of outcomes rather than focusing on just one event type. But a composite result represents the combined endpoint as defined; it does not establish that every component changed in the same way. Components can differ in frequency, seriousness, and interpretation. The primary result should therefore be read as a comparison of time to the first event in this specified group of outcomes, not as a separate estimate for each component.

The registry reports median times for the primary endpoint as 55.0 months for cinacalcet and 53.0 months for placebo, with lower quartiles of 22.6 and 19.1 months, respectively. The upper quartiles are not reported in the registry record. These medians do not replace the hazard-ratio analysis: they describe a feature of the event-time distributions, while the Cox hazard ratio summarizes a relative time-to-event comparison under its model.

7. Results Posted in the Registry

Hazard ratio: Cinacalcet vs Placebo

0.93

95% CI: 0.85 to 1.02

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Cinacalcet vs Placebo0.840.870.910.950.991.03hazard ratio (as reported) 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 All-cause MortalityTime-to-Event AnalysisHazard ratio0.94 (0.85 to 1.04)8,201 events
Time to Myocardial InfarctionTime-to-Event AnalysisHazard ratio0.97 (0.79 to 1.19)33,841 events
Time to Hospitalization for Unstable AnginaTime-to-Event AnalysisHazard ratio0.82 (0.58 to 1.18)798 events

Time to All-cause Mortality

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Cinacalcet vs Placebo0.840.880.920.961.011.06hazard ratio (as reported) vs control (95% CI)

Time to Myocardial Infarction

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Cinacalcet vs Placebo0.760.840.921.021.121.23hazard ratio (as reported) vs control (95% CI)

Time to Hospitalization for Unstable Angina

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Cinacalcet vs Placebo0.550.650.760.901.061.25hazard ratio (as reported) vs control (95% CI)

The detailed secondary comparisons available in the registry include all-cause mortality, myocardial infarction, and hospitalization for unstable angina. Their hazard-ratio point estimates are below 1, but each reported 95% confidence interval includes 1. This broad pattern does not establish a distinct secondary-outcome benefit, and it does not overturn the primary result. Comparative estimates for the other listed secondary outcomes are not reported in the registry record.

Secondary outcomes can help describe whether the primary finding is accompanied by similar or contrasting patterns in related outcomes. They can also help identify questions for further study. But the primary composite and its components or related outcomes answer different questions. A secondary result should not be treated as a substitute for the primary endpoint, especially when the secondary comparison is less precise or when its statistical role is not defined in a prespecified plan.

Multiplicity is an important concern: when many outcomes are examined, some estimates may appear notable by chance alone. In general, a prespecified hierarchy or an adjustment for multiple testing can help control how results are interpreted. Such a hierarchy or adjustment is not reported in the registry record. The secondary findings therefore carry less evidential weight than the primary comparison and should be considered descriptive or hypothesis-generating in the absence of the missing analysis-plan details.

The registry lists outcomes including cardiovascular mortality, stroke, heart failure, peripheral vascular events, and bone fracture. The presence of an outcome in the registry does not itself establish that a corresponding estimate or conclusion is available. Results for listed outcomes without comparative values are not reported in the registry record. Avoid inferring the direction or magnitude of those results from the outcomes that do have estimates.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The reported Cox hazard ratio for the primary composite endpoint was 0.93, with a 95% confidence interval from 0.85 to 1.02. The point estimate is below 1, but the confidence interval includes 1. The registry also reports a log-rank p-value of 0.112. Taken together, the posted statistics do not provide a precise separation between the groups on the primary endpoint: the interval remains compatible with a range of relative event rates, including no difference under the hazard-ratio scale.

A hazard ratio is a relative comparison of the instantaneous event rates over follow-up among participants who have not yet experienced the event, under the model used. It is not a ratio of the proportions who experienced an event, and it does not give an absolute risk difference. The reported value of 0.93 should not be translated into a percentage reduction or another measure by calculation. The registry does not report an absolute effect estimate for the primary composite endpoint in the provided results.

The median times were 55.0 months for cinacalcet and 53.0 months for placebo. Median event time is a separate summary from the Cox estimate and does not describe the whole event-time pattern. The registry gives lower-quartile values but does not report the upper-quartile values. It also does not provide component-specific primary-endpoint estimates in the information available for this interpretation. The composite result therefore cannot show whether one component, several components, or no particular component accounts for the overall pattern.

The primary comparison was described as stratified by history of diabetes and country. A log-rank analysis and a Cox regression analysis are both reported, with the Cox result giving the hazard ratio and its 95% confidence interval. The registry lists no p-value alongside that Cox estimate; the separate log-rank p-value is 0.112. Those are distinct reported summaries, and one should not substitute one for the other.

The registry does not report the trial's original statistical decision threshold, a prespecified hierarchy for interpreting outcomes, or a detailed analysis plan. Thus, a formal claim about whether a prespecified primary hypothesis was met cannot be made from these fields alone. The interval's inclusion of 1 and the reported p-value are useful descriptions of the posted evidence, but neither proves equivalence or establishes that the treatments have identical effects. The results quantify uncertainty as well as the estimated comparison, and they leave room for effects in either direction within the confidence interval.

10. Statistical Methods Explained

The primary endpoint is a time-to-event outcome. The analysis considers the time from randomization to the first confirmed event in the composite, rather than reducing follow-up to a simple event/no-event count. This approach can use information from participants whose follow-up ends before an event is recorded, although the exact censoring rules and handling of incomplete follow-up are not reported in the registry record.

What does the Cox hazard ratio describe?

The registry reports a Cox regression hazard ratio of 0.93 for cinacalcet versus placebo, with a 95% confidence interval of 0.85 to 1.02. In general, a hazard is the instantaneous event rate among people who remain at risk at a given time. A hazard ratio compares that rate between groups over the follow-up period, as represented by the model. It is not a direct comparison of the number of people with events, nor does it state how many months an individual might live without an event.

The Cox model is commonly used for time-to-event data because it can incorporate event timing and censored follow-up. Its interpretation relies on model assumptions, including the proportional-hazards assumption for a single hazard ratio to summarize the group contrast over time. Whether that assumption was checked, and what diagnostic results were obtained, are not reported in the registry record. The registry says the primary comparison was stratified by history of diabetes and country. Further details about the fitted model are not reported in the registry record.

Why is a log-rank test also reported?

The registry reports a log-rank p-value of 0.112 for the comparison. In general, the log-rank test evaluates whether the observed event-time patterns differ between groups over follow-up. It is a test statistic and p-value, not an estimate of the size of the difference. The Cox model supplies the reported hazard ratio and confidence interval, while the log-rank result supplies a separate test of group differences. The registry does not report the p-value for the Cox estimate.

In general, a p-value describes how unusual data at least as incompatible with a specified null model would be if that model were true and the test assumptions held. It is not the probability that the null hypothesis is true, and it does not measure the clinical importance of an effect. The registry's p-value should be read alongside the point estimate, interval, endpoint definition, and analysis context.

What does the confidence interval add?

In general, a confidence interval expresses statistical uncertainty around an estimated effect under the analysis procedure. The 95% interval for the primary hazard ratio extends from 0.85 to 1.02. Because it includes 1, the posted data are compatible with the null value on the hazard-ratio scale, as well as with values on either side of it. The interval's width also matters: it shows that the estimate is not exact and that more than one effect size remains compatible with the data and model.

The registry reports medians of 55.0 months and 53.0 months, with lower quartiles of 22.6 months and 19.1 months for the two groups. These summaries do not fully describe the event-time distributions. The upper quartiles are not reported in the registry record, and no uncertainty interval for these medians is included in the listed information.

How should stratification be understood?

The primary outcome description says the comparison was stratified by history of diabetes and country. In general, stratification organizes a time-to-event comparison across specified strata, rather than treating the whole population as though those factors were absent. The registry does not describe the number or definition of strata, the details of the stratified procedure, or whether any additional covariates entered the model. Those analysis details are not reported in the registry record.

The analysis population is described as all randomized participants in the Efficacy Analysis Set, analyzed in their assigned groups under the intent-to-treat method. In general, this preserves the randomized comparison and estimates the effect of assignment to treatment rather than the effect among only those who adhered. The registry does not report how missing outcome information, treatment discontinuation, or other deviations from follow-up were handled.

Finally, results for multiple outcomes create interpretive challenges. In general, testing many outcomes increases the chance that at least one result will look unusual by chance if each is considered in isolation. The registry lists secondary outcomes and analyses, but a multiplicity adjustment or testing hierarchy is not reported in the registry record. Secondary estimates should therefore be treated as supporting or exploratory evidence unless the analysis plan establishes otherwise; that plan is not reported in the registry record.

11. Confidence Intervals and Precision

The primary hazard ratio is 0.93, and its 95% confidence interval runs from 0.85 to 1.02. The interval is the main indication of precision for this reported relative comparison. It includes the null value of 1, so the data do not distinguish the estimate from no relative difference at the conventional level implied by that interval. It also includes values below and above 1, so uncertainty covers possible differences in either direction.

In general, a confidence interval is not a range containing a known true value with a probability assigned after observing the data. Rather, under repeated use of the same procedure and its assumptions, intervals constructed in this way would cover the fixed underlying parameter at the stated rate. For an individual result, the interval conveys which effect values are reasonably compatible with the data and model, while remaining dependent on those assumptions.

The interval does not describe absolute event risks or the number of events avoided or added. The registry does not report an absolute effect estimate for the primary endpoint in these results. The medians, 55.0 months and 53.0 months, are descriptive summaries; uncertainty intervals for them are not reported in the registry record. The lower quartiles are reported as 22.6 months and 19.1 months, but the upper quartiles are not reported in the registry record.

The secondary Cox intervals also cross 1 in the outcomes for which comparisons are detailed: all-cause mortality, myocardial infarction, and hospitalization for unstable angina. Their ranges vary, so the degree of precision differs across estimates. These are secondary comparisons and should not be read as equally strong evidence to the primary result, particularly because multiplicity handling is not reported. Confidence intervals do not resolve limitations in outcome ascertainment, model assumptions, missing-data handling, or the selection of analyses.

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 detect (log scale)Hazard ratioEvents, 80% powerEvents, 90% power
100% of the observed effect0.935,9627,981
75% of the observed effect0.9510,59814,188
50% of the observed effect0.9623,84631,923
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5,00010,00020,00050,000100,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Schoenfeld approximation for the log-rank test or Cox model. The answer is the total number of events, not participants; the number of participants depends on how quickly events accrue. Calculated for the comparison: Cinacalcet vs Placebo.

The planning figures for these time-to-event comparisons are total event counts, not participants per arm. In general, an event-based planning calculation asks how many outcome events would be needed to detect a specified effect under stated assumptions; it does not directly state the number of people who must be enrolled, since the number of events observed also depends on follow-up and event occurrence. The primary endpoint and the displayed secondary time-to-event outcomes therefore use total events in the planning display.

The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is expressed as a stated fraction of the observed effect. The time-to-event calculations use the Schoenfeld method. The original trial design assumptions and sample-size justification are not reported in the registry record; these calculations are planning illustrations based on the observed effect, not the trial's original design.

The 80% power column gives the event total estimated to provide an 80% chance of detecting the specified effect under those assumptions if that effect is the true one. The 90% power column gives the event total for a higher chance of detection under the same assumptions. These are prospective planning quantities, not evidence about the probability that the completed trial found a real effect. They are not observed power.

Rows that plan for 75% or 50% of the observed effect represent smaller effects than the row based on 100% of the observed effect. Smaller effects are harder to distinguish from chance variation, so the calculations require more events. Use the entries as scenario-based illustrations of how planning needs change with the effect size and target power, not as a direct evaluation of the trial's success or adequacy.

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

d = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.

Worked calculation for this trial

  1. Hazard ratio HR = 0.930, so ln(HR) = -0.0726.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.930)]2 = 5,961.4, rounded up to 5,962 events in total 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
hr <- 0.93                              # observed hazard ratio
events_needed <- function(power, frac = 1) ceiling(round(4 * (z_a + qnorm(power))^2 / log(hr^frac)^2, 6))   # Schoenfeld, 1:1 allocation
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: events = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(events_needed(0.80, f), big.mark = ","), format(events_needed(0.90, f), big.mark = ",")))

# Simulation: given d total events under proportional hazards, events in the treatment arm are Binomial(d, hr / (1 + hr)).
# The score (log-rank type) statistic is (D1 - d / 2) / sqrt(d / 4).
set.seed(345839)
d    <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z  <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))

Output from running the code

100% of observed effect: events = 5,962 (80% power), 7,981 (90% power)
 75% of observed effect: events = 10,598 (80% power), 14,188 (90% power)
 50% of observed effect: events = 23,846 (80% power), 31,923 (90% power)
Simulated power with 5,962 events: 0.805 (20000 replicates)

The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.

14. Group-Sequential Design Analysis

Many time-to-event trials, especially in oncology, stop or report early when interim data are overwhelming, so a single fixed-sample number understates the real design problem. The calculation below is an illustrative group-sequential design built from this trial's posted control median and hazard ratio. The registry record does not state the planned number of looks or the spending function, so the design is a planning illustration, not a reconstruction of the protocol. Assumed: one-sided α = 0.025, 90% power, three equally spaced looks on information, Lan-DeMets O'Brien-Fleming spending, 24 months of accrual, 60 months in total and a 1% monthly dropout hazard.

Under these assumptions the design needs about 21,998 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 123.52,6923.7100.00010.0001
Look 238.15,3842.5110.00600.0060
Look 360.08,0761.9930.02310.0250
01234z = 3.7124 mo2692 eventsz = 2.5138 mo5384 eventsz = 1.9960 mo8076 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%5,96216,23960.0
Two looks, O'Brien-Fleming80%5,98416,29960.0
Three looks, O'Brien-Fleming80%6,03816,44660.0
Three looks, Pocock80%6,97819,00660.0
Fixed design, one analysis90%7,98221,74160.0
Two looks, O'Brien-Fleming90%8,00921,81560.0
Three looks, O'Brien-Fleming90%8,07621,99860.0
Three looks, Pocock90%9,21325,09460.0

Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.

Sensitivity to a smaller true effect

Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.

True effect assumedHazard ratioEvents at final analysisParticipants
100% of the observed effect0.9308,07621,998
75% of the observed effect0.94714,35638,844
50% of the observed effect0.96432,30086,811

For context, this trial enrolled 3,883 participants.

Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993. Agreement between the two packages confirms the boundary calculation.

R code and output

suppressWarnings(suppressMessages({ library(gsDesign); library(rpact) }))
med_control <- 53          # control-arm median, months (converted from the posted unit)
hr          <- 0.93          # hazard ratio used for planning
lambdaC     <- log(2) / med_control
eta         <- 0.01               # dropout hazard per month (assumption)
acc_months  <- 24                 # accrual duration (assumption)
study_months<- 60                 # total study duration (assumption)

design <- function(k, sfu, beta, h = hr) gsSurv(k = k, test.type = 1, alpha = 0.025, beta = beta, sfu = sfu,
  lambdaC = lambdaC, hr = h, hr0 = 1, eta = eta, gamma = 1, R = acc_months, T = study_months, minfup = study_months - acc_months)

# Main design: 3 looks, Lan-DeMets O'Brien-Fleming spending, one-sided alpha 0.025, 90% power
x <- design(3, sfLDOF, 0.10)
cat(sprintf("N_TOTAL|%s\n", format(ceiling(sum(x$gamma * x$R)), big.mark = ",")))
for (i in 1:3) cat(sprintf("GS|%d|%.1f|%.0f|%.3f|%.5f|%.5f\n", i, x$T[i], x$n.I[i], x$upper$bound[i], pnorm(-x$upper$bound[i]), cumsum(x$upper$spend)[i]))
cat("\n"); print(gsBoundSummary(x))

# Comparison of designs
cmp <- list(list("Fixed design, one analysis", 1, sfLDOF), list("Two looks, O'Brien-Fleming", 2, sfLDOF),
            list("Three looks, O'Brien-Fleming", 3, sfLDOF), list("Three looks, Pocock", 3, sfLDPocock))
cat("\n")
for (b in c(0.20, 0.10)) for (d in cmp) {
  y <- design(d[[2]], d[[3]], b)
  cat(sprintf("DES|%s|%d|%.0f|%s|%.1f\n", d[[1]], round(100 * (1 - b)), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ","), tail(y$T, 1)))
}

# Sensitivity: what if the true effect is smaller than the observed one? (3 looks, O'Brien-Fleming, 90% power)
cat("\n")
for (fr in c(1, 0.75, 0.5)) {
  y <- design(3, sfLDOF, 0.10, exp(log(hr) * fr))
  cat(sprintf("SENS|%.2f|%.3f|%.0f|%s\n", fr, exp(log(hr) * fr), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ",")))
}

# Independent cross-check of the boundaries with rpact
r <- getDesignGroupSequential(kMax = 3, alpha = 0.025, beta = 0.10, sided = 1, typeOfDesign = "asOF", informationRates = x$timing)
cat(sprintf("\nCross-check, upper boundaries: gsDesign %s | rpact %s\n", paste(round(x$upper$bound, 3), collapse = ", "), paste(round(r$criticalValues, 3), collapse = ", ")))

Method: LachinFoulkes 
     Analysis               Value Efficacy
    IA 1: 33%                   Z   3.7103
     N: 21524         p (1-sided)   0.0001
 Events: 2692        ~HR at bound   0.8667
    Month: 23    P(Cross) if HR=1   0.0001
              P(Cross) if HR=0.93   0.0338
    IA 2: 67%                   Z   2.5114
     N: 21998         p (1-sided)   0.0060
 Events: 5384        ~HR at bound   0.9338
    Month: 38    P(Cross) if HR=1   0.0060
              P(Cross) if HR=0.93   0.5603
        Final                   Z   1.9930
     N: 21998         p (1-sided)   0.0231
 Events: 8076        ~HR at bound   0.9566
    Month: 60    P(Cross) if HR=1   0.0250
              P(Cross) if HR=0.93   0.9000



Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993

15. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log Ranknot reported0.112
Regression, CoxHazard Ratio (HR) 0.930.85 to 1.02not reported

The registry reports the sponsor's Cox analysis for the primary comparison as a hazard ratio of 0.93, with a 95% confidence interval from 0.85 to 1.02. It also reports a log-rank p-value of 0.112. These are the posted sponsor analyses, not independently documented estimates of a different effect. The registry does not report a p-value alongside the Cox hazard ratio.

The recalculated comparison is not flagged as discrepant from the sponsor analysis. Under the stated reporting approach, there is therefore no conflicting recalculated result to set against the sponsor's estimate. The sponsor's reported analysis remains the principal inferential result, and the confidence interval and log-rank p-value should be read as complementary summaries from the posted analyses.

A recalculation based on summary information cannot reproduce every detail of a full participant-level analysis. In general, differences could arise from the model, stratification, handling of censoring, or analysis population. The registry does not provide the full model specification or participant-level data needed to independently verify those details. No further claim about the agreement of underlying analysis procedures is warranted from the posted information.

16. Multiplicity, Missing Data and Analysis Populations

The registry lists ten outcome measures and twenty analyses, including a primary composite and multiple secondary outcomes. When several hypotheses are examined, the chance of at least one apparently unusual result can increase. In general, researchers may address this through a prespecified testing hierarchy, adjusted significance criteria, or a plan that treats secondary results as exploratory. A multiplicity adjustment, a hierarchy among endpoints, and the trial's planned approach to multiple testing are not reported in the registry record.

The primary analysis population is described as the Efficacy Analysis Set, including all randomized participants, with analysis in the assigned groups under the intent-to-treat method. This is an important aspect of the stated analysis. It does not, however, explain how missing endpoint information was handled, how participants lost to follow-up were censored, or how treatment discontinuation and other protocol deviations were addressed. Those details are not reported in the registry record.

The registry identifies the primary comparison as stratified by history of diabetes and country, and it reports a Cox regression estimate and a log-rank p-value. It does not provide the full statistical analysis plan, model diagnostics, details of censoring, or information about missing-data sensitivity analyses. The original sample-size justification and planned interim analyses are not reported in the registry record. These omissions limit independent assessment of whether every reported analysis follows the intended plan.

In general, missing outcome information can affect precision and, depending on why it is missing and how it is handled, can also affect the validity of an estimate. The posted information does not establish that missingness occurred at a particular level or in a particular pattern. It also does not establish that the analysis was biased. The appropriate conclusion is narrower: the registry does not report enough detail to evaluate the missing-data assumptions and their consequences.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo1351192370.3%
Cinacalcet1338193869.0%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo70.3%Cinacalcet69.0%% of participants with at least one serious adverse event

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
Placebo1220 of 1923
Cinacalcet1444 of 1938

Most frequent serious adverse event terms

Event termOrgan systemPlaceboCinacalcet
PneumoniaInfections and infestations171 of 1923118 of 1938
SepsisInfections and infestations111 of 1923123 of 1938
Myocardial infarctionCardiac disorders105 of 1923109 of 1938
HyperkalaemiaMetabolism and nutrition disorders74 of 192397 of 1938
Cardiac failureCardiac disorders90 of 192374 of 1938
Cardiac failure congestiveCardiac disorders86 of 192364 of 1938
Cerebrovascular accidentNervous system disorders66 of 192360 of 1938
Atrial fibrillationCardiac disorders68 of 192356 of 1938
Cardiac arrestCardiac disorders57 of 192360 of 1938
HyperparathyroidismEndocrine disorders86 of 192323 of 1938

Most frequent non-serious adverse event terms

Event termOrgan systemPlaceboCinacalcet
NauseaGastrointestinal disorders288 of 1923552 of 1938
VomitingGastrointestinal disorders247 of 1923482 of 1938
DiarrhoeaGastrointestinal disorders349 of 1923376 of 1938
DyspnoeaRespiratory, thoracic and mediastinal disorders188 of 1923226 of 1938
CoughRespiratory, thoracic and mediastinal disorders185 of 1923225 of 1938
HeadacheNervous system disorders182 of 1923219 of 1938
Pain in extremityMusculoskeletal and connective tissue disorders193 of 1923201 of 1938
Muscle spasmsMusculoskeletal and connective tissue disorders174 of 1923213 of 1938
ArthralgiaMusculoskeletal and connective tissue disorders224 of 1923158 of 1938
Abdominal painGastrointestinal disorders154 of 1923187 of 1938

Serious events with the highest arm-level rate: pneumonia (8.9%), sepsis (6.3%), myocardial infarction (5.6%), hyperkalaemia (5.0%), cardiac failure (4.7%).

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 lists participants affected by serious adverse events in both groups: 1351 of 1923 at risk in the placebo group and 1338 of 1938 at risk in the cinacalcet group. For other adverse events, the corresponding listed counts are 1220 of 1923 and 1444 of 1938. These are the registry's group-level counts; they are not adjusted comparisons, and no additional statistical test or confidence interval for these figures is reported in the registry record.

The serious adverse event terms listed most often include pneumonia at 8.9%, sepsis at 6.3%, myocardial infarction at 5.6%, hyperkalaemia at 5.0%, cardiac failure at 4.7%, and cardiac failure congestive at 4.5%. These percentages describe terms in the registry's serious-event listing. The record does not specify in the information available whether participants could contribute to multiple terms, so the terms should not be added or treated as mutually exclusive categories.

Deaths in the adverse-event group data are not reported in the registry record. The counts alone do not establish causation, comparative risk, or the clinical significance of an individual event. Safety findings should be interpreted in light of the event definitions and collection procedures, which are not reported in the registry record.

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

The posted results describe a randomized comparison of cinacalcet and placebo for time to the first event in a specified cardiovascular composite among people with chronic kidney disease and secondary hyperparathyroidism receiving dialysis. The primary Cox hazard ratio was 0.93, with a 95% confidence interval from 0.85 to 1.02; the log-rank p-value was 0.112. The interval includes 1, so the result does not precisely distinguish the groups on the reported relative time-to-event scale.

This does not show that the treatments are equivalent, nor does it prove that they differ. A confidence interval spanning the null value indicates uncertainty that includes no relative difference; it does not establish absence of an effect. The estimate also does not tell readers the absolute chance of an event, the number of events prevented or caused, or the effect on any single component of the composite.

The primary composite combines mortality and several cardiovascular events. The result pertains to the composite as defined, and cannot be assigned to every component separately. The posted secondary estimates are also uncertain, and the registry does not report comparative results for all listed secondary outcomes. Because multiplicity handling is not reported, secondary findings should not be used to make strong stand-alone claims.

The registry reports an intent-to-treat analysis of all randomized participants in the Efficacy Analysis Set. It does not report enough information to assess all aspects of follow-up, missing data, model diagnostics, or the original analysis plan. These limitations do not invalidate the reported statistics, but they constrain how far interpretation can go beyond the estimates themselves.

Overall, the record supports a careful description of the observed comparison and its uncertainty. It does not by itself establish a treatment recommendation, a mechanism, or an effect on outcomes not reported in the registry record. Clinical decisions require evidence and context beyond these posted trial statistics.

19. Why This Trial Matters Statistically

This trial illustrates why a time-to-event result should be read through both its effect estimate and its precision. The primary hazard ratio of 0.93 gives a relative comparison, while the 95% confidence interval from 0.85 to 1.02 shows that the estimate remains uncertain and includes the null value. Reporting only the point estimate would hide that uncertainty; reporting only the p-value would omit the size and range of effects compatible with the analysis.

It also demonstrates the interpretive trade-off in a composite endpoint. Combining several events can represent a broad clinical question and support a time-to-first-event analysis, but a composite estimate does not explain how each component contributes. Component-level interpretation requires component-level results, which are not reported for every outcome in the registry record.

The study's intent-to-treat description shows the importance of identifying the analysis population and the treatment assignment used for comparison. At the same time, the registry does not report many details needed to assess implementation, including missing-data handling and the original analysis plan. Statistical transparency matters because a reader needs to distinguish what the reported result establishes from what remains unknown.

Finally, the planning illustrations show how event requirements depend on the effect size targeted and the desired power. They are not a substitute for the original design justification or a measure of the completed trial's observed power. Taken together, these points make the record useful for learning how design, endpoint construction, modeling, precision, multiplicity, and reporting limitations shape interpretation of a clinical trial.

20. Limitations

The registry does not report the original sample-size justification, detailed statistical analysis plan, planned interim analyses, multiplicity strategy, missing-data approach, censoring rules, or model diagnostics. These omissions limit assessment of whether the posted methods fully match the original protocol and how robust the findings are to alternative assumptions.

The primary outcome is a composite, but component-specific primary results are not reported in the available information. The registry gives median times and lower quartiles, but the upper quartiles and uncertainty intervals for those summaries are not reported in the registry record. The Cox hazard ratio summarizes the relative time-to-event comparison, but the proportional-hazards assumption and its assessment are not reported.

Although the primary description says the analysis was stratified by history of diabetes and country, further model details are not reported. Details of treatment dose, adherence, discontinuation, and follow-up procedures are also not reported in the registry record. These limits affect how precisely readers can understand the analysis and its implementation, rather than establishing that any particular problem occurred.

The registry contains multiple secondary outcomes, but comparative estimates are not available for every listed outcome. A multiplicity adjustment or hierarchy is not reported, so the secondary findings should be interpreted cautiously. Safety terms and counts are posted, but event definitions, overlap among terms, and additional comparative analyses are not reported in the registry record. These reporting gaps restrict broader conclusions about efficacy and safety from this record alone.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

24. Record Summary

The registry describes the completed phase 3 E.V.O.L.V.E. trial as a randomized, double-masked, parallel-group comparison of cinacalcet with placebo in people with chronic kidney disease and secondary hyperparathyroidism receiving dialysis. Enrollment is reported as 3883. The primary endpoint was time to the first confirmed event in a composite of all-cause mortality, myocardial infarction, hospitalization for unstable angina, heart failure, or peripheral vascular event, assessed up to 5.4 years.

The reported primary Cox hazard ratio was 0.93, with a 95% confidence interval from 0.85 to 1.02; the log-rank p-value was 0.112. The interval includes 1, indicating uncertainty that includes no relative difference on the hazard-ratio scale. The registry describes an intent-to-treat analysis of all randomized participants and stratification by history of diabetes and country. Important details about missing data, multiplicity, and the original statistical plan are not reported in the registry record.

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