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 A Research Study to See How Semaglutide Works Compared to Placebo in People With Type 2 Diabetes and Chronic Kidney Disease (NCT03819153), a randomized phase 3 study. The primary outcome is Number of Participants From Time of Randomization to First Occurrence of Onset of Persistent ≥50% Reduction in eGFR(CKD-EPI); Onset of Persistent eGFR(CKD-EPI) <15mL/Min/1.73m^2; Initiation of Chronic Renal Replacement Therapy; Renal Death; CV Death.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03819153 |
| Phase | Phase 3 |
| Condition | Diabetes Mellitus, Type 2 |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 3533 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Novo Nordisk A/S |
| Results posted | Yes |
2. Clinical Question
Population
Participants had type 2 diabetes and chronic kidney disease. The registry describes the primary analysis population as the full analysis set: unique randomized participants grouped according to the treatment assigned at randomization. The study enrolled 3533 participants. More detailed eligibility criteria are not reported in the registry record.
Intervention
Participants were assigned semaglutide, described in the registry as an active study medicine administered by injection once a week. The arm description says treatment could continue for up to 5 years or longer, with the trial event driven. Details of dose and dose adjustment are not reported in the registry record.
Comparator
The comparison group was assigned placebo. The registry describes the study medicine as allocated by chance and lists a randomized, parallel-group design. The masking designation was quadruple; the particular roles masked are not reported in the registry record.
Primary question
The primary endpoint counted participants with a first occurrence of a composite event: persistent at least 50% reduction in eGFR, persistent eGFR below 15 mL/min/1.73m^2, initiation of chronic renal replacement therapy, renal death, or cardiovascular death. The endpoint period was from Week 0 up to Week 234. The registry’s reported analysis compared time to that first event between assigned groups.
In statistical terms, the question is whether the randomized groups had different observed times to the first qualifying event during follow-up. The composite combines several types of kidney disease progression and death into a single primary outcome. A participant meeting more than one component contributes to the composite through the first occurrence, as specified in the registry description. The posted primary result is a hazard ratio from a regression, Cox analysis, alongside the numbers of participants with events in each group. Those statistics address related but distinct aspects of the comparison: the event counts describe how many participants had an event, while the hazard ratio summarizes the relative event rate over follow-up under the analysis model.
3. Trial Design
This was a completed phase 3, randomized, quadruple-masked, parallel-group trial sponsored by Novo Nordisk A/S. The registry reports enrollment of 3533 participants. The study start date was 2019-06-17 and the primary completion date was 2024-01-09. The brief description says participants could be in the study for about 3 to 5 years, possibly longer. The arm descriptions characterize the trial as event driven, with a predefined minimum number of renal endpoint events for the primary endpoint. The number of events specified in that design target is not reported in the registry record.
Participants were assigned semaglutide or placebo. The registry states that assignment was by chance and describes use of a pen for weekly injections. It does not report the randomization ratio or further information about sequence generation or concealment. Quadruple masking is recorded, but which participant, investigator, or other roles were masked is not reported in the registry record. The reasons for any treatment discontinuation, adherence information, and permitted background care are also not reported in the registry record.
The primary outcome was a composite of kidney events and cardiovascular death, assessed from Week 0 up to Week 234. The analysis population included all unique randomized participants grouped by assigned treatment. That description indicates an assignment-based grouping for the primary analysis; detailed handling of participants with incomplete follow-up or missing outcome information is not reported in the registry record.
The registry lists 22 outcome measures and one reported analysis for the primary endpoint. It lists 21 posted secondary outcomes, including eGFR measures and individual kidney or death events. The trial’s original sample-size justification, target number of participants, statistical analysis plan, prespecified significance level, and interim analysis arrangements are not reported in the registry record. The planning illustrations associated with the posted results are separate from those original design details.
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: A total of 3533 eligible participants were randomized (1:1) to treatment with semaglutide 1 milligram (mg) (1767) or placebo (1766). The study included a treatment period (up to 60 months or more) and a follow-up period (5 weeks).
Overall Study
| Stage | Semaglutide | Placebo |
|---|---|---|
| STARTED | 1767 | 1766 |
| Full Analysis Set (FAS) | 1767 | 1766 |
| COMPLETED | 1724 | 1708 |
| NOT COMPLETED | 43 | 58 |
Reasons for not completing this period:
| Reason | Semaglutide | Placebo |
|---|---|---|
| Withdrawal by Subject | 20 | 28 |
| Lost to Follow-up | 23 | 30 |
Analysis population for the primary outcome, as defined in the registry: FAS included all unique randomized participants who were grouped according to the treatment assigned at randomization.
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.
Population: Analysis of participants were performed on full analysis set (FAS) that was defined as all unique randomised participants and were grouped according to the treatment assigned at randomization.
| Characteristic | Unit | Semaglutide | Placebo | Total |
|---|---|---|---|---|
| Participants analysed | 1767 | 1766 | 3533 | |
| Age, Continuous | Years | 66.6 (SD 9.0) | 66.7 (SD 9.0) | 66.6 (SD 9.0) |
| Sex: Female, Male: Female | Participants | 519 | 550 | 1069 |
| Sex: Female, Male: Male | Participants | 1248 | 1216 | 2464 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 273 | 283 | 556 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 1421 | 1411 | 2832 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 73 | 72 | 145 |
| Race/Ethnicity, Customized: Race – American Indian or Alaska Native | Participants | 9 | 16 | 25 |
| Race/Ethnicity, Customized: Race – Asian | Participants | 439 | 407 | 846 |
| Race/Ethnicity, Customized: Race – Black or African American | Participants | 78 | 82 | 160 |
| Race/Ethnicity, Customized: Race – Native Hawaiian or Other Pacific Islander | Participants | 2 | 3 | 5 |
| Race/Ethnicity, Customized: Race – White | Participants | 1155 | 1168 | 2323 |
| Race/Ethnicity, Customized: Race – Other | Participants | 45 | 50 | 95 |
| Race/Ethnicity, Customized: Race – Not reported | Participants | 39 | 40 | 79 |
6. Primary Endpoint
The registry lists the primary outcome as Number of Participants From Time of Randomization to First Occurrence of Onset of Persistent ≥50% Reduction in eGFR(CKD-EPI); Onset of Persistent eGFR(CKD-EPI) <15mL/Min/1.73m^2; Initiation of Chronic Renal Replacement Therapy; Renal Death; CV Death, measured over From Week 0 up to Week 234.
| Element | Registry entry |
|---|---|
| Result type | Count Of Participants |
| Measure of spread | not applicable |
| Unit | Participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the number of participants whose first qualifying event occurred after randomization. It combines five components: onset of persistent at least 50% reduction in eGFR, onset of persistent eGFR below 15 mL/min/1.73m^2, initiation of chronic renal replacement therapy, renal death, and cardiovascular death. The registry describes the measure as a composite renal event while including cardiovascular death as a component. The period is from Week 0 up to Week 234.
A composite endpoint can capture several clinically consequential outcomes in one analysis. General statistical context: combining events can increase the number of observed endpoint events and can represent a broader progression question than any one component alone. However, composite components are not necessarily equally frequent or equally consequential. A combined result does not by itself show which component chiefly accounts for the group comparison. Component-specific event counts and analyses are needed to examine that pattern, and not every such result is reported in the registry record.
The endpoint focuses on time to the first occurrence, rather than counting every event each participant may experience. The registry’s primary analysis uses a Cox regression and reports a hazard ratio. General statistical context: this type of analysis compares event rates over follow-up, subject to the model and assumptions used. The registry also posts the number of participants with a composite event in each group. These counts provide a direct description of the observed event burden, but do not capture the timing of events in the same way as a time-to-event model.
The registry does not report component-specific weights or a rationale for selecting this particular composite, so those design considerations cannot be assessed from the record.
7. Results Posted in the Registry
- Semaglutide: 18.7% (331/1767) versus 23.2% (410/1766) on control; risk difference -4.5 percentage points (95% CI -7.2 to -1.8), risk ratio 0.81 (0.71–0.92); unadjusted two-proportion z-test p = 0.001.
Risk difference: Semaglutide
95% CI: -7.2 to -1.8 percentage points
Recalculated from the posted summary statistics
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Annual Rate of Change in eGFR (CKD-EPI) (Total eGFR Slope) | Continuous Endpoint | Mean difference | 1.17 (0.89 to 1.45) | 203 per arm |
| Number of Participants From Time of Randomization to Occurrence of Onset of Persistent ≥50% Reduction in eGFR (CKD-EPI) | Binary Endpoint | Risk difference | -2.7 pts (-4.8 to -0.7) | 2,022 per arm |
| Number of Participants From Time of Randomization to Occurrence of Onset of Persistent eGFR (CKD-EPI) <15mL/Min/1.73m^2 | Binary Endpoint | Risk difference | -1.0 pts (-2.6 to 0.5) | 8,098 per arm |
Annual Rate of Change in eGFR (CKD-EPI) (Total eGFR Slope)
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Semaglutide: mean -2.19 versus -3.36 on control; difference 1.17 (95% CI 0.89 to 1.45), standardized effect d = 0.28; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Semaglutide than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Number of Participants From Time of Randomization to Occurrence of Onset of Persistent ≥50% Reduction in eGFR (CKD-EPI)
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Semaglutide: 9.3% (165/1767) versus 12.1% (213/1766) on control; risk difference -2.7 percentage points (95% CI -4.8 to -0.7), risk ratio 0.77 (0.64–0.94); unadjusted two-proportion z-test p = 0.009.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Semaglutide than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Number of Participants From Time of Randomization to Occurrence of Onset of Persistent eGFR (CKD-EPI) <15mL/Min/1.73m^2
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Semaglutide: 5.2% (92/1767) versus 6.2% (110/1766) on control; risk difference -1.0 percentage points (95% CI -2.6 to 0.5), risk ratio 0.84 (0.64–1.09); unadjusted two-proportion z-test p = 0.191.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Semaglutide and the control. The interval gives the range of effects that remain compatible with the data.
The detailed secondary outcomes show a varied pattern rather than a single uniform result. The posted eGFR slope estimate and the separate persistent at least 50% reduction outcome have recalculated comparisons with p-values below 0.05, while the comparison for persistent eGFR below 15 does not. The registry also lists other secondary outcomes, including chronic renal replacement therapy, renal death, cardiovascular death, chronic eGFR slope, and eGFR change at Week 12. Their detailed results are not reported in the registry record.
These outcomes relate to the primary composite because some measure kidney function over time and others correspond to individual events included in, or related to, its components. They can add context about the broader outcome pattern, but they do not replace the primary time-to-event analysis. A component outcome may have fewer events and therefore less precision than the composite, and each secondary measure can address a distinct question.
General statistical context: secondary endpoints are often useful for examining consistency, mechanisms, and particular components, but a collection of unadjusted tests creates a multiplicity concern. If many comparisons are performed, some may appear notable by chance even when there is no underlying effect. The registry record does not report whether multiplicity adjustment was planned or applied. The unadjusted secondary results therefore carry less confirmatory weight than the designated primary analysis and should be interpreted as supporting context, not as a separate set of definitive conclusions.
The registry lists 21 posted secondary outcomes and one reported primary analysis. Since complete estimates are not available for every listed secondary outcome in the registry record, the overall pattern cannot be fully assessed from the detailed statistics reported. Nor can secondary findings alone determine whether the primary composite result is driven by a particular event type.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Annual Rate of Change in eGFR (CKD-EPI) (Total eGFR Slope)
- Number of Participants From Time of Randomization to Occurrence of Onset of Persistent ≥50% Reduction in eGFR (CKD-EPI)
- Number of Participants From Time of Randomization to Occurrence of Onset of Persistent eGFR (CKD-EPI) <15mL/Min/1.73m^2
- Number of Participants From Time of Randomization to Occurrence of Initiation of Chronic Renal Replacement Therapy
- Number of Participants From Time of Randomization to Occurrence of Renal Death
- Number of Participants From Time of Randomization to Occurrence of CV Death
- Annual Rate of Change in eGFR (Chronic Kidney Disease CKD-EPI) (Chronic eGFR Slope)
- Change From Baseline in eGFR (CKD-EPI) at Week 12
9. Statistical Interpretation
The registry reports a Cox regression hazard ratio of 0.76 for semaglutide compared with placebo, with a 95% confidence interval from 0.66 to 0.88 and p < 0.001. The interval lies below 1, and the reported p-value is below 0.001. These posted results indicate a difference between assigned groups in time to the first composite event under the sponsor’s reported analysis. They do not, by themselves, identify which component contributed most to that difference.
The event counts were 331 of 1767 participants assigned semaglutide and 410 of 1766 assigned placebo. A separate simple, unadjusted recalculation from these counts gives a risk difference of -0.045, with a confidence interval from -0.072 to -0.018 and p = 0.001. The negative direction means the observed event proportion was lower in the semaglutide group in this calculation. This calculation is not the same estimand or method as the registry’s Cox hazard ratio: it compares event proportions, whereas the Cox analysis uses time-to-event information. The registry’s own analysis is the primary reported result, and no discrepancy is flagged between it and the recalculation.
Secondary findings include an annual eGFR slope of -2.19 in the semaglutide group and -3.36 in the placebo group, with a posted mean difference of 1.17 and p < 0.001 in the simple recalculation. The separate persistent at least 50% eGFR reduction outcome had 165 participants with events in the semaglutide group and 213 in the placebo group; its recalculated p-value is 0.009. For persistent eGFR below 15, the corresponding counts were 92 and 110, and the recalculated p-value is 0.191. These endpoints provide additional context but do not replace the composite primary result.
General statistical context: a small p-value is evidence against a specified no-difference model, conditional on the analysis assumptions. It does not describe the size or practical importance of an effect, and it is not the probability that the null hypothesis is true. The confidence interval is more informative about the range of effect estimates compatible with the analysis than a p-value alone. The displayed counts and estimates describe this trial’s posted results; they do not establish that every participant experienced the same course or that one treatment will have the same result in other populations or settings.
The registry does not report multiplicity procedures for the secondary outcomes. Their unadjusted comparisons should therefore be treated as exploratory context, rather than as a collection of independently confirmatory findings. The full analysis plan and handling of missing data are not reported in the registry record.
10. Statistical Methods Explained
The primary analysis is described as regression using a Cox method, with a hazard ratio as its parameter. The registry labels the analysis as superiority. The reported estimate is 0.76, with a 95% confidence interval from 0.66 to 0.88 and p < 0.001. The analysis population is the full analysis set, defined as all unique randomized participants grouped by treatment assigned at randomization.
What does a hazard ratio describe?
General statistical context: a hazard is the instantaneous rate of an event among participants who have not yet had that event, as follow-up proceeds. A hazard ratio compares those rates between groups under the fitted model. It is not a direct comparison of the number of events, nor is it an absolute risk difference. Interpreting a single hazard ratio across follow-up generally depends on assumptions about how the relative hazards behave over time. The registry record does not report diagnostics for those assumptions or further model details.
The reported hazard ratio is below 1, and the confidence interval also lies below 1. The result is therefore consistent with a lower modeled hazard of the first composite event in the semaglutide group during the analyzed follow-up. This phrasing describes the statistical comparison and does not establish a cause for any individual event. The registry’s label of superiority identifies the type of comparison reported; details of the prespecified decision rule are not reported in the registry record.
How do event counts and the recalculation differ?
The posted counts, 331 of 1767 and 410 of 1766, can also be compared as simple event proportions. The unadjusted recalculation expresses that contrast as a risk difference of -0.045, with a confidence interval from -0.072 to -0.018 and p = 0.001. This calculation uses the posted summary counts and is not an adjusted or time-to-event model. It does not incorporate the timing of each event or any covariates. It is useful as a transparent descriptive contrast, but it should not be substituted for the sponsor’s Cox analysis.
General statistical context: a risk difference is an absolute contrast between event proportions over the specified observation period. A hazard ratio is a relative comparison of modeled event rates over time. Since they answer different statistical questions, their numerical values are not expected to match. The registry does not flag a discrepancy between the sponsor result and the recalculation.
Why does the composite matter for the analysis?
The endpoint counts the first occurrence of any listed component. General statistical context: this approach avoids treating several events in one participant as separate primary events, but it also means the composite estimate summarizes a mixture of outcomes. A result for the composite does not establish that every component changes to the same degree or in the same direction. The registry posts some component outcomes separately, but complete component-level results are not reported in the registry record.
How should the secondary comparisons be understood?
The continuous eGFR outcome is reported as an annual rate of change, with means of -2.19 for semaglutide and -3.36 for placebo. The recalculated mean difference is 1.17 and the unadjusted p-value is <0.001. The posted dispersion measure is standard error. General statistical context: a standard error describes uncertainty in an estimated mean, rather than the spread of individual participant measurements. The registry record does not report a sponsor analysis for this secondary comparison.
For the separate persistent at least 50% eGFR reduction outcome, the posted counts were 165 and 213, and the recalculated unadjusted p-value was 0.009. For persistent eGFR below 15, the counts were 92 and 110, and the unadjusted p-value was 0.191. The latter comparison’s recalculated confidence interval includes zero. These are simple comparisons derived from the posted group counts, not results of a reported adjusted analysis. Other outcome measures are listed, but their detailed estimates are not reported in the registry record.
General statistical context: when many outcomes are examined, the chance of obtaining one or more apparently notable results by chance can increase. Multiplicity methods can address that issue, but whether they were planned or applied is not reported in the registry record. Accordingly, the secondary p-values should not be read as if each were a separately controlled confirmatory test.
11. Confidence Intervals and Precision
The sponsor-reported primary hazard ratio is 0.76, with a 95% confidence interval from 0.66 to 0.88. The interval is entirely below 1, so the reported estimate is separated from the no-relative-difference value under this model. The interval gives a range of values compatible with the data and analysis at the stated confidence level; it is not a guarantee that the true effect lies within that range.
The unadjusted risk-difference recalculation from the event counts is -0.045, with a confidence interval from -0.072 to -0.018. This interval does not include zero, the value representing no absolute difference in event proportions. It describes the uncertainty in a different measure from the hazard ratio and should not be treated as its interval. The recalculated p-value is 0.001.
General statistical context: confidence intervals reflect both the observed data and the method used to construct the interval. Wider intervals indicate less precision for the particular estimate; narrower intervals indicate greater precision, all else equal. The interval’s meaning depends on the model and assumptions, and a confidence interval is not a range covering every participant’s outcome. The interval also does not establish whether an effect is important for patients or clinicians; that requires a substantive judgment beyond statistical precision.
The posted secondary estimates also have differing precision. For the persistent at least 50% eGFR reduction comparison, the recalculated interval excludes zero, whereas the interval for persistent eGFR below 15 includes zero. The registry record does not provide sponsor-reported confidence intervals for those secondary comparisons. Estimates for eGFR slope include a posted mean difference of 1.17; its recalculated confidence interval is based on the posted summary statistics. The numerical endpoints of that interval are not repeated.
Precision should be considered alongside the analysis scale, composite definition, follow-up period, and multiplicity context. The registry’s primary analysis provides a time-to-event estimate, while the recalculation uses event proportions. Neither one alone conveys all uncertainty about the trial’s design, missing outcomes, or applicability beyond the enrolled participants.
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 | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 1,293 | 1,731 |
| 75% of the observed effect | 2,345 | 3,138 |
| 50% of the observed effect | 5,375 | 7,195 |
The planning illustrations describe hypothetical group sizes for detecting effects set to stated fractions of the observed effect. They are not the trial’s original design calculations. For the binary primary outcome and other non-time-to-event comparisons, the figures are participants per arm. A time-to-event planning calculation, if presented, is expressed as the total number of events rather than participants per arm.
The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. The original trial’s sample-size justification and its own design assumptions are not reported in the registry record. The arm descriptions do state that the trial was event driven and had a predefined minimum number of primary endpoint events, but the target event count is not reported.
The 80% power column gives the number of participants per arm in the planning illustration for an 80% chance of detecting the specified effect under those assumptions, if that effect were the true one. The 90% power column gives the corresponding group size for a 90% chance. These are planning probabilities under an assumed effect and analysis framework, not probabilities that the observed result is true. This is not observed power.
Rows for 100%, 75%, and 50% of the observed effect illustrate how the required group size changes when the target effect changes. Smaller effects require more participants to distinguish them from no difference at the same planning settings. The illustrations do not account for every practical feature of a trial, and they should not be interpreted as evidence that the original trial was designed using these particular assumptions.
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 is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.232; treatment proportion p1 = 0.187; average p̄ = 0.210.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5758 = 1.1285.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5749 = 0.4838.
- n = (1.1285 + 0.4838)2 / (-0.0448)2 = 1,292.9, rounded up to 1,293 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
p0 <- 0.232163080407701 # control proportion
p1 <- 0.187323146576118 # treatment proportion
n_per_arm <- function(power, frac = 1) {
q1 <- p0 + (p1 - p0) * frac # smaller effect = fraction of the observed difference
pbar <- (p0 + q1) / 2
z_b <- qnorm(power)
ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")
# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(3819153)
n <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))
Output from running the code
100% of observed effect: n per arm = 1,293 (80% power), 1,731 (90% power)
75% of observed effect: n per arm = 2,345 (80% power), 3,138 (90% power)
50% of observed effect: n per arm = 5,375 (80% power), 7,195 (90% power)
power.prop.test: 1292.9
Simulated power at n = 1,293 per arm: 0.799 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Regression, Cox | Hazard Ratio (HR) 0.76 | 0.66 to 0.88 | < 0.001 |
The registry’s own primary analysis is a Cox regression reporting a hazard ratio of 0.76, a 95% confidence interval from 0.66 to 0.88, and p < 0.001. That is the sponsor-reported time-to-event result and should be distinguished from the simple recalculation based on the posted event counts.
The recalculation compares the event proportions using a risk difference of -0.045, with a confidence interval from -0.072 to -0.018 and p = 0.001. It is an unadjusted summary-statistic calculation, not a reproduction of the Cox regression. It does not use the event timing or any covariates. The hazard ratio and risk difference therefore have different scales and use different information, so their values and p-values need not be identical.
The registry does not flag a discrepancy between the sponsor’s analysis and the recalculation. The sponsor result remains the primary reported analysis; the recalculation offers a complementary absolute comparison using the counts. The registry record does not report enough model detail to independently reconstruct the sponsor’s regression or assess all of its assumptions.
15. Multiplicity, Missing Data and Analysis Populations
The registry identifies a primary endpoint and lists 21 secondary outcomes. It reports one analysis for the primary outcome, but does not report a multiplicity procedure for the secondary analyses. The record also does not report whether any hierarchy, gatekeeping strategy, or family-wise error control was used. This leaves uncertainty about how to interpret the collection of secondary p-values as a whole.
General statistical context: testing multiple outcomes can raise the probability of at least one apparently unusual result under a global no-effect situation. Adjustments or a prespecified testing sequence can help manage that issue. Without a reported approach, secondary p-values are best treated as exploratory evidence and considered alongside estimates, confidence intervals, endpoint relevance, and consistency with the primary question. This does not invalidate a secondary result, but it limits how strongly it can support a confirmatory claim.
The primary analysis population is described as the full analysis set, including all unique randomized participants grouped according to assigned treatment. This is important because the comparison is organized by randomized assignment rather than by a participant’s later treatment exposure. The registry does not report the handling of missing outcome data, loss to follow-up, censoring rules, treatment discontinuation, or other deviations for the primary analysis. It also does not report sensitivity analyses addressing those matters.
The study is described as event driven, with a predefined minimum number of renal endpoint events. The actual target event count is not reported in the registry record. Interim analyses, stopping boundaries, the original statistical analysis plan, and the original sample-size justification are likewise not reported. These omissions mean that the timing and details of the trial’s design and analysis decisions cannot be evaluated from the registry record alone.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Semaglutide | 877 | 1767 | 49.6% |
| Placebo | 950 | 1766 | 53.8% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Semaglutide | 227 of 1767 |
| Placebo | 279 of 1766 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Semaglutide | 507 of 1767 |
| Placebo | 522 of 1766 |
Most frequent serious adverse event terms
| Event term | Organ system | Semaglutide | Placebo |
|---|---|---|---|
| Acute kidney injury | Renal and urinary disorders | 124 of 1767 | 123 of 1766 |
| COVID-19 pneumonia | Infections and infestations | 68 of 1767 | 83 of 1766 |
| Pneumonia | Infections and infestations | 66 of 1767 | 75 of 1766 |
| COVID-19 | Infections and infestations | 58 of 1767 | 74 of 1766 |
| Acute myocardial infarction | Cardiac disorders | 49 of 1767 | 67 of 1766 |
| Cardiac failure | Cardiac disorders | 48 of 1767 | 66 of 1766 |
| Cardiac failure congestive | Cardiac disorders | 33 of 1767 | 49 of 1766 |
| Chronic kidney disease | Renal and urinary disorders | 42 of 1767 | 37 of 1766 |
| End stage renal disease | Renal and urinary disorders | 31 of 1767 | 36 of 1766 |
| Acute respiratory failure | Respiratory, thoracic and mediastinal disorders | 30 of 1767 | 32 of 1766 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Semaglutide | Placebo |
|---|---|---|---|
| Diabetic retinopathy | Eye disorders | 339 of 1767 | 325 of 1766 |
| COVID-19 | Infections and infestations | 221 of 1767 | 246 of 1766 |
Serious events with the highest arm-level rate: acute kidney injury (7.0%), covid-19 pneumonia (4.7%), pneumonia (4.2%), covid-19 (4.2%), acute myocardial infarction (3.8%).
The registry reports serious adverse events affecting 877 of 1767 participants assigned semaglutide and 950 of 1766 assigned placebo. It separately reports other adverse events affecting 507 and 522 participants, respectively. Deaths were reported for 227 participants in the semaglutide group and 279 in the placebo group. These are posted group counts, not estimates of whether treatment caused an event.
The registry lists serious adverse event terms and percentages, including acute kidney injury at 7.0%, COVID-19 pneumonia at 4.7%, pneumonia at 4.2%, COVID-19 at 4.2%, acute myocardial infarction at 3.8%, and cardiac failure at 3.7%. The group attribution for these listed term percentages is not reported in the registry record. The figures should therefore be read as the registry’s listed serious-event terms, not as a complete comparative analysis of each event by randomized group.
General statistical context: serious adverse event totals can include different types of events and may not indicate how many participants experienced each specific term unless the record says so. The posted counts alone do not establish causality, severity patterns, timing, or exposure-adjusted rates. Definitions, event adjudication details, and comparative safety analyses are not reported in the registry record. These data describe the registry’s safety reporting and do not provide individualized medical guidance.
17. What the Result Does, and Does Not, Mean
The posted primary result is a difference in time to the first occurrence of a composite kidney or cardiovascular event between randomized groups, as estimated by the registry’s Cox regression. The hazard ratio is 0.76, with a 95% confidence interval from 0.66 to 0.88 and p < 0.001. The observed event counts were 331 of 1767 participants assigned semaglutide and 410 of 1766 assigned placebo. These results describe the participants and follow-up analyzed in this trial.
The result does not mean that every participant assigned to one group experienced the same outcome, or that an individual participant’s future can be predicted from the group estimate. It does not show which component of the composite accounted for the primary comparison. It does not establish that the treatment altered every kidney outcome, and the registry’s secondary results are incomplete and not accompanied by a reported multiplicity plan.
General statistical context: the hazard ratio is a relative measure from a time-to-event model, while the event counts and risk-difference recalculation describe an absolute comparison over the observed period. Neither measure is a substitute for the other. The confidence interval conveys statistical precision under the analysis method, but does not address every source of uncertainty, including unreported assumptions, missing-data handling, or applicability to people who differ from the trial population.
The registry record describes participants with type 2 diabetes and chronic kidney disease and a randomized comparison with placebo. The detailed eligibility criteria and many aspects of the trial’s conduct are not reported in the registry record. Therefore, the results should be understood as trial-level evidence in the specified study population, rather than as a universal statement about all people with kidney disease or diabetes. No individual treatment recommendation follows from these statistical results alone.
18. Why This Trial Matters Statistically
This trial is statistically notable for combining a randomized, masked comparison with a time-to-event primary endpoint and a composite that includes kidney progression, renal replacement therapy, and death. The registry reports enrollment of 3533 participants and an event-driven design with a predefined minimum number of renal endpoint events. These features frame the analysis around accumulating primary events over follow-up rather than only around a fixed visit measurement.
The posted primary analysis and the simple event-count recalculation illustrate why statistical estimands matter. The Cox hazard ratio uses event timing, while the risk difference summarizes the contrast in observed event proportions. The two provide complementary descriptions, not competing versions of the same statistic. Considering both can help readers distinguish a relative time-to-event measure from an absolute count-based comparison.
The secondary eGFR outcomes add another statistical perspective: they include change over time as well as event counts. This variety can illuminate different aspects of disease progression, but also raises questions about multiplicity and the hierarchy of evidence. Because the registry does not report the adjustment strategy or full analysis plan, secondary comparisons warrant more cautious interpretation than the designated primary result.
The record also illustrates limits of registry-level interpretation. It supplies a high-level population definition and outcome summary, but does not report the original sample-size justification, detailed model assumptions, missing-data procedures, or component-level results for all listed outcomes. These absences matter when assessing precision, robustness, and how much of the composite result is attributable to each component. Statistical reading therefore depends not only on the headline estimate but also on the endpoint definition, analysis population, and level of reporting detail.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
The primary endpoint is a composite, but the registry does not report how much each component contributed to the overall result. The composite includes persistent eGFR decline, a low eGFR threshold, chronic renal replacement therapy, renal death, and cardiovascular death. Without complete component-level results and event timing, the relative contribution of these outcomes cannot be assessed from the registry record.
The trial is described as event driven and as having a predefined minimum number of renal endpoint events, but the target number is not reported. The original sample-size justification, design assumptions, statistical analysis plan, and interim analysis arrangements are also not reported in the registry record. The planning illustrations are not a substitute for those original design details.
The record describes the primary population as all unique randomized participants grouped by assigned treatment. However, it does not report how missing outcome data, incomplete follow-up, censoring, treatment discontinuation, or protocol deviations were handled. Model diagnostics and the assumptions underlying the Cox regression are not reported. These details affect how fully the primary estimate can be independently evaluated.
Although 21 secondary outcomes are listed, detailed numerical results are reported for only some of them in the statistical data. The registry does not report whether multiplicity was controlled. This limits assessment of the secondary findings as a family of tests. The serious adverse event counts and listed terms are also not accompanied by detailed group-specific term comparisons, causal assessments, or fuller safety methods.
Finally, eligibility details beyond the broad population description are not reported in the registry record. The numerical results therefore cannot establish how well the enrolled population represents other populations or care settings. These limits do not erase the posted findings, but they define what can and cannot be concluded from the registry information alone.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: A Research Study to See How Semaglutide Works Compared to Placebo in People With Type 2 Diabetes and Chronic Kidney Disease — NCT03819153.
- Registry record last updated 2025-03-20; status last verified 2025-03.
- Results first posted 2025-03-20.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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23. Record Summary
The registry record describes a completed phase 3 randomized, quadruple-masked, parallel-group comparison of semaglutide with placebo in people with type 2 diabetes and chronic kidney disease. Enrollment was 3533. The primary endpoint was time to the first occurrence of a composite kidney or cardiovascular event, assessed from Week 0 up to Week 234.
The reported Cox hazard ratio was 0.76, with a 95% confidence interval from 0.66 to 0.88 and p < 0.001. The event counts were 331 of 1767 in the semaglutide group and 410 of 1766 in the placebo group. A simple unadjusted recalculation gives a risk difference of -0.045, with a confidence interval from -0.072 to -0.018 and p = 0.001. These measures use different methods and answer related but distinct statistical questions.
The registry lists secondary kidney-function and event outcomes, along with serious adverse event counts. Multiplicity procedures, missing-data handling, full design assumptions, and detailed results for all listed outcomes are not reported in the registry record. The posted findings should be interpreted with those reporting limits in mind.