A Study to Evaluate the Effect of VX-661 in Combination With Ivacaftor on Chest Imaging Endpoints in Subjects With Cystic Fibrosis, Homozygous for the F508del CFTR Mutation: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study to Evaluate the Effect of VX-661 in Combination With Ivacaftor on Chest Imaging Endpoints in Subjects With Cystic Fibrosis, Homozygous for the F508del CFTR Mutation (NCT02730208), a randomized phase 2 study. The primary outcome is Absolute Change in Total Brody/CF-CT Score.

2. Clinical Question

3. Trial Design

This was a Phase 2, randomized, placebo-controlled, parallel-group study. The official title describes a double-blind study, while the registry’s masking classification is triple. The registry does not identify which parties were masked, so the precise masking arrangements are not reported in the registry record. The sponsor was Vertex Pharmaceuticals Incorporated. The study status is completed; the registry lists a start of 2016-09 and primary completion of 2018-07.

The treatment period was 72 weeks. Participants assigned to TEZ/IVA took a fixed-dose combination tablet containing tezacaftor 100 mg and ivacaftor 150 mg in the morning, together with ivacaftor 150 mg in the evening. Participants assigned to placebo received matching morning and evening placebo tablets. The registry lists enrollment of 41.

The primary purpose was to evaluate TEZ/IVA’s effect on chest imaging endpoints using low-dose computed tomography at Week 72, and to evaluate safety through Week 72. The primary outcome discussed in the posted results is absolute change in total Brody/CF-CT score from baseline at Week 72. The registry also lists treatment-emergent adverse events and serious adverse events as a secondary outcome.

The primary analysis population is described as the full analysis set: participants who were randomized and received at least 1 dose of study drug. Details on randomization procedures, allocation concealment, the original sample-size rationale, and the trial’s full statistical analysis plan are not reported in the registry record. The record also does not explain how participants who discontinued or missed imaging were handled in the endpoint analysis.

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 41 participants were randomized and treated in the study.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: FAS included all participants who were randomized and received at least 1 dose of study drug.

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.

6. Primary Endpoint

The registry lists the primary outcome as Absolute Change in Total Brody/CF-CT Score, measured over From Baseline at Week 72.

The primary endpoint was absolute change from baseline in total Brody/CF-CT score at Week 72. This is a continuous imaging measure: it assigns a numerical score to structural lung disease visible on CT. The registry describes a range from 0 to 219, with higher values indicating more severe structural lung disease. A change from baseline expresses how the score at follow-up differs from the starting score.

Chest imaging can capture structural features of lung disease that may not be represented by a single symptom or clinical event. The score provides a quantitative way to compare imaging findings across study groups and over time. The registry characterizes the score as exploratory and semi-quantitative, so it should be understood as a structured assessment of CT findings rather than a direct measure of every aspect of disease or daily functioning.

The posted group estimates for change were 0.9 for TEZ/IVA and 2.38 for placebo. The reported least-squares mean difference, defined as TEZ/IVA minus placebo, was -1.48. A negative difference means that the estimated change was lower in the TEZ/IVA group than in the placebo group. The confidence interval is broad and includes values on either side of zero, so the estimate alone does not establish a precise group difference.

The registry record does not report a threshold for a clinically important change in this score. It also does not provide enough endpoint detail to determine how particular CT features contributed to the total score.

7. Results Posted in the Registry

• TEZ/IVA: mean 0.90 versus 2.38 on control; difference -1.48 (95% CI -7.25 to 4.29), standardized effect d = -0.16; z-test p = 0.615.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: each participant’s change in score is represented by a numerical value, and the posted group summaries are least-squares means with standard errors. A least-squares mean is a model-based estimate of a group mean. The registry’s reported analysis identifies the contrast as a least-squares mean difference, but does not specify the model or adjustments used to obtain it.

What does the mean difference represent?

The contrast is TEZ/IVA minus placebo. The reported estimate of -1.48 indicates that the estimated mean change was lower in the TEZ/IVA group by 1.48 score points. This is an estimate of the difference between groups, not a count of participants whose scores improved or worsened. It also does not describe the experience of every participant: individual changes can vary around a group mean.

The posted group values are 0.9 for TEZ/IVA and 2.38 for placebo. Their reported standard errors are 2.09 and 2.07, respectively. A standard error describes the statistical uncertainty in an estimated mean; it is not the standard deviation of participant-level changes. The standard deviations are not directly reported. The recalculation approximates a pooled standard deviation from the standard errors and group sizes, so the resulting standardized effect is approximate.

How should the confidence interval be read?

A confidence interval describes the range of values reasonably compatible with the data and the statistical method used, under the method’s assumptions. It conveys uncertainty around the estimate rather than a range containing a specified proportion of individual participants. The sponsor-reported 95% interval runs from -7.47 to 4.52. Because it crosses zero, it includes the value corresponding to no difference between group means. It also reaches both negative and positive values, so it does not settle the direction of the underlying contrast.

The recalculated interval, from -7.245 to 4.285, is an unadjusted calculation based on the posted summary values. It is not the sponsor’s model-based estimate. Small differences between a summary-statistic recalculation and a reported analysis can arise because the trial analysis may use model details or data handling not captured by the summary statistics. The registry record does not report the model specification needed to reproduce the sponsor’s result in full.

What does the p-value convey?

The recalculated unadjusted p-value is 0.615. In general, a p-value summarizes how surprising data at least as incompatible with a specified null model would be if that model and its assumptions held. It is not the probability that the null hypothesis is true, nor is it a measure of the size or clinical importance of an effect. The sponsor’s posted analysis does not include a p-value for this comparison, and the recalculated p-value should not be presented as the sponsor’s result.

Why can over-dispersion matter?

General statistical explanation: over-dispersion occurs when observed variability is greater than a model expects. It is especially relevant to count outcomes, where a basic model may assume that variability is tightly linked to the mean. If that assumption is too restrictive, standard errors and confidence intervals can be too small, making results appear more precise than they are. The primary endpoint in this study is continuous rather than a count, and the registry does not report a particular over-dispersion adjustment for its analysis.

What is the role of the standardized effect?

The recalculation gives a standardized effect of -0.157. Standardization expresses a difference in relation to an estimate of variability, allowing effects measured on different scales to be compared more readily. It does not change the original score-point difference, and it does not supply a clinical interpretation for the Brody/CF-CT score. Because the pooled standard deviation used in this calculation is approximated from the posted standard errors and group sizes, the standardized result is also approximate.

The registry record does not report the detailed model assumptions, handling of missing endpoint data, or a prespecified hierarchy of statistical tests. Those omissions limit independent reproduction and make it important to distinguish the sponsor’s reported estimate from the unadjusted recalculation.

10. Confidence Intervals and Precision

Precision is best judged by considering the estimate together with its confidence interval, not by reading the point estimate alone. The sponsor-reported least-squares mean difference was -1.48, with a 95% confidence interval from -7.47 to 4.52. The point estimate gives the central estimate of the contrast; the interval communicates that substantial uncertainty remains about its magnitude and direction.

The interval includes zero, the value corresponding to no difference. It also includes negative and positive values. Given the score’s direction, negative values favor a smaller estimated change in the TEZ/IVA group, while positive values favor a smaller estimated change in the placebo group. The interval therefore does not identify a single direction with precision. The registry record does not specify a clinically important threshold for interpreting the score-point values.

The unadjusted recalculation gives an interval from -7.245 to 4.285. This is close in overall interpretation to the sponsor’s interval: it crosses zero and covers values in both directions. The recalculated interval should be treated as a summary-statistic check, not as a substitute for the sponsor’s model-based analysis. The registry does not report enough methodological detail to reproduce the sponsor’s analysis exactly.

Standard errors for the group estimates were 2.09 for TEZ/IVA and 2.07 for placebo. These describe uncertainty in the estimated group means, not the spread of individual participants’ scores. With the relatively small group sizes recorded, estimates may be sensitive to individual observations. The breadth of the difference interval is a direct reminder that the point estimate is not a precise measurement of the underlying group contrast.

11. 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.

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design rationale. They are participants per arm, not total participants. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row considers detecting a stated fraction of the observed effect.

For planning at 100% of the observed effect, the figures are 636 participants per arm for 80% power and 852 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,131 participants per arm for 80% power and 1,513 participants per arm for 90% power. Planning for 50% of the observed effect gives 2,543 participants per arm for 80% power and 3,405 participants per arm for 90% power.

In general, the 80% power column represents a design intended to have an 80% chance of detecting the specified effect under the assumptions used, if that effect is the true one. The 90% power column represents a higher target chance under the same kind of assumptions. These are planning probabilities, not guarantees for an individual trial. Smaller effects require more participants to detect than larger effects, which is why the figures increase as the planned fraction of the observed effect gets smaller.

The curve represents the same planning relationship across effects: as the effect to detect becomes smaller, the required sample size grows. These calculations are not observed power and do not describe the probability that this completed study detected its actual treatment effect. The trial’s own original sample-size assumptions and justification are not reported in the registry record.

12. 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 z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

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

Worked calculation for this trial

1. Observed difference Δ = -1.480; pooled standard deviation σ = 9.418.
2. n = 2 × (1.96 + 0.842)² × 9.418² / -1.480² = 635.7, rounded up to 636 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -1.48                      # observed difference in means
sigma <- 9.41838899611028                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

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

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(2730208)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 636 (80% power), 852 (90% power)
 75% of observed effect: n per arm = 1,131 (80% power), 1,513 (90% power)
 50% of observed effect: n per arm = 2,543 (80% power), 3,405 (90% power)
power.t.test: 636.7 
Simulated power at n = 636 per arm: 0.795 (20000 replicates)

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

13. Analyses Reported by the Sponsor

The registry reports a sponsor analysis for the primary comparison as a least-squares mean difference of -1.48, with a 95% confidence interval from -7.47 to 4.52. The reported analysis does not include a p-value. This is the trial’s posted result and should be distinguished from the simple unadjusted recalculation based on the group summary statistics.

The recalculation gives the same point estimate, -1.48, but an interval from -7.245 to 4.285 and an unadjusted p-value of 0.615. It uses an approximation based on the posted group values, standard errors, and sizes; it does not reproduce an analysis model that the registry does not describe. The difference between the intervals should therefore be read as a limitation of the recalculation, rather than as evidence that one posted number is an error.

Both intervals include zero and extend to values on either side of it. Their shared broad interpretation is that the estimated contrast is uncertain. The sponsor-reported analysis remains the relevant trial result, while the recalculation is useful as a transparent check of the summary data. The registry record does not provide enough detail to determine exactly which model features account for the interval difference.

14. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when several outcomes or statistical comparisons are assessed: the more tests considered, the greater the chance that at least one result appears unusual by chance. A prespecified strategy may address this through test ordering, adjusted significance thresholds, or other methods. The registry record does not report a multiplicity adjustment or a testing hierarchy for the reported outcomes.

The primary imaging endpoint is described as exploratory. The registry lists two outcome measures and one analysis. It does not state whether other imaging endpoints were tested, whether the primary endpoint was selected from a larger set, or how any related comparisons were accounted for. Without those details, the reported unadjusted recalculation should not be treated as a multiplicity-adjusted confirmatory test.

The full analysis set is defined as all participants who were randomized and received at least 1 dose of study drug. The registry does not report whether the endpoint analysis used that population without modification, nor does it describe a separate per-protocol population. The specific analysis population for the sponsor’s least-squares mean comparison is not reported in the registry record beyond the stated full analysis set definition.

Missing endpoint data can affect a comparison if participants with unavailable Week 72 imaging differ from those whose data are observed. Statistical approaches may use assumptions or models to handle incomplete data, but the registry does not report the amount or pattern of missing imaging data, the method used to address missing values, or sensitivity analyses examining alternative assumptions. It is therefore not possible to assess from the record whether the result is robust to missing-data choices.

The registry also does not provide details of the model specification, covariates, or assumptions used for the sponsor’s analysis. These missing details limit independent reproduction and make it difficult to judge how the estimate might change under alternative analysis choices.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: infective pulmonary exacerbation of cystic fibrosis (28.6%), lung infection pseudomonal (10.0%), atrioventricular block first degree (5.0%), abdominal pain upper (5.0%), testicular torsion (5.0%).

The registry reports serious adverse events for 8 of 20 participants at risk in the TEZ/IVA group and 13 of 21 at risk in the placebo group. These are participant counts, not event totals; a participant may experience more than one event. The record also reports other adverse events for 19 of 20 participants at risk with TEZ/IVA and 20 of 21 at risk with placebo. Deaths were recorded as 0 in each group.

The listed serious adverse event terms include infective pulmonary exacerbation of cystic fibrosis at 28.6%, lung infection pseudomonal at 10.0%, atrioventricular block first degree at 5.0%, abdominal pain upper at 5.0%, testicular torsion at 5.0%, and atypical mycobacterial lower respiratory tract infection at 4.8%. These are the registry’s listed terms and percentages; they should not be treated as evidence that the study treatment caused an event.

Safety counts describe events recorded during the study and do not establish comparative risk on their own. The registry excerpt does not provide event timing, severity grades beyond the serious classification, or detailed attribution by investigators. The counts should be interpreted alongside the study’s limited size and follow-up period, rather than as a complete account of safety in other populations or over longer periods.

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

The central statistical result is a sponsor-reported least-squares mean difference of -1.48 in absolute change in total Brody/CF-CT score at Week 72, comparing TEZ/IVA with placebo. The negative direction means the estimated change was lower in the TEZ/IVA group. Since higher scores indicate more severe structural lung disease, that direction corresponds to a smaller estimated increase in score in the treatment group. The estimate remains uncertain: the sponsor-reported 95% confidence interval, from -7.47 to 4.52, includes zero and values in both directions.

The posted data do not establish whether the difference is clinically meaningful. The registry does not report a threshold for meaningful change in this score, and it describes the score as exploratory and semi-quantitative. The point estimate should not be interpreted as a guaranteed effect for individual participants or as a direct measure of every aspect of cystic fibrosis.

The study compared a specific treatment regimen with matching placebo over 72 weeks in people aged 12 years and older with cystic fibrosis who were homozygous for the F508del CFTR mutation. The results do not automatically apply to other populations, treatment regimens, outcomes, or follow-up periods. The registry’s safety results are counts of observed events and do not establish that a treatment caused or prevented them.

The recalculated unadjusted interval also includes zero, and its unadjusted p-value is 0.615. Those calculations are not the sponsor’s analysis. The sponsor’s posted estimate is the trial result to use, while the recalculation illustrates how the summary data can be examined with simplified assumptions.

Overall, the posted results describe an uncertain difference in an imaging score, alongside recorded safety events. They do not justify a broad conclusion about treatment effectiveness or safety beyond the reported endpoint, population, and study period.

17. Why This Trial Matters Statistically

This trial is statistically informative because it uses a quantitative imaging endpoint rather than relying only on clinical events or symptoms. CT scoring can represent structural changes in a way that permits group-level comparison over time. At the same time, semi-quantitative scoring involves choices about how imaging features are graded and combined, so clarity about scoring procedures and analysis methods is important.

The study also illustrates why an estimated treatment contrast should be read with its uncertainty. The point estimate is -1.48, but the sponsor’s 95% confidence interval ranges from -7.47 to 4.52. The interval crosses zero and includes effects in either direction. Reporting the estimate without that interval would give an incomplete picture of how much the data constrain the possible difference.

The difference between a sponsor-reported model-based result and a simple summary-statistic recalculation is another practical lesson. A recalculation can be a useful check, but it cannot reproduce details that are not reported, such as the fitted model and handling of missing data. The registry’s limited analysis detail makes transparent reporting especially valuable for independent interpretation.

Finally, the planning illustrations show how sample-size requirements depend on the effect a study aims to detect. Smaller planned effects require more participants under the stated assumptions. These planning values should not be confused with the number enrolled or with evidence that a completed trial had adequate power for its actual effect. They are illustrations derived from the observed estimate, which itself is imprecise.

18. 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 registry record provides limited detail about the primary analysis. It does not report the model specification, covariate adjustments, or the method used to handle missing Week 72 imaging. Those omissions make it difficult to reproduce the sponsor’s least-squares mean difference or assess how sensitive it is to analysis choices.

The endpoint is described as exploratory and semi-quantitative. The record does not report a clinically important threshold for a change in total Brody/CF-CT score, or explain how component imaging features contribute to the total. This limits interpretation of the score-point difference in clinical terms.

The study was a Phase 2 trial with registry enrollment of 41 and relatively small groups in the posted primary results: 20 for TEZ/IVA and 21 for placebo. Estimates from small groups can be imprecise, as reflected in the broad confidence interval. The registry does not report the original sample-size justification, so the adequacy of the planned size for the primary endpoint cannot be assessed from the record.

Although the registry classifies the study as triple-masked and the official title describes it as double-blind, it does not specify who was masked. It also does not provide detailed information about allocation procedures, participant flow, or missing endpoint observations. The outcome is reported at Week 72; longer-term results are not included in the registry record.

The safety summaries give participant counts and listed serious adverse event terms, but not detailed event timing, severity, or attribution. These limitations restrict what can be concluded about comparative safety from the posted counts.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: A Study to Evaluate the Effect of VX-661 in Combination With Ivacaftor on Chest Imaging Endpoints in Subjects With Cystic Fibrosis, Homozygous for the F508del CFTR Mutation — NCT02730208.
• Registry record last updated 2019-10-23; status last verified 2019-10.
• Results first posted 2019-08-21.
• 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.

22. Record Summary

This completed Phase 2 study evaluated tezacaftor and ivacaftor against matching placebo in people aged 12 years and older with cystic fibrosis who were homozygous for the F508del CFTR mutation. Treatment continued for 72 weeks, and the primary endpoint was absolute change from baseline in total Brody/CF-CT score at Week 72.

The sponsor-reported least-squares mean difference was -1.48, with a 95% confidence interval from -7.47 to 4.52. The interval includes zero and values in both directions, leaving uncertainty about the magnitude and direction of the underlying difference. The registry also reports serious and other adverse event counts by group and records 0 deaths in each group.

Important analysis details, including missing-data handling, the full statistical model, and the original sample-size rationale, are not reported in the registry record. The findings should therefore be read as a limited account of the posted imaging and safety results, not as a definitive statement beyond this study’s population and follow-up.