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 Safety and Efficacy Study of Switching From Epzicom to Truvada (NCT00724711), a randomized phase 4 study. The primary outcome is Percentage of Participants With HIV-1 Ribonucleic Acid (RNA) < 200 Copies/mL Through Week 48 Based on Time to Loss of Virologic Response (TLOVR) Algorithm.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00724711 |
| Phase | Phase 4 |
| Condition | HIV Infection |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 312 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Gilead Sciences |
| Results posted | Yes |
2. Clinical Question
Population
Participants had HIV-1 infection, were virologically suppressed, and were maintained on an antiretroviral regimen containing a ritonavir-boosted protease inhibitor. The primary analysis population consisted of participants treated with at least one dose of study drug and without documented resistance to study drug before screening. The registry record reports enrollment of 312 participants.
Intervention
Participants switched from fixed-dose abacavir and lamivudine to fixed-dose emtricitabine and tenofovir disoproxil fumarate. The prestudy ritonavir-boosted protease inhibitor was continued unmodified. Treatment duration was 48 weeks.
Comparator
Participants continued their prestudy fixed-dose abacavir and lamivudine regimen together with the ritonavir-boosted protease inhibitor. The listed dose was ABC 600 mg/3TC 300 mg as one tablet orally once daily, for 48 weeks.
Primary question
What percentage of participants in each group had HIV-1 RNA below 200 copies/mL through Week 48, using the TLOVR algorithm? The registry also records an analysis of the difference in percentages using inverted two one-sided tests. The noninferiority margin and the trial's original design assumptions are not reported in the registry record.
The question is about virologic response after changing the nucleoside backbone while keeping the ritonavir-boosted protease inhibitor regimen in place. It is not a comparison of regimens that differ in every component: the intervention group switched from ABC/3TC to FTC/TDF, whereas the comparator group continued ABC/3TC, and the PI/r component was continued in both groups. The registry describes the study as prospective, randomized, open label, multicenter, and phase IV. Participants were followed for 48 weeks. The primary endpoint uses a response definition that treats specified events as nonresponse, rather than simply recording a single viral RNA measurement. That distinction is important when interpreting the endpoint: the proportion reflects both the measured viral RNA status and the TLOVR rules for rebound, discontinuation, and adding an antiretroviral agent.
3. Trial Design
This was a prospective, randomized, open-label, parallel-group phase IV study. The registry lists HIV infection as the condition, an enrollment of 312, and a completed status. The study started in 2008-07, with primary completion in 2011-03. The listed treatment duration was 48 weeks. Masking is recorded as none, so the study was not blinded according to the registry record.
The two groups differed in the nucleoside combination. Participants assigned to FTC/TDF received fixed-dose FTC 200 mg/TDF 300 mg, with their prestudy ritonavir-boosted protease inhibitor continued unmodified. Participants assigned to ABC/3TC continued their prestudy ABC 600 mg/3TC 300 mg tablet once daily together with the PI/r regimen. The primary analysis included participants treated with at least one dose of study drug and with no documented resistance to study drug before screening. The reported arm counts for the primary endpoint were 154 for TVD + PI/r and 156 for ABC/3TC + PI/r.
Random allocation supports a comparison between groups, but the record does not describe the allocation sequence or concealment procedures. It also does not report the original sample-size calculation, the noninferiority margin, or the intended statistical assumptions for trial planning. These aspects cannot be reconstructed from the observed enrollment or from planning illustrations based on the observed results. The registry records a primary endpoint and several secondary outcomes, including virologic response at another RNA cutoff, CD4 cell-count change, renal-function measures, and fasting glucose. Results for all listed secondary measures are not present in the numerical results described in the record. The open-label design is relevant when considering outcomes or decisions that may be influenced by knowledge of assigned treatment; the primary endpoint itself is based on HIV-1 RNA measurements and prespecified TLOVR response rules.
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 393 subjects were screened for entry into this study, and 312 subjects were randomized (156 to each treatment group). One participant randomized to the TVD+PI/r group was never treated.
Overall Study
| Stage | FTC/TDF (Truvada [TVD]) + PI/r (Ritonavir-boosted PI Regimen) | Abacavir (ABC) /Lamivudine (3TC) + PI/r (Ritonavir-boosted PI) |
|---|---|---|
| STARTED | 155 | 156 |
| COMPLETED | 138 | 139 |
| NOT COMPLETED | 17 | 17 |
Reasons for not completing this period:
| Reason | FTC/TDF (Truvada [TVD]) + PI/r (Ritonavir-boosted PI Regimen) | Abacavir (ABC) /Lamivudine (3TC) + PI/r (Ritonavir-boosted PI) |
|---|---|---|
| Adverse Event | 7 | 3 |
| Pregnancy | 0 | 1 |
| Lack of Efficacy | 0 | 1 |
| Physician Decision | 0 | 3 |
| Withdrawal by Subject | 5 | 4 |
| Lost to Follow-up | 4 | 5 |
| Protocol Violation | 1 | 0 |
Analysis population for the primary outcome, as defined in the registry: Intent-to-treat (ITT) Analysis Set: Participants who were treated with at least one dose of study drug with no documented resistance to study drug prior to screening.
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.
| Characteristic | Unit | TVD + PI/r | ABC/3TC + PI/r | Total |
|---|---|---|---|---|
| Participants analysed | 155 | 156 | 311 | |
| Age Continuous | years | 46 (SD 9.0) | 47 (SD 9.7) | 46 (SD 9.3) |
| Sex: Female, Male: Female | Participants | 26 | 22 | 48 |
| Sex: Female, Male: Male | Participants | 129 | 134 | 263 |
| Race/Ethnicity, Customized: American Indian or Alaska Native | participants | 0 | 0 | 0 |
| Race/Ethnicity, Customized: Asian | participants | 4 | 3 | 7 |
| Race/Ethnicity, Customized: Native Hawaiian or Other Pacific Islander | participants | 0 | 0 | 0 |
| Race/Ethnicity, Customized: Black or African American | participants | 43 | 44 | 87 |
| Race/Ethnicity, Customized: White | participants | 96 | 106 | 202 |
| Race/Ethnicity, Customized: Other | participants | 12 | 3 | 15 |
| Race/Ethnicity, Customized: Hispanic/Latino | participants | 38 | 36 | 74 |
| Race/Ethnicity, Customized: Non-Hispanic/Latino | participants | 117 | 120 | 237 |
| Region of Enrollment: United States | participants | 146 | 142 | 288 |
| Region of Enrollment: Puerto Rico | participants | 4 | 5 | 9 |
| Region of Enrollment: Canada | participants | 5 | 9 | 14 |
| Weight | kg | 82.2 (SD 17.40) | 82.5 (SD 15.65) | 82.3 (SD 16.52) |
| Height | cm | 173.8 (SD 9.52) | 174.1 (SD 9.55) | 173.9 (SD 9.52) |
| Body Mass Index (BMI) | kg/m^2 | 27.3 (SD 5.96) | 27.2 (SD 4.93) | 27.3 (SD 5.46) |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Participants With HIV-1 Ribonucleic Acid (RNA) < 200 Copies/mL Through Week 48 Based on Time to Loss of Virologic Response (TLOVR) Algorithm, measured over Baseline to 48 weeks.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | percentage of participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the percentage of participants with HIV-1 RNA below 200 copies/mL through Week 48, based on the TLOVR algorithm. The stated timeframe is baseline to 48 weeks. The record defines the primary analysis population as participants who received at least one dose of study drug and had no documented resistance to study drug before screening.
TLOVR does not classify response solely from a viral RNA value at Week 48. A participant was considered a nonresponder if virologic rebound occurred before or at Week 48, if study treatment was discontinued before Week 48, or if a new antiretroviral agent was added before study completion. Virologic rebound was defined as two consecutive HIV-1 RNA values at or above 200 copies/mL, or a last HIV-1 RNA value at or above 200 copies/mL followed by discontinuation. Thus, the endpoint combines virologic status with treatment-course events according to the algorithm.
General statistical context: a binary response endpoint expresses the fraction of participants classified as responders, and a between-group difference expresses the contrast in those fractions. This kind of endpoint is useful for comparing the frequency of a defined response, but its interpretation depends on the response definition, the analysis population, and how missing observations or treatment changes are handled. The TLOVR rules for certain events are reported; further details of missing-data handling beyond those rules are not reported in the registry record.
7. Results Posted in the Registry
- ABC/3TC + PI/r: 83.3% (130/156) versus 86.4% (133/154) on control; risk difference -3.0 percentage points (95% CI -11.0 to 4.9), risk ratio 0.96 (0.88–1.06); unadjusted two-proportion z-test p = 0.457.
Risk difference: ABC/3TC + PI/r
95% CI: -11.0 to 4.9 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 |
|---|---|---|---|---|
| Percentage of Participants With Pure Virologic Response (PVR) for HIV-1 RNA Cutoff at 200 Copies/mL Through Week 48 | Binary Endpoint | Risk difference | -1.9 pts (-4.7 to 0.9) | 676 per arm |
| Percentage of Participants With Pure Virologic Response (PVR) for HIV-1 RNA Cutoff at 50 Copies/mL Through Week 48 | Binary Endpoint | Risk difference | -1.8 pts (-7.9 to 4.2) | 3,467 per arm |
| Change From Baseline in Cluster Determinant 4 (CD4) Cell Count at Week 48 | Continuous Endpoint | Mean difference | 26.00 (-9.40 to 61.40) | 518 per arm |
Percentage of Participants With Pure Virologic Response (PVR) for HIV-1 RNA Cutoff at 200 Copies/mL Through Week 48
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- ABC/3TC + PI/r: 97.4% (152/156) versus 99.4% (153/154) on control; risk difference -1.9 percentage points (95% CI -4.7 to 0.9), risk ratio 0.98 (0.95–1.01); unadjusted two-proportion z-test p = 0.181.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between ABC/3TC + PI/r and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Participants With Pure Virologic Response (PVR) for HIV-1 RNA Cutoff at 50 Copies/mL Through Week 48
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- ABC/3TC + PI/r: 91.0% (142/156) versus 92.9% (143/154) on control; risk difference -1.8 percentage points (95% CI -7.9 to 4.2), risk ratio 0.98 (0.92–1.05); unadjusted two-proportion z-test p = 0.554.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between ABC/3TC + PI/r and the control. The interval gives the range of effects that remain compatible with the data.
Change From Baseline in Cluster Determinant 4 (CD4) Cell Count at Week 48
- 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 deviations.
- Result:
- ABC/3TC + PI/r: mean 34.00 versus 8.00 on control; difference 26.00 (95% CI -9.40 to 61.40), standardized effect d = 0.17; z-test p = 0.150.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between ABC/3TC + PI/r and the control. The interval gives the range of effects that remain compatible with the data.
The numerical secondary results available in the registry record show a broadly similar pattern across the posted virologic response measures: response percentages are high in both groups at the reported RNA cutoffs, and the recalculated differences have confidence intervals that include zero. These outcomes provide context alongside the primary TLOVR result, but they use distinct response definitions and should not be treated as interchangeable replications of the primary endpoint. The CD4 change outcome is on a continuous scale and has a mean difference whose confidence interval also includes zero.
The registry lists additional secondary measures, including CD4 cell count, calculated creatinine clearance, estimated glomerular filtration rate, and fasting glucose. Numerical results for those other listed measures are not reported in the registry record. Their absence means that no conclusion about their between-group patterns can be drawn from the numerical results.
Each secondary comparison is an additional opportunity to observe a seemingly notable result by chance. General statistical explanation: when many outcomes are tested, the chance of at least one apparently unusual finding can increase, even if there is no true effect for any outcome. The registry information does not report a multiplicity adjustment or identify a confirmatory hierarchy among the secondary outcomes. Accordingly, unadjusted secondary results carry less weight than a prespecified primary result and should be regarded as supportive or exploratory. Their confidence intervals and endpoint definitions remain important, but they do not independently establish a broad treatment effect.
The secondary outcomes also address different aspects of the treatment course. Virologic response proportions concern whether a participant meets a defined viral RNA criterion; CD4 change concerns an average change in cell count; renal and glucose measures concern different laboratory outcomes. A consistent statistical interpretation requires attention to each outcome's scale, population, timeframe, and analysis rather than combining them into a single overall judgment.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Participants With Pure Virologic Response (PVR) for HIV-1 RNA Cutoff at 200 Copies/mL Through Week 48
- Percentage of Participants With Pure Virologic Response (PVR) for HIV-1 RNA Cutoff at 50 Copies/mL Through Week 48
- Percentage of Participants With HIV-1 RNA < 200 Copies/mL at Week 48
- Percentage of Participants With HIV-1 RNA < 50 Copies/mL at Week 48
- Change From Baseline in Cluster Determinant 4 (CD4) Cell Count at Week 48
- Change From Baseline Calculated Creatinine Clearance (CLcr) Using Ideal Body Weight by Cockcroft-Gault Method at Week 48
- Change From Baseline Estimated Glomerular Filtration Rate (eGFR) by Modified Diet in Renal Disease (MDRD) at Week 48
- Change From Baseline Fasting Glucose at Week 48
9. Statistical Interpretation
For the primary endpoint, the registry reports response percentages of 86.4% for TVD + PI/r and 83.3% for ABC/3TC + PI/r. The recalculated unadjusted risk difference, expressed as ABC/3TC + PI/r relative to TVD + PI/r, is -0.030, with a 95% confidence interval from -0.11 to 0.049 and an unadjusted p-value of 0.457. This interval is compatible with a range of differences in either direction; it does not establish that the groups are identical.
The sponsor's reported analysis is an inverted two one-sided tests analysis of the difference in percentages. The registry reports a difference of 3.0 with a 95% confidence interval from -5.1 to 11.2. The registry labels this analysis as noninferiority or equivalence, but the noninferiority margin and the direction convention for the reported difference are not reported in the registry record. Without the margin, the numerical result alone cannot establish whether the prespecified noninferiority criterion was met. The sponsor's analysis should be interpreted according to its own method and assumptions; the simple unadjusted recalculation is not a substitute for that analysis.
The estimate and its interval are more informative than treating the unadjusted p-value as a yes-or-no verdict. A p-value of 0.457 does not show that there is no difference; it indicates that the observed data are not unusual under the null model used for that unadjusted comparison. The interval includes differences that could matter in either direction, and its width reflects uncertainty in the estimate. The registry's reported analysis and the unadjusted recalculation use different approaches, so their estimates should not be blended into one result.
The secondary numerical results broadly show high percentages for the posted virologic response measures at both RNA cutoffs, while the CD4 change estimate is imprecise. The individual confidence intervals and estimates are available in the reported results, but secondary comparisons were not adjusted for multiplicity in the information recorded. Consequently, secondary patterns should be treated as supporting or exploratory evidence rather than as independent confirmatory findings. Results for the other listed secondary measures are not reported in the registry record.
These results describe outcomes among participants in this trial, using its eligibility criteria, assigned regimens, duration, analysis population, and endpoint rules. They do not by themselves establish equivalence, identify the effect of switching for every patient or clinical setting, or address outcomes beyond the reported follow-up. No medical recommendation follows from the numerical comparison alone.
10. Statistical Methods Explained
The primary result is a binary outcome: each participant is classified as a responder or nonresponder under the TLOVR definition, and the result is expressed as a percentage. The registry reports the percentages for each randomized group and a sponsor analysis of the difference in percentages. A separate unadjusted recalculation expresses the contrast as a risk difference and includes a confidence interval and p-value. These are related ways to describe the same broad comparison, but they are not identical analyses.
What does the TLOVR endpoint classify?
The TLOVR algorithm counts a participant as a nonresponder if there is virologic rebound before or at Week 48, discontinuation before Week 48, or addition of a new antiretroviral before study completion. Rebound is defined in the record as two consecutive HIV-1 RNA values at or above 200 copies/mL, or a last value at or above 200 copies/mL followed by discontinuation. These rules make treatment-course events part of the endpoint. A percentage based on TLOVR therefore should not be read as if it were simply the fraction with one observed RNA value below the cutoff at the final visit.
What is a risk difference?
General statistical explanation: a risk difference subtracts one group's event probability from the other group's event probability. For this endpoint, the event is response, not an adverse event. A risk difference of zero corresponds to equal response probabilities under the chosen comparison and analysis. A negative or positive estimate indicates which group has the lower or higher observed response probability according to the stated orientation. The recalculated comparison is ABC/3TC + PI/r relative to TVD + PI/r, so the negative point estimate corresponds to a lower observed response percentage in the ABC/3TC + PI/r group. The estimate remains uncertain, as indicated by its confidence interval.
What does the sponsor's method do?
The registry reports an inverted two one-sided tests method for the difference in percentages and labels the analysis as noninferiority or equivalence. General statistical explanation: noninferiority analyses assess whether a treatment's result is not worse than a comparator by more than a prespecified margin. Such a conclusion depends on the margin, the direction of comparison, and the confidence interval or test criterion. The registry reports the method and a difference with a 95% confidence interval, but it does not report the margin or the design assumptions. It is therefore not possible to independently verify the formal noninferiority criterion from the registry record alone. The sponsor's analysis remains the relevant reported analysis for that objective.
How should the unadjusted p-value be read?
General statistical explanation: a p-value measures how compatible the observed data are with a specified null hypothesis under the analysis assumptions. It is not the probability that the null hypothesis is true, nor is it a measure of the size or clinical importance of a difference. The unadjusted p-value of 0.457 is attached to the recalculated comparison, not to the sponsor's reported inverted two one-sided tests result. The registry does not report a p-value for the sponsor analysis. The distinction matters because a test for a difference and a noninferiority analysis answer different statistical questions.
Why do confidence intervals matter?
General statistical explanation: a confidence interval represents a range of values reasonably compatible with the data and the method used to construct it. A wide interval indicates less precision than a narrow interval. The primary recalculated interval includes values on both sides of zero, so the result is not a precise estimate of a single direction of difference. It should not be paraphrased as proof that the treatments are the same. The sponsor's interval also describes uncertainty for its reported difference, but formal interpretation against a noninferiority margin requires knowing that margin.
What is known about populations and missingness?
The primary analysis population is described as treated participants without documented resistance to study drug before screening. The TLOVR rules explicitly classify discontinuation and addition of a new antiretroviral as nonresponse in specified circumstances. The registry does not report further missing-data procedures, sensitivity analyses, or how other absent measurements were handled. It also does not report interim analyses or a multiplicity adjustment for the secondary endpoints. These omissions limit how fully the analysis can be reproduced or assessed from the registry record.
The secondary outcomes use different measurement scales. The PVR outcomes are percentages, while CD4 change is reported as a mean with a standard deviation. General statistical explanation: a mean summarizes the average change, whereas a standard deviation describes participant-level spread around that mean. The corresponding mean difference and confidence interval address a different quantity from a risk difference. Because endpoints differ in scale and clinical meaning, their numerical estimates should not be compared as though they were the same measure.
11. Confidence Intervals and Precision
The primary recalculated risk difference is -0.030, with a 95% confidence interval from -0.11 to 0.049. The interval spans negative and positive values, so the data are compatible with a lower response percentage in the ABC/3TC + PI/r group or with a higher one. The point estimate is only one value within that range; the interval conveys the uncertainty around it. The result does not demonstrate exact equality between groups.
The sponsor's reported difference is 3.0, with a 95% confidence interval from -5.1 to 11.2. The result is reported using inverted two one-sided tests. The record does not provide the noninferiority margin, so the interval cannot be assessed against that criterion from the registry information alone. The two intervals should not be read as contradictory estimates without accounting for their respective analysis methods and difference conventions.
General statistical explanation: precision depends in part on how much information is available and on the variability of the outcome. For percentages, the number of participants and the response proportions influence the uncertainty; for continuous outcomes, spread also matters. The primary endpoint's confidence interval is the appropriate indicator of uncertainty for the recalculated contrast. A p-value cannot replace that interval because it does not show the range of plausible effect sizes.
The secondary confidence intervals also convey uncertainty, and several are broad enough to include effects in either direction. Their interpretation is further limited by the number of outcomes considered and the absence of a reported multiplicity adjustment. Statistical precision is not the same as clinical importance: the registry does not specify a threshold for a meaningful difference, and the noninferiority margin is not reported.
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 | 2,197 | 2,941 |
| 75% of the observed effect | 3,826 | 5,121 |
| 50% of the observed effect | 8,425 | 11,278 |
The planning figures are participants per arm for 80% power and participants per arm for 90% power; they are not total event counts. The displayed planning values for these outcomes are per arm. 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 set to the stated fraction of the observed effect. These are planning illustrations computed from the observed effect, not the trial's original design assumptions; those original assumptions are not reported in the registry record.
The 80% power column means that, under the specified planning assumptions and if the effect used for planning were the true effect, the proposed sample size would give an 80% chance of detecting that effect using the assumed test criterion. The 90% column describes a higher chance of detection under the same assumptions, and it therefore requires more participants than the corresponding 80% figure. For the primary endpoint, the planning figures for 100% of the observed effect are 2,197 participants per arm for 80% power and 2,941 participants per arm for 90% power. For planning at 75% of the observed effect, the figures are 3,826 and 5,121 participants per arm; at 50% of the observed effect, they are 8,425 and 11,278 participants per arm.
Smaller effects are harder to distinguish from random variation, so detecting a smaller effect generally requires more participants. The values depend on the assumptions and should not be treated as a recommended design for another study without considering its endpoint, target effect, analysis, and design. This is not observed power: it does not measure the chance that the completed trial was successful, and it does not replace interpretation of the observed estimates and confidence intervals.
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 = 0.864; treatment proportion p1 = 0.833; average p̄ = 0.848.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5071 = 0.9938.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5066 = 0.4264.
- n = (0.9938 + 0.4264)2 / (-0.0303)2 = 2,196.5, rounded up to 2,197 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 <- 0.863636363636364 # control proportion
p1 <- 0.833333333333333 # 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(724711)
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 = 2,197 (80% power), 2,941 (90% power)
75% of observed effect: n per arm = 3,826 (80% power), 5,121 (90% power)
50% of observed effect: n per arm = 8,425 (80% power), 11,278 (90% power)
power.prop.test: 2196.5
Simulated power at n = 2,197 per arm: 0.802 (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 |
|---|---|---|---|
| Inverted two one-sided tests | Difference in percentages between groups 3.0 | -5.1 to 11.2 | not reported |
The registry reports the sponsor's primary comparison as an inverted two one-sided tests analysis of the difference in percentages. The reported difference is 3.0, with a 95% confidence interval from -5.1 to 11.2. The analysis is classified in the registry as noninferiority or equivalence. The noninferiority margin and the direction convention for the reported difference are not reported in the registry record, so the interval cannot be assessed against the formal noninferiority criterion from these details alone.
The recalculated comparison is a simple unadjusted risk difference, expressed as ABC/3TC + PI/r relative to TVD + PI/r. It is -0.030, with a 95% confidence interval from -0.11 to 0.049 and an unadjusted p-value of 0.457. It is not the sponsor's two one-sided tests analysis, and it does not reproduce the sponsor's analytic objective. The registry record reports no discrepancy between the sponsor result and the recalculation. Even so, the sponsor's own analysis takes precedence for interpreting the sponsor's stated noninferiority or equivalence analysis; the recalculation is a supplementary descriptive comparison, not a replacement.
No p-value is reported for the sponsor analysis. The unadjusted p-value belongs only to the recalculated comparison and should not be assigned to the sponsor result. A formal noninferiority interpretation would require the margin and its prespecified direction, neither of which is reported in the registry record.
15. Multiplicity, Missing Data and Analysis Populations
The primary analysis population is described in the registry: participants treated with at least one dose of study drug and without documented resistance to study drug before screening. The primary endpoint applies the TLOVR algorithm, which counts specified virologic rebound, treatment discontinuation, and addition of a new antiretroviral as nonresponse. The rebound definition is also stated. These details help define the endpoint and the population to which its result applies.
Other missing-data procedures are not reported in the registry record. In particular, the record does not describe how missing viral RNA measurements not covered by the stated TLOVR rules were handled, whether sensitivity analyses were conducted, or how participants with incomplete follow-up contributed to secondary outcome analyses. The endpoint's nonresponder rules should not be mistaken for a complete account of every missing-data decision.
The registry lists multiple secondary outcomes, but a multiplicity adjustment is not reported. General statistical explanation: testing several outcomes can increase the overall chance of a false-positive finding if each is interpreted as a standalone confirmatory test. Prespecified outcome hierarchies, adjusted procedures, or a clearly exploratory interpretation can address that issue, but their use in this trial is not reported in the registry record. The unadjusted secondary comparisons should therefore be read with restraint.
The registry does not report the original sample-size justification, the noninferiority margin, interim analyses, or a full statistical analysis plan. It also does not report the allocation sequence or concealment procedures. These omissions limit assessment of design decisions and analytic safeguards. The open-label masking status is recorded as none; the record does not describe procedures to reduce potential effects of treatment knowledge on outcome collection or other study decisions. Such unreported details cannot be inferred from the reported response percentages or enrollment.
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 |
|---|---|---|---|
| TVD + PI/r | 12 | 155 | 7.7% |
| ABC/3TC + PI/r | 11 | 156 | 7.1% |
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 |
|---|---|
| TVD + PI/r | 35 of 155 |
| ABC/3TC + PI/r | 32 of 156 |
Most frequent serious adverse event terms
| Event term | Organ system | TVD + PI/r | ABC/3TC + PI/r |
|---|---|---|---|
| Cellulitis | Infections and infestations | 3 of 155 | 0 of 156 |
| Pulmonary Embolism | Respiratory, thoracic and mediastinal disorders | 0 of 155 | 2 of 156 |
| Myocardial Infarction | Cardiac disorders | 1 of 155 | 0 of 156 |
| Bradycardia | Cardiac disorders | 0 of 155 | 1 of 156 |
| Pancreatitis | Gastrointestinal disorders | 0 of 155 | 1 of 156 |
| Gastric Ulcer | Gastrointestinal disorders | 0 of 155 | 1 of 156 |
| Gastritis | Gastrointestinal disorders | 0 of 155 | 1 of 156 |
| Rectal Haemorrhage | Gastrointestinal disorders | 1 of 155 | 0 of 156 |
| Chest Pain | General disorders | 0 of 155 | 1 of 156 |
| Giardiasis | Infections and infestations | 1 of 155 | 0 of 156 |
Most frequent non-serious adverse event terms
| Event term | Organ system | TVD + PI/r | ABC/3TC + PI/r |
|---|---|---|---|
| Upper Respiratory Tract Infection | Infections and infestations | 14 of 155 | 14 of 156 |
| Diarrhea | Gastrointestinal disorders | 13 of 155 | 11 of 156 |
| Cough | Respiratory, thoracic and mediastinal disorders | 8 of 155 | 8 of 156 |
| Headache | Nervous system disorders | 8 of 155 | 5 of 156 |
Serious events with the highest arm-level rate: cellulitis (1.9%), pulmonary embolism (1.3%), myocardial infarction (0.6%), rectal haemorrhage (0.6%), giardiasis (0.6%).
The registry reports serious adverse events among 12 of 155 participants at risk in the TVD + PI/r group and 11 of 156 participants at risk in the ABC/3TC + PI/r group. Other adverse events are reported among 35 of 155 and 32 of 156 participants at risk, respectively. These are participant counts with the listed denominators; they are not a measure of severity beyond the serious-versus-other classification and do not establish that treatment caused an event.
The serious-event terms listed include cellulitis at 1.9%, pulmonary embolism at 1.3%, myocardial infarction at 0.6%, rectal haemorrhage at 0.6%, giardiasis at 0.6%, and pneumonia at 0.6%. The registry does not specify an arm for these top-term percentages in the information. Death counts are not reported in the registry record.
General statistical explanation: adverse-event counts are descriptive and should be interpreted with their denominators, follow-up period, event definitions, and attribution procedures. The registry figures alone do not show whether an event was considered related to study treatment, and they do not establish comparative safety. The listed numbers should not be used to infer unreported event rates or causal effects.
17. What the Result Does, and Does Not, Mean
The posted primary results describe the proportions classified as responders under the TLOVR algorithm in each randomized group. The recalculated risk difference is imprecise, with a confidence interval extending in both directions. The sponsor's analysis is separately reported as an inverted two one-sided tests analysis, but the margin needed to assess its noninferiority interpretation is not reported in the registry record. Taken together, the numerical information describes the observed results and their uncertainty; it does not support treating the groups as proven identical.
General statistical explanation: failure to find evidence of a difference in a conventional unadjusted test is not evidence that two treatments are equivalent. Equivalence and noninferiority require a defined margin and a suitable analysis. The registry labels the sponsor analysis as noninferiority or equivalence, but the margin is not available in the registry record, so its formal criterion cannot be independently assessed from the information reported.
The endpoint incorporates events during follow-up, including specified rebound, discontinuation, and treatment changes. Consequently, the result reflects the TLOVR classification rule, not just the final RNA measurement. It applies to the primary analysis population and the study's 48-week observation period. The study involved participants with virologically suppressed HIV-1 infection who were already on a ritonavir-boosted protease inhibitor regimen; the registry record does not establish how results would apply to other populations, regimens, or follow-up durations.
The secondary results add descriptive context but are subject to uncertainty and the lack of a reported multiplicity adjustment. Numerical results for other listed secondary measures are not reported in the registry record. The adverse-event counts likewise describe events recorded in the study and cannot establish causation or settle comparative safety. None of these statistical results is medical advice; they describe trial data within the boundaries of the recorded design and analyses.
18. Why This Trial Matters Statistically
This trial illustrates why the analysis definition matters as much as the headline percentage. The primary endpoint is not simply a Week 48 viral RNA value: TLOVR also classifies specified rebound, discontinuation, and addition of a new antiretroviral as nonresponse. That structure can affect the response proportion and the interpretation of a treatment comparison. Readers need to know what qualifies as response before interpreting group percentages.
It also illustrates the distinction between a difference test and a noninferiority analysis. The sponsor's reported method is inverted two one-sided tests, while the recalculation is an unadjusted risk difference with a conventional confidence interval and p-value. These analyses address different questions. A margin is essential to interpret a noninferiority claim, yet the margin is not reported in the registry record. The reported method, estimate, and uncertainty should be distinguished from a formal conclusion that cannot be checked without that information.
The example also shows how confidence intervals prevent over-reading a point estimate or p-value. The recalculated primary interval includes values in both directions, and the unadjusted p-value alone does not establish equivalence. The trial's randomized parallel-group structure supports a direct group comparison, but open-label status, analysis-population choices, secondary testing, and unreported analysis details remain relevant to interpretation.
Finally, planning calculations based on the observed effect are not the same as the trial's original sample-size justification. The registry record does not report that original justification. Keeping those planning illustrations separate from observed results avoids treating a post hoc illustration as evidence that the completed study had a particular probability of success.
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.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
The registry record does not report the noninferiority margin, so the sponsor's reported noninferiority or equivalence analysis cannot be independently evaluated against its decision threshold. The original sample-size assumptions and justification are also not reported. Planning illustrations based on the observed effect cannot fill that gap.
The primary analysis population is specified, and the TLOVR rules define several circumstances that count as nonresponse. Beyond those rules, missing-data methods and sensitivity analyses are not reported. The record also does not describe allocation concealment, interim analyses, or a full statistical analysis plan. These omissions restrict assessment of the safeguards and assumptions underlying the reported results.
The study was open label. The registry records no masking, but does not describe how treatment knowledge may have affected other study procedures or decisions. The primary outcome is based on viral RNA and algorithmic criteria, but this does not eliminate the need to consider the implications of open-label conduct for other aspects of follow-up.
The secondary outcome results are incomplete in the numerical information reported: several measures are listed, but their numerical results are not reported in the registry record. No multiplicity adjustment is reported for the secondary comparisons. The study's follow-up was 48 weeks, so the recorded results do not describe outcomes beyond that period. Finally, the primary population was virologically suppressed and maintained on a ritonavir-boosted protease inhibitor regimen; results should not be assumed to generalize to populations or treatment settings that differ from those recorded.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Safety and Efficacy Study of Switching From Epzicom to Truvada — NCT00724711.
- Registry record last updated 2012-05-28; status last verified 2012-05.
- Results first posted 2012-04-19.
- 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
NCT00724711 is a completed, randomized, open-label, parallel-group phase IV study sponsored by Gilead Sciences. It enrolled 312 participants with HIV-1 infection who were virologically suppressed and maintained on a ritonavir-boosted protease inhibitor regimen. The study compared switching from ABC/3TC to FTC/TDF with continuing ABC/3TC, while the PI/r regimen continued in both groups. Treatment duration was 48 weeks.
The primary endpoint was the percentage with HIV-1 RNA below 200 copies/mL through Week 48 under TLOVR. The registry reports group response percentages and a sponsor analysis using inverted two one-sided tests. A simple unadjusted recalculation is also available, but it is not a substitute for the sponsor's analysis. The registry does not report the noninferiority margin or the trial's original sample-size assumptions. Secondary outcomes and adverse-event counts provide additional descriptive information, with the limitations described in the registry record.