Steroids After Laser Trabeculoplasty for Glaucoma: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Steroids After Laser Trabeculoplasty for Glaucoma (NCT00981435), a randomized phase 4 study. The primary outcome is Intraocular Pressure (IOP) Change.

2. Clinical Question

The central statistical comparison is not simply whether pressure changed in each group. It is whether the average change differed between each active-drop group and the artificial-tears group. The posted estimates indicate how far apart those group averages were, while their confidence intervals describe uncertainty around the estimated differences. Because the outcome data were incomplete, the reported group means reflect participants with available Week 12 measurements rather than every person enrolled.

3. Trial Design

This was a Phase 4, randomized, triple-masked, parallel-group trial sponsored by Stanford University. The registry record gives enrollment as 97 and status as completed. The study start is recorded as 2009-09 and primary completion as 2015-09. The record does not identify which groups of people were masked, describe the randomization procedure, or report the original statistical analysis plan.

Participants received one of three post-laser eye-drop regimens in the treated eye: artificial tears, ketorolac 0.5%, or prednisolone 1%. Each regimen was dosed 4 times per day for 4 days after selective laser trabeculoplasty. The parallel design means the groups were compared with each other, rather than participants crossing over between regimens.

The primary endpoint was intraocular pressure change from baseline to Week 12. The description says pressure was measured before treatment and at 6 and 12 weeks after intervention using Goldman tonometry. The registry record reports Week 12 outcome data for 25 participants receiving artificial tears, 27 receiving the non-steroidal anti-inflammatory regimen, and 29 receiving the steroid regimen. It also gives lower available counts at 6 weeks for the artificial-tears and steroid groups. These changing counts indicate that the primary outcome was not available for every enrolled participant at every stated follow-up time.

The record lists intraocular inflammation as a secondary outcome, but does not provide a result for it in the information summarized in the outcome entries. Details of the trial's planned sample-size justification, original analysis methods, and handling of missing measurements are not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: Patient data was incomplete due to inadequate measurement or follow up as follows: Artificial tears (31 enrolled, 27 available at 6 weeks, 25 at 12 weeks); Non-steroidal anti-inflammatory (28 enrolled, 27 available at 6 and 12 weeks); Steroid (37 enrolled, 33 available at 6 weeks, 29 at 12 weeks).

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 Intraocular Pressure (IOP) Change, measured over Baseline to Week 12.

The primary endpoint is mean change in intraocular pressure (IOP), measured in mmHg, from baseline to Week 12. IOP is the pressure measured inside the eye. The record says measurements were obtained before intervention and at 6 and 12 weeks after intervention using Goldman tonometry. Although the endpoint is defined by the baseline-to-Week-12 change, the measurement schedule also includes the earlier follow-up visit.

A change score expresses how the measurement at follow-up differs from the participant's baseline measurement. A negative mean change is consistent with a reduction if the change is calculated as follow-up minus baseline. The registry record does not explicitly state the subtraction order, so the sign should be interpreted in that context. The posted group means are -3.0 mmHg for artificial tears, -6.2 mmHg for the non-steroidal anti-inflammatory group, and -5.2 mmHg for the steroid group.

Mean change is used to describe the average difference from baseline within a group. Comparing those average changes between randomized groups addresses whether outcomes differed across assigned regimens, rather than treating a within-group change as evidence of a treatment contrast. The standard deviations describe the spread of individual changes around each group mean. The Week 12 participant counts are smaller than the enrollment counts, so these averages are based on participants with available measurements at that time.

7. Results Posted in the Registry

• Non-steroidal Anti-inflammatory: mean -6.20 versus -3.00 on control; difference -3.20 (95% CI -5.25 to -1.15), standardized effect d = -0.86; z-test p = 0.002.
• Steroid: mean -5.20 versus -3.00 on control; difference -2.20 (95% CI -4.15 to -0.25), standardized effect d = -0.62; z-test p = 0.027.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a mean change describe?

For a continuous outcome such as IOP, a group mean summarizes the average observed change among participants with measurements. The posted means are -3.0 mmHg for artificial tears, -6.2 mmHg for the non-steroidal anti-inflammatory regimen, and -5.2 mmHg for the steroid regimen. The standard deviations are 4.3, 3.1, and 2.7 mmHg, respectively. A standard deviation describes variability among individual observations; it is not the uncertainty in the group mean and is not a range containing every participant's result.

The group sizes used for the Week 12 outcome summaries are 25, 27, and 29. These are smaller than the enrollment counts stated for the primary outcome. A mean calculated among participants with observed measurements may differ from the mean that would have been seen if outcomes were available for everyone. The registry record does not report enough detail to assess whether the observed participants differ from those whose measurements are missing.

How should a between-group mean difference be read?

A mean difference compares the average change in one group with the average change in another. The registry record uses artificial tears as the comparator for each active regimen. The recalculated estimate is -3.2 mmHg for the non-steroidal anti-inflammatory regimen versus artificial tears, and -2.2 mmHg for steroid versus artificial tears. These are differences between group means, not additional changes experienced by participants. Given the negative mean changes, a negative contrast is consistent with a more negative average change in the active-regimen group, using the displayed comparison orientation.

These calculations are unadjusted: they compare the reported group summaries without adjustment for other variables. The record does not give an adjusted analysis or enough information to infer one. The comparison is also limited to the groups and endpoint as recorded; it does not establish how the contrast might change in other populations or settings.

What does the confidence interval add?

A confidence interval gives a range of values compatible with the observed data under the calculation's assumptions. It communicates precision as well as direction. For the non-steroidal anti-inflammatory comparison, the 95% interval runs from -5.251 to -1.149 mmHg. For the steroid comparison, its lower limit is -4.151 mmHg and its upper limit is negative and close to zero. The intervals indicate that the estimated differences are not perfectly precise. They should not be read as a guarantee that the true difference lies within the particular interval, nor as the probability that a specific value is true.

What does a p-value address?

A p-value measures how unusual data at least as extreme as those observed would be under a statistical model in which the comparison's true mean difference is zero. The reported unadjusted p-values are 0.002 and 0.027. A smaller p-value indicates greater incompatibility with that zero-difference model under the calculation's assumptions. It does not measure the probability that the null hypothesis is true, the probability that the result arose by chance, or the clinical importance of the estimated difference.

The p-values are unadjusted for the two comparisons reported against artificial tears. If multiple comparisons are considered together, the chance of at least one false-positive result can differ from the chance associated with a single test. The registry record does not state a multiplicity plan or report adjusted p-values. The estimates and p-values should therefore be understood as unadjusted comparisons rather than as a family-wise adjusted analysis.

Why do group sizes and spread affect precision?

In general, estimates of group means tend to be more precise when more outcome measurements are available and less variable. Greater variability makes it harder to distinguish a group contrast from random variation. This general principle explains why sample size and standard deviation appear in calculations of confidence intervals and planning illustrations. It does not establish the design assumptions used by the trial investigators: the original sample-size justification is not reported in the registry record.

The posted available group sizes and standard deviations are the inputs for the recalculated unadjusted comparisons. These calculations are not a substitute for a trial analysis plan, particularly when missing outcomes, masking, or multiple comparisons might affect the analysis. The record does not report an analysis population definition, a method for imputing missing measurements, or an adjustment for baseline values.

What is over-dispersion, in general?

Over-dispersion is a general concern when observed variation is greater than a statistical model assumes. If a model understates variation, standard errors may be too small and confidence intervals too narrow. This trial's primary outcome is continuous and the posted summaries include standard deviations; no evidence or model for over-dispersion is reported in the registry record. It is therefore not possible to say that over-dispersion was present or that it affected these results.

What cannot be inferred from the methods record?

The record identifies the study as randomized, triple-masked, and parallel-group, but does not explain the randomization procedure or identify who was masked. It does not report the original analysis plan, planned sample-size calculation, interim analyses, or a detailed method for handling incomplete follow-up. The posted results support interpretation of the reported summaries and unadjusted contrasts, but not reconstruction of unreported design or analysis decisions.

10. Confidence Intervals and Precision

The recalculated 95% confidence interval for the non-steroidal anti-inflammatory regimen versus artificial tears extends from -5.251 to -1.149 mmHg around an estimated mean difference of -3.2 mmHg. For steroid versus artificial tears, the estimated mean difference is -2.2 mmHg; the interval extends from -4.151 mmHg to an upper limit that is negative and close to zero. Both intervals exclude zero, but neither identifies a single exact value for the underlying group difference.

In general, a confidence interval describes the range of estimates compatible with the data under the statistical assumptions used. A narrower interval indicates greater precision than a wider interval, while an interval that includes values near zero signals uncertainty about how large the contrast is. The steroid comparison's upper limit being close to zero illustrates that its estimated difference is less clearly separated from no difference than the point estimate alone might suggest. This is a statement about statistical precision, not clinical importance.

These intervals are unadjusted recalculations from the posted summary statistics. They do not account for a reported multiplicity adjustment, and the registry record does not describe a missing-data adjustment. The underlying outcomes were available for fewer participants than were enrolled, which limits how confidently these summaries can represent the full randomized groups. Confidence intervals quantify sampling uncertainty under their assumptions; they do not remove potential bias from missing outcomes or unreported analysis choices.

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 planning figures are participants per arm for 80% power and participants per arm for 90% power. These are not total event counts: the endpoint is continuous, so the figures refer to people in each of the two arms of a hypothetical comparison. The illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It bases the effect to detect on a stated fraction of the observed effect, separately for each comparison.

The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed for an 80% chance of obtaining a statistically significant result if the specified effect were the true effect and the assumptions held. The 90% column gives the corresponding planning count for a 90% chance. These are prospective planning quantities, not a measure of the probability that the completed trial's result is correct.

The scenarios use 100%, 75%, and 50% of the observed effect. Smaller assumed effects require more participants per arm to distinguish the difference from random variation under the same planning assumptions. For the non-steroidal anti-inflammatory comparison, the figures rise from 22 participants per arm for 80% power and 29 for 90% power at 100% of the observed effect, to 86 and 114 at 50% of the observed effect. For the steroid comparison, the corresponding figures are 41 and 55 at 100%, and 162 and 217 at 50%.

This is a planning illustration based on observed results, not observed power. The registry record does not report the trial's original sample-size justification or original design assumptions, so these calculations should not be read as the investigators' planned enrollment target.

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 = -3.200; pooled standard deviation σ = 3.725.
2. n = 2 × (1.96 + 0.842)² × 3.725² / -3.200² = 21.3, rounded up to 22 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 <- -3.2                      # observed difference in means
sigma <- 3.72456708893799                     # 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(981435)
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 = 22 (80% power), 29 (90% power)
 75% of observed effect: n per arm = 38 (80% power), 51 (90% power)
 50% of observed effect: n per arm = 86 (80% power), 114 (90% power)
power.t.test: 22.3 
Simulated power at n = 22 per arm: 0.788 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary outcome, IOP change from baseline to Week 12, and one secondary outcome, intraocular inflammation. It also reports two unadjusted comparisons of active regimens against artificial tears. The record does not describe whether these comparisons were prespecified as a family, whether a multiplicity procedure was planned, or whether any adjustment was made. The p-values and confidence intervals should therefore be interpreted as unadjusted results, not as evidence that multiplicity was addressed.

Outcome availability declined between enrollment and follow-up. For the primary outcome, the artificial-tears group had 31 enrolled, 27 available at 6 weeks, and 25 at 12 weeks; the non-steroidal anti-inflammatory group had 28 enrolled and 27 available at each follow-up; and the steroid group had 37 enrolled, 33 available at 6 weeks, and 29 at 12 weeks. The record describes these gaps as due to inadequate measurement or follow-up. It does not give reasons for each missing measurement or report an approach to imputation, sensitivity analysis, or adjustment for missing data.

For a randomized trial, missing outcomes can affect the interpretation of group comparisons if the availability of measurements is related to outcomes or differs meaningfully across groups. The posted means describe participants with available Week 12 measurements. The registry record does not specify an intention-to-treat analysis population, a per-protocol population, or another formal analysis population, and does not explain how participants lacking outcome measurements were handled.

The record lists zero serious adverse events and zero other adverse events in the safety entries, but the death entries are not reported in the registry record. The record also does not report interim analyses, stopping rules, or a detailed statistical analysis plan. These omissions limit assessment of the planned multiplicity strategy, the effect of missing data, and the relationship between the posted summaries and any original prespecified analysis.

14. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The safety entries report zero serious adverse events among 31 participants at risk in the artificial-tears group, zero among 29 at risk in the non-steroidal anti-inflammatory group, and zero among 37 at risk in the steroid group. The entries also report zero other adverse events among the same respective at-risk counts. These are the recorded event counts; they should not be interpreted as proof that no adverse events occurred beyond the scope or reporting captured in the registry record.

The death entries are not reported in the registry record. The safety at-risk denominators differ from some enrollment counts in the primary outcome description; the record does not explain the difference. Safety counts and primary outcome availability are distinct entries and should not be treated as interchangeable participant totals. The adverse-event information does not provide event descriptions, severity beyond the serious/non-serious categories, timing, or an assessment of causality for events, and no serious-event terms are listed.

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

The posted results show lower mean IOP change values in both active-regimen groups than in the artificial-tears group, assuming negative change represents a reduction from baseline. The unadjusted recalculated comparisons estimate mean differences of -3.2 mmHg for the non-steroidal anti-inflammatory regimen and -2.2 mmHg for the steroid regimen, each versus artificial tears. Their reported confidence intervals exclude zero, although the steroid comparison's upper limit is close to zero.

These statistics describe group averages among participants with available Week 12 measurements. They do not mean that every participant had a change equal to the group mean, and they do not show the full distribution of individual outcomes. The standard deviations indicate variation within groups. The comparisons also do not establish that a particular difference is clinically important: the registry record does not report a threshold for clinical importance.

The estimates do not answer every question about the post-laser regimens. The record does not report an adjusted analysis, a multiplicity plan, or the method used to address missing outcome data. The outcome counts were smaller than enrollment counts, so the available-case summaries may not represent everyone randomized if missingness was related to outcomes. The record lists intraocular inflammation as a secondary outcome but does not provide its result in the outcome information summarized.

Likewise, the adverse-event entries report zero serious and zero other adverse events within their stated at-risk groups, while deaths are not reported in the registry record. Those entries do not establish the absence of all possible harms. In general, trial results should be interpreted in light of their endpoint, analysis methods, completeness of follow-up, and precision. The posted summaries inform the specific average-change comparisons recorded, but they do not establish effects beyond those data or support individual treatment decisions.

16. Why This Trial Matters Statistically

This trial illustrates why a randomized comparison focuses on differences between groups rather than on change within a single group. All three reported group means are negative. The relevant statistical question is whether the average change differs between each active regimen and artificial tears, and by how much. The recalculated mean differences and confidence intervals address that question more directly than the separate group means alone.

It also demonstrates the importance of precision. A point estimate gives one summary of a contrast, whereas a confidence interval shows a range of values consistent with the observed data under the calculation's assumptions. The two contrasts have different estimates and interval limits; the steroid comparison's upper limit is close to zero. Readers can therefore see uncertainty that would be obscured by reporting only a point estimate or p-value.

Incomplete follow-up is another central statistical issue. The primary outcome counts at Week 12 are below the enrollment counts, and the registry record does not report how missing measurements were handled in an analysis. Such gaps can affect the representativeness of group averages and the interpretation of a randomized comparison. Reporting outcome availability alongside the means helps readers recognize that limitation.

Finally, the record offers a useful distinction between trial results and planning illustrations. Sample-size calculations based on observed effects can show how assumed effect size relates to required enrollment under stated assumptions, but they do not reveal the trial's original planning process. In this case the original sample-size justification and analysis plan are not reported in the registry record. Separating documented results from unreported design details is essential for a statistically careful reading.

17. 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 outcome is incomplete at both stated follow-up times. By Week 12, the available counts were 25 for artificial tears, 27 for non-steroidal anti-inflammatory treatment, and 29 for steroid treatment. The registry record attributes incomplete data to inadequate measurement or follow-up but does not give participant-level reasons or an analysis of how missingness could affect estimates.

There is a denominator difference within the record: the primary outcome description states that 28 participants were enrolled in the non-steroidal anti-inflammatory group, while the safety entry lists 29 participants at risk in that group. The record does not explain this discrepancy, so the counts should be read in the context of their respective outcome entries rather than reconciled by assumption.

The comparison results are unadjusted recalculations from posted summary statistics. The registry record does not provide a full statistical analysis plan, adjusted estimates, a multiplicity strategy, a missing-data method, or the trial's original sample-size justification. It also does not report an analysis population definition or an interim analysis plan. These omissions limit assessment of how closely the posted calculations match prespecified analyses.

The record lists intraocular inflammation as a secondary outcome but does not include a result for it in the outcome entries described. Safety entries report zero serious and zero other adverse events, but deaths are not reported in the registry record and event details are not listed. The record also does not state the change-score subtraction order or identify which individuals were masked. These limitations restrict interpretation to the outcome summaries and trial characteristics explicitly recorded.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Steroids After Laser Trabeculoplasty for Glaucoma — NCT00981435.
• Registry record last updated 2019-08-07; status last verified 2019-07.
• Results first posted 2017-04-14.
• 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.

21. Record Summary

The completed Phase 4 trial NCT00981435, titled “Steroids After Laser Trabeculoplasty for Glaucoma,” was a randomized, triple-masked, parallel-group study sponsored by Stanford University. Enrollment was 97. It compared artificial tears, ketorolac 0.5%, and prednisolone 1%, each dosed 4 times per day for 4 days after selective laser trabeculoplasty.

The primary outcome was mean IOP change from baseline to Week 12, with measurements described at baseline and 6 and 12 weeks. The posted Week 12 means were -3.0 mmHg for artificial tears, -6.2 mmHg for non-steroidal anti-inflammatory treatment, and -5.2 mmHg for steroid treatment. Unadjusted recalculated comparisons versus artificial tears were -3.2 mmHg and -2.2 mmHg, respectively. Outcome data were incomplete, and the record does not report the original sample-size justification, detailed analysis plan, or handling of missing outcomes. Intraocular inflammation was listed as a secondary outcome. Safety entries report zero serious and zero other adverse events; deaths are not reported in the registry record.