Stimulating Private Sector Malaria Control: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Stimulating Private Sector Malaria Control (NCT01397851), a randomized na study. The primary outcome is Cotton Yields.

2. Clinical Question

The trial was registered under the title Stimulating Private Sector Malaria Control, with an official title that adds The Outgrower Opportunity. Its background rationale concerns whether protecting farmers from malaria could be profitable for outgrowing agribusinesses, and the study team describes investigating that possibility experimentally. The primary endpoint, however, is cotton yield, not malaria incidence or a direct measure of business profitability. The registry also lists malaria-related self-report and other secondary outcomes, but the presence of an outcome name does not establish that a numerical result was posted for it.

3. Trial Design

The registry identifies this as a randomized, parallel-group trial with no masking. It records an enrollment of 81597 and a status of completed. The listed intervention was an insecticide-treated net; the two groups differed in whether farmers were told they had won and received a free net or were told they did not win. The registry does not report details of sequence generation, concealment of allocation, or the procedures used to implement the raffle.

The trial began in 2010-12, with primary completion in 2011-12. The primary outcome timeframe is the 2010-2011 season, described as up to 1 year. The endpoint is based on routine data collection by the participating cotton outgrowing agribusiness, rather than a measure described as collected specifically for the trial. The posted primary summaries include 39920 farmers in the net group and 41560 in the control group. The registry record does not explain how these outcome counts relate to the enrollment figure, or whether any enrolled participants lacked an observed primary outcome.

The title and background frame the work around malaria control and agricultural productivity, while the primary endpoint is cotton delivered per household. Secondary outcomes listed in the record include contract defaults, increase in maize productivity, and self-reported malaria prevalence. Numerical arm summaries and a comparison are posted for maize productivity; numerical results for the other listed secondary outcomes are not reported in the registry record.

The phase is recorded as NA. The sponsor is PATH. The registry does not report the trial's original sample-size justification, a detailed statistical analysis plan, interim analyses, or the methods used to handle missing outcome data. Those absences limit what can be concluded about the prespecified analysis choices, even though the registry presents arm-level primary results and a primary comparison.

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

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 Cotton Yields, measured over 2010-2011 season (up to 1 year).

The primary endpoint is cotton yield, defined as kilograms of cotton delivered per household according to the routine data collection system of the participating cotton outgrowing agribusiness. Its timeframe is the 2010-2011 season, up to 1 year. The posted summaries describe the endpoint as a continuous measure and report a mean and standard deviation for each group.

This outcome is relevant to the study's stated economic rationale because cotton delivered per household captures agricultural production recorded by the agribusiness. It is not itself a direct measure of malaria infection, illness, net use, farmer income, or agribusiness profit. A difference in recorded yield can therefore address the trial's specified production question, but it cannot alone establish the mechanism that might account for that difference or the broader business case described in the background.

Routine records can provide an outcome linked to actual deliveries rather than relying on a farmer's recall of yield. At the same time, the registry does not describe data completeness, measurement validation, household linkage, or whether the routine collection process differed between trial groups. Because masking was listed as none, knowledge of assignment may have been possible; the record does not say whether that could have influenced recording or delivery behavior. These are considerations about measurement and interpretation, not evidence that the endpoint was mismeasured.

7. Results Posted in the Registry

• Treatment: Insecticide-treated Net: mean 544.00 versus 548.00 on control; difference -4.00 (95% CI -4.15 to -3.85), standardized effect d = -0.36; z-test p = <0.001.

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.

Increase in Maize Productivity

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
• Result:
  • Treatment: Insecticide-treated Net: mean 55.00 versus 59.00 on control; difference -4.00 (95% CI -20.63 to 12.63), standardized effect d = -0.02; z-test p = 0.637.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Treatment: Insecticide-treated Net and the control. The interval gives the range of effects that remain compatible with the data.

The registry lists three secondary outcomes: contract defaults, increase in maize productivity, and self-reported malaria prevalence. Detailed numerical arm summaries and a comparison are posted for maize productivity. Numerical results for contract defaults and self-reported malaria prevalence are not reported in the registry record, so the pattern across all listed secondary outcomes cannot be fully characterized from the posted results.

The maize comparison does not provide clear statistical evidence of a difference: its interval spans negative and positive values, and its unadjusted p-value is 0.637. This contrasts with the more precise primary cotton-yield comparison, but the two endpoints are not interchangeable measures. They concern different crops, and the maize summaries use a timeframe covering the 2009-2010 and 2010-2011 seasons, whereas the primary endpoint concerns cotton yields during the 2010-2011 season. The secondary result does not confirm or explain the primary finding.

Unadjusted secondary results carry less weight when multiple outcomes are examined because each additional statistical test creates another opportunity for an apparently unusual result under a no-effect scenario. The registry record does not report a multiplicity adjustment or a hierarchy specifying how secondary outcomes were to be interpreted. The maize p-value should therefore be understood as an unadjusted result, not as evidence from a familywise-controlled set of tests.

The record's outcome list and posted numerical results are not the same thing: an outcome can be named without a corresponding estimate being available. For the unreported outcomes, conclusions about direction, size, precision, or consistency with the primary endpoint cannot be drawn. Overall, the secondary information is limited and does not establish a broad pattern across agricultural and malaria-related outcomes.

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

• Contract Defaults
• Increase in Maize Productivity
• Self-reported Malaria Prevalence

9. Statistical Interpretation

10. Statistical Methods Explained

The primary endpoint is continuous: cotton yield is expressed in kilograms per household, and the posted group summaries use means and standard deviations. A mean is the arithmetic average of observed values in a group. The standard deviation describes the spread of individual household yields around that group's mean; it is not the uncertainty in the mean itself. The posted standard deviation is 11 kg in each group.

What does the mean difference represent?

The comparison is expressed as treatment minus control. A negative mean difference therefore means that the posted treatment-group average is lower than the control-group average. The estimate is -4.0 kg. This contrast is on the original measurement scale, which makes it directly interpretable in kilograms per household during the stated outcome period. It is an average contrast; it does not mean that every household had a yield difference of that size, nor does it describe the distribution of individual outcomes.

How should the confidence interval be understood?

A confidence interval gives a range of values compatible with the observed data under the statistical procedure and its assumptions. For the primary mean difference, the reported interval extends from -4.151 to -3.849. It conveys the statistical precision of the estimate: the interval is close to the point estimate. In repeated use of the same method under its assumptions, confidence intervals have a defined coverage property. A particular interval is not a probability statement that the true difference lies inside it, and it does not account for biases or uncertainties that the analysis did not model.

What does the p-value test?

The unadjusted p-value is <0.001. In general, a p-value measures how surprising data at least as extreme as those observed would be if a specified null model were correct. It is not an effect size, a measure of practical importance, or the probability that chance alone caused the observed result. The word unadjusted matters: the posted value is not described as corrected for multiple outcome comparisons. The registry record does not report a broader testing strategy.

Why do the outcome scale and spread matter?

The mean difference retains the kilogram scale, while the standard deviation expresses variation among households on that same scale. Standard errors, by contrast, describe uncertainty in estimated quantities such as a mean or a difference. They typically become smaller as the amount of information increases, but their interpretation depends on the design and model. The registry gives standard errors for the group means in the comparison details, but does not provide a full account of the estimation procedure or any clustering adjustments.

General statistical consideration: if observations are more variable than a model assumes, or if outcomes are correlated within groups, standard errors can be understated and confidence intervals too narrow unless the analysis accounts for those features. The registry record does not describe whether households were clustered in a way that required such adjustments. This is not evidence that the posted analysis failed to account for clustering; the relevant details are not reported in the registry record.

What does randomization contribute?

Random allocation is intended to make trial groups comparable, on average, with respect to factors that could influence outcomes. A parallel-group design assigns participants to one of the groups and compares their outcomes over the relevant period. That design makes an assignment-based comparison possible. The registry does not report the randomization sequence, allocation concealment, compliance, crossover, or analysis population. Consequently, the degree to which the posted analysis follows the randomized assignment and preserves the intended comparison cannot be fully assessed from the record alone.

No masking is recorded. In general, lack of masking can matter if awareness of group assignment changes behavior, reporting, or measurement. The primary outcome is described as a routine agribusiness record, which may differ from a self-reported outcome, but the registry does not specify who entered or verified those records or whether they knew assignment. The possibility of measurement or behavioral effects is therefore a limitation to consider, not a demonstrated source of bias.

What is and is not documented?

The registry presents descriptive summaries and a primary comparison. It reports zero analyses in the analysis listing and no reported analyses in the detailed analysis entries. A detailed prespecified statistical plan, model specification, missing-data strategy, covariate adjustment, interim analysis plan, and original sample-size rationale are not reported in the registry record. The presence of a posted comparison does not fill in those missing methodological details. Statistical interpretation should therefore distinguish the result that is posted from the analysis choices that cannot be verified.

11. Confidence Intervals and Precision

The primary estimate is -4.0 kg per household, and its reported confidence interval ranges from -4.151 to -3.849 kg. The interval is narrow relative to the scale of the reported estimate, indicating high statistical precision for this particular unadjusted mean difference under the method used. Precision concerns the uncertainty represented by the interval; it does not establish that all relevant sources of error have been captured.

The interval lies entirely on the negative side of zero, which is consistent with the reported unadjusted p-value of <0.001 for a test of no mean difference under the analysis assumptions. That relationship is expected for common two-sided procedures, but the registry does not give enough methodological detail to identify every aspect of the test and interval construction. The reported values should be interpreted as they appear in the registry rather than reverse-engineering an unstated model.

Large outcome counts can contribute to narrow intervals, but a narrow interval does not automatically make an estimate free from bias. Randomization procedures, missing outcomes, measurement quality, dependence among observations, and analysis decisions can affect how representative the uncertainty interval is. Several of these details are not reported in the registry record. The outcome counts posted for the two arms are 39920 and 41560; the record does not explain the relationship between those counts and the enrollment figure.

Precision also differs from practical importance. A precisely estimated difference is not, on its own, a judgment about whether the difference matters for farmers or agribusinesses. The primary measure is kilograms delivered per household, while the registry does not report a threshold for an important difference or a direct economic valuation of the observed contrast. The confidence interval addresses statistical uncertainty in the mean difference, not those broader questions.

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.

The planning figures are participants per arm, not total events. They are illustrations based on the observed effect and are not the trial's original design calculation. The 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 in turn at 100% of the observed effect, 75% of the observed effect, or 50% of the observed effect. The trial's own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the planned number of participants in each arm for a design with an 80% chance of detecting the specified effect under those assumptions, if that effect is the true one and the model assumptions hold. The 90% power column gives the corresponding planning count for a 90% chance. Power is a design property for a specified effect and analysis, not a measure of how likely the observed result is true. The figures are planning illustrations, not observed power.

The primary-outcome illustrations list 119 participants per arm when planning for 100% of the observed effect, 212 per arm for 75% of the observed effect, and 475 per arm for 50% of the observed effect for 80% power. For 90% power, the corresponding listed counts are 159, 283, and 636 participants per arm. Smaller effects are harder to distinguish from random variation, so detecting them generally requires more participants. The same pattern appears in the listed maize planning figures, which are substantially larger because the observed standardized effect used for those calculations is smaller.

The curve should be read as another representation of this planning relationship: as the effect targeted for detection becomes smaller, the participant requirement increases, holding the stated assumptions fixed. These calculations do not establish what the trial was designed to detect, and they should not be used to infer that the trial had adequate power for every endpoint or analysis.

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 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 = -4.000; pooled standard deviation σ = 11.000.
2. n = 2 × (1.96 + 0.842)² × 11.000² / -4.000² = 118.7, rounded up to 119 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 <- -4                      # observed difference in means
sigma <- 11                     # 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(1397851)
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 = 119 (80% power), 159 (90% power)
 75% of observed effect: n per arm = 212 (80% power), 283 (90% power)
 50% of observed effect: n per arm = 475 (80% power), 636 (90% power)
power.t.test: 119.7 
Simulated power at n = 119 per arm: 0.801 (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.

14. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a study assesses several outcomes, comparisons, time points, or subgroups. Even when no true differences exist, repeated testing can increase the chance of observing one or more small p-values. This is a general statistical issue; it does not mean that any particular posted finding is false. The registry lists multiple secondary outcomes in addition to the primary endpoint, but the statistical approach to multiplicity is not reported in the registry record.

The primary comparison is reported with an unadjusted p-value. A plan for prioritizing outcomes, controlling familywise error, or distinguishing confirmatory from exploratory analyses is not reported in the registry record. As a result, the primary estimate can be described on its own terms, but the evidential status of a set of outcome tests cannot be fully evaluated. Secondary p-values should not be treated as if they were automatically protected against the additional chance of false-positive findings.

Missing-data methods and analysis populations are also not described. The registry gives arm-specific outcome counts, but does not report whether those counts represent all randomized participants with data, a defined analysis population, or a subset determined by other criteria. It does not describe imputation, complete-case analysis, exclusions, or sensitivity analyses. The relationship between the enrollment count and the posted outcome counts is not explained in the registry record.

General statistical consideration: missing outcome data can affect both precision and the validity of a comparison if the chance of an outcome being observed is related to assignment or the outcome itself. The direction and magnitude of any such effect cannot be inferred without information about missingness and the analysis methods. No claim about the presence or absence of a missing-data problem is supported by the registry entries alone.

The record also does not report interim analyses or stopping rules. That absence does not show that interim monitoring did or did not occur; it means those details are not reported in the registry record. Together, the missing analysis-plan, missing-data, and multiplicity details limit reconstruction of the full inferential framework behind the posted comparisons.

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

The posted primary result describes a lower average cotton yield in the group assigned a free insecticide-treated net than in the control group, with a narrow confidence interval for the mean difference. It is evidence about cotton delivered per household in the stated season, as measured through the participating agribusiness's routine data system. That is the scope of the primary endpoint and of the reported comparison.

The result does not directly measure malaria prevention. Although the trial background concerns malaria control, and self-reported malaria prevalence is among the listed secondary outcomes, numerical results for that outcome are not reported in the registry record. The primary result therefore cannot establish whether the intervention changed malaria illness or prevalence, or whether any health pathway explains the cotton comparison.

Nor is cotton yield equivalent to farmer income, contract performance, or agribusiness profit. Contract defaults are listed as a secondary outcome, but numerical results for them are not reported in the registry record. The record does not provide a financial analysis translating cotton deliveries into costs, revenues, or profitability. The broader economic rationale in the trial background should not be mistaken for a reported economic result.

Randomization is an important design feature because it is intended to support comparisons between assigned groups. However, the registry does not give details of allocation implementation, missing outcomes, or the analysis population. The posted estimate should therefore be interpreted with the available design and reporting information in mind, rather than as a complete account of every potential source of bias or uncertainty.

The results also do not determine how farmers would respond to other net offers, delivery arrangements, crops, or settings. The intervention is described as a free net awarded through a raffle, and the endpoint is linked to participating cotton outgrowers. Generalization beyond that context requires evidence not contained in this registry record. No medical or policy recommendation follows from the statistical estimate alone.

16. Why This Trial Matters Statistically

This trial illustrates why the outcome used to evaluate an intervention must be distinguished from the rationale motivating the intervention. The background concerns malaria control and potential profitability for outgrowing agribusinesses, while the primary endpoint is routine-record cotton delivery per household. Interpreting the result accurately requires keeping those constructs separate rather than treating an agricultural outcome as a direct health outcome or a profitability calculation.

It also demonstrates the difference between statistical significance and the scope of an inference. The primary comparison is estimated precisely and has an unadjusted p-value below 0.001, but the confidence interval only quantifies uncertainty in the specified mean difference under the analysis assumptions. It does not resolve unreported questions about missingness, allocation procedures, measurement, or the trial's analysis plan.

The registry's secondary-outcome list is broader than the numerical results available for interpretation. This makes transparent reporting important: named endpoints without posted results do not allow readers to assess their direction or precision. The lack of a reported multiplicity approach also means that secondary tests require particular caution.

Finally, planning illustrations based on an observed effect answer a different question from the trial's original design rationale. They show how participant requirements change when the target effect is varied under stated assumptions, but cannot establish whether the study was originally sized appropriately. This distinction helps prevent a retrospective planning exercise from being mistaken for evidence about the trial's design or observed inferential strength.

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.

Several features limit interpretation beyond the posted primary comparison. The registry identifies randomization but does not report sequence generation, allocation concealment, or implementation details. It records no masking, while the primary endpoint comes from routine agribusiness data. The record does not identify who recorded or verified deliveries, whether they knew group assignment, or whether outcome measurement procedures were comparable between groups.

The registry reports enrollment of 81597 and primary outcome counts of 39920 in the net group and 41560 in control, but does not explain how these figures relate or describe missing outcomes. No analysis population, exclusion criteria, or missing-data method is reported. Consequently, it is not possible to assess from the record whether the posted comparison includes all randomized participants or how incomplete outcome recording was handled.

The intervention is described as provision of a free net following a raffle outcome, but adherence, net use, and any additional implementation details are not reported. The primary endpoint captures cotton delivered per household; it does not identify mechanisms linking the intervention to production. The reported secondary numerical evidence is limited to maize productivity. Numerical results for contract defaults and self-reported malaria prevalence are not reported in the registry record.

The adverse-event fields list zero participants at risk and zero affected in the serious and other categories for both groups, while deaths are not reported. Those entries do not provide a basis for a broad safety assessment, particularly because the record does not describe adverse-event ascertainment or clarify the zero at-risk counts.

Finally, the original sample-size justification, detailed statistical plan, interim analyses, multiplicity strategy, and sensitivity analyses are not reported in the registry record. These gaps do not invalidate the posted estimates, but they restrict evaluation of how the reported analysis relates to the trial's intended methods.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Stimulating Private Sector Malaria Control — NCT01397851.
• Registry record last updated 2023-12-15; status last verified 2023-11.
• Results first posted 2015-01-15.
• 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

NCT01397851, Stimulating Private Sector Malaria Control, is a completed randomized parallel-group trial with no masking recorded. PATH is listed as sponsor. The intervention was a free insecticide-treated net awarded through a raffle; control participants were told they did not win. Enrollment is recorded as 81597, with the trial beginning in 2010-12 and primary completion in 2011-12.

The primary endpoint is mean cotton yield in kilograms delivered per household during the 2010-2011 season. The posted mean difference is -4.0 kg, with a 95% confidence interval from -4.151 to -3.849 and an unadjusted p-value of <0.001. A numerical secondary comparison is posted for maize productivity; numerical results for contract defaults and self-reported malaria prevalence are not reported in the registry record.

Details on the original sample-size justification, statistical plan, missing-data handling, analysis population, and multiplicity strategy are not reported in the registry record. The findings describe the posted outcome comparisons and should be interpreted within those reporting limits.