We found that efficiency increased (unit costs decreased) with scale, across all countries and interventions we examined. This association varies within intervention and country, in terms of the observed range in efficiency and scale, the type of regression equation that provides the best fit, and slope of the regression line, and the proportion of variation in efficiency explained by scale. Of the 15 country-intervention pairs studied, the regression lines for two, STI and MTCT programs in India, suggest an inflection point beyond which we expect to see an up-turn in unit costs. Of these two, only one, the regression line for MTCT programs, was statistically significant. With simple linear functions, the regression trends were downward sloping in all cases.
Table summarizes the rate at which unit costs change when output levels double (from 25th percentile scale) and the portion of variability in unit costs that are explained by scale (R2). Both unit cost declines associated with a doubling of output and R2 vary dramatically between countries and between interventions. Declines for VCT programs range from 32.5% in India to 2.4% in South Africa and R2 values ranged from 0.83 in India to 0.29 in Uganda. The strongest association between decrease in unit cost and doubling of scale were found in India and Russia's STI programs, although these associations were not statistically significant. All other observed associations were substantial and statistically significant except for that found in Mexico's VCT sites which had a p-value of 0.066, just exceeding the usual 0.05 p-value for statistical significance.
Strength of the relationship and coefficient of determination between unit cost and program scale
Voluntary Counseling and Testing Programs
For VCT, data from all five countries show strong scale effects, i.e., sites with higher service volume tend to have lower unit costs (See Figure ). Scale varied 100-fold within countries, and 1,000-fold across the full sample. Efficiency (cost per person receiving full VCT) varies from 10-fold to more than 100-fold within country, and over all five countries varies from $668 (in Mexico) down to $1.50 (in Russia, where counseling may be just a few minutes). The proportion of variation explained by scale varied from 20% (Mexico) to 83% (India). In Mexico, each doubling in scale is associated with a drop of $30 per VCT client (7–27%, depending on starting point). In South Africa, the effect of doubling in scale is low until more than 10,000 VCT clients (with the curve shape driven by one large program). For India, Uganda, and Russia, a doubling in size is associated with 27% to 32% lower costs.
VCT unit cost and quality
We found no statistically significant relationship between any of our VCT program quality indicators and unit cost. The R-square for the full model, which included dummy variables for countries and adjustments for purchasing power parity was 0.05, suggesting that quality, as reflected in our analysis, explains almost none of the variation in observed unit costs.
Sex Worker Programs
For sex worker (SW) programs, data from three countries show very strong scale effects (See Figure ). Scale ranges 100-fold within countries, and more than 1,000-fold across the sample. Efficiency (cost per hour of contact with SWs) varies 100-fold within country, and over all three countries varies from $378 for a program in South Africa that provided only 692 hours of client contact, down to $0.04 for a program in Russia with very large group sessions, and thus many client-hours of contact. The proportion of variation explained by scale is high: 38% (South Africa), 84% (Russia), and 88% (India). All regressions were statistically significant. For South Africa, each doubling in scale is associated with a 31% decrease in cost per hour. For Russia, there is a $5 decrease per hour of contact for a doubling in scale. For India, doubling leads to a 42% drop in cost per hour. The data from India includes a program that includes large public gatherings. This generates high service volumes and very low unit costs as shown in the data point in the lower right corner of Figure . If this atypical program is removed, the R2 for the remaining Indian sites is 0.72.
Sexually Transmitted Infection programs
For sexually transmitted infection (STI) programs, data from three countries show at least modest scale effects over a smaller range in scale (See Figure ). Scale varies 50-fold within Mexico, and 5-fold within Russia and India. Efficiency (cost per first visit for suspected STI) varies 100-fold within Mexico and 10-fold within Russia and India. Over all three countries, this cost varies from $650 to $0.82 per first visit. The proportion of variation explained by scale also varies widely: 70% (Mexico), 26% (Russia), and 42% (India). For Mexico, each doubling in scale is associated with a 35% – 90% decrease in cost per first visit, depending on starting point. For Russia, there is a 58% decrease in cost per first visit for a doubling in scale. STI programs in India were one of two intervention-country pairs that exhibited an upturn in unit costs. After declining from $53.77 per first visit at a program with 324 first visits, to $6.31 per first visit at a program with 1,357 first visits, unit cost rose to $27.33 for a program with 2,664 first visits.
Information, Education and Communication programs
PANCEA data on information, education and communication (IEC) programs are restricted to Mexico. Scale varies widely: 10,000-fold, due to some programs having large electronic media components (See Figure ). Efficiency (cost per hour of media contact) varies 5,000-fold. The proportion of variation explained by scale is 91%. A doubling in scale results in a 64% drop in cost per hour of contact and this association is highly statistically significant (p-value < 0.001).
Risk reduction programs
Data on risk reduction program for injection drug users come only from Russia. Most programs focus on needle-syringe exchange. For these programs, scale varies 50-fold, and efficiency varies 40-fold. Scale explains 45% of variation in efficiency (cost per 50 needles exchanged). A doubling in scale is associated with a 34.5% reduction in cost per output (p-value = 0.004).
For inpatient rehabilitation programs (n = 4), scale explains 96% of variation in efficiency (cost per treatment episode). A doubling in scale is associated with a 47.9% reduction in cost per output (p-value = 0.022). The two programs that specialize in counseling also exhibit significant economies of scale, though this finding is weakly suggestive only because of the sample size (See Figure ).
Prevention of Mother to Child Transmission programs
For prevention of mother-to-child HIV transmission programs (PMTCT), we report data only from India (other countries collected data from only one site each). For these programs, scale varies 6-fold, and efficiency varies 2-fold. Scale explains 42% of variation in efficiency (cost per mother completing post-test counseling). A doubling in scale from the first quartile output level is associated with a 23% reduction in cost per output. As shown in Figure , unit costs rise at output levels exceeding 10,000 women per year who receive post-test counseling. However, this up-turn in unit costs is due to only one data point. Without it, costs level off but do not increase. If the number of mother-neonate pairs receiving nevirapine is used as the output measure, we see strongly declining costs with scale up to 264 per year and no indication of an up-turn in unit costs (R2 = 0.84) (Figure not shown).