Recruitment Cost Versus Participant Count

Why Participant Savings Are Not the Same as Cost Savings

A shared control can reduce the number of people recruited across several treatment comparisons: one control group is used in place of a separate control group for each comparison. But a reduction in headcount does not tell a trial team how large the budget saving will be. A control participant and a treatment participant may require different amounts of recruitment, treatment, monitoring, or follow-up. The monetary saving depends on which participants are no longer recruited and how much each would have cost.

This tutorial compares costs for a shared-control design and a set of separate two-arm comparisons. It treats the sample sizes as already determined for a valid comparison; it does not determine those sample sizes or choose an allocation. The comparison is meaningful only when both designs answer the same treatment questions under comparable assumptions about precision, follow-up, and data collection.

Definition: The participant total is the number of people enrolled across all groups in a design. The total variable participant cost is the sum, over groups, of the number enrolled multiplied by the applicable cost per participant. Costs may include recruitment, intervention delivery, monitoring, and follow-up, provided the chosen cost definition is applied consistently to both designs.

Writing Down the Two Cost Totals

Suppose $K$ treatment arms are compared with a control. In a shared-control design, let $n_0$ be the number of control participants and $n_j$ the number in treatment arm $j$, for $j=1,\ldots,K$. Let $c_0$ be the variable cost per control participant and $c_j$ the variable cost per participant in treatment arm $j$. These costs are measured in the same monetary units and refer to the same cost components.

N_{\text{shared}}=n_0+\sum_{j=1}^{K}n_j, \qquad C_{\text{shared}}=c_0n_0+\sum_{j=1}^{K}c_jn_j.

For separate two-arm comparisons, each treatment comparison has its own control group. Write $n_{0j}$ for the control sample size in comparison $j$, and $c_{0j}$ for its control cost per participant. The treatment group retains size $n_j$ and cost $c_j$. Separate comparisons therefore have the totals

N_{\text{separate}}=\sum_{j=1}^{K}(n_{0j}+n_j), \qquad C_{\text{separate}}=\sum_{j=1}^{K}(c_{0j}n_{0j}+c_jn_j).

The treatment costs appear in both totals because both designs recruit participants into each treatment arm. If the treatment groups have the same sizes and costs under both designs, those terms cancel when calculating the cost difference. What remains depends on the control groups that are omitted by sharing. Costs are not sample sizes: adding a control participant and adding a treatment participant can change the budget by different amounts.

Worked Example: Equal Per-Participant Costs Within Each Type

Hypothetical trial planning data: Three treatment arms each require 120 participants, and each treatment comparison requires 120 control participants. Each control participant costs $800 and each treatment participant costs $1,500. Compare the participant totals and variable costs.

With one shared control, the total is $120+3(120)=480$ participants. The cost is

C_{\text{shared}} =(120)(\$800)+3(120)(\$1{,}500) =\$96{,}000+\$540{,}000 =\$636{,}000.

With three separate comparisons, there are three groups of 120 controls and the same three treatment groups. The total is $3(120+120)=720$ participants, and the cost is

C_{\text{separate}} =3\big[(120)(\$800)+(120)(\$1{,}500)\big] =3(\$276{,}000) =\$828{,}000.

Sharing saves $720-480=240$ participants, or $240/720=33.3\%$ of the separate-design headcount. It saves $\$828{,}000-\$636{,}000=\$192{,}000$, or $\$192{,}000/\$828{,}000=23.2\%$ of the separate-design variable cost. These percentages differ because the treatment participants, whose per-person cost is higher, are still needed in both designs.

Deriving the Cost Saving When Control Requirements Match

A useful special case makes the accounting transparent. Suppose every separate comparison requires the same $n_0$ controls as the shared design, and every control participant has the same cost $c_0$. Suppose also that the treatment group sizes and costs are unchanged when moving between designs. The separate design then has $K n_0$ control participants, while the shared design has $n_0$. Thus the reduction in control headcount is $(K-1)n_0$.

The treatment costs are identical in the two designs, so subtracting the shared cost from the separate cost leaves only the control-cost difference:

\begin{aligned} C_{\text{separate}}-C_{\text{shared}} &=\left(Kc_0n_0+\sum_{j=1}^{K}c_jn_j\right) -\left(c_0n_0+\sum_{j=1}^{K}c_jn_j\right)\\ &=(K-1)c_0n_0. \end{aligned}

This result is not a claim that the percentage reduction in cost equals the percentage reduction in participants. It says that, under these conditions, the absolute variable-cost saving equals the number of avoided control participants multiplied by the cost per control participant. The percentage saving uses the full separate-design cost as its denominator:

\text{Proportion of variable cost saved} =\frac{C_{\text{separate}}-C_{\text{shared}}}{C_{\text{separate}}}.

A large treatment cost can make the denominator large, so the monetary percentage saved may be modest even when a substantial fraction of participants is avoided. Conversely, a costly control group can make the monetary saving large relative to total cost. Neither percentage can be inferred from the other without knowing the arm-specific costs.

Worked Example: Treatment Arms With Different Costs

Hypothetical trial planning data: Two comparisons each require 100 control participants. The shared-control design also requires 90 participants in each treatment arm. The control cost is $500 per participant; the first treatment costs $1,800 per participant and the second costs $900. Assume these sizes and costs are the same in the separate comparisons. Calculate both designs.

The shared-control design has $100+90+90=280$ participants. Its cost is

C_{\text{shared}} =(100)(\$500)+(90)(\$1{,}800)+(90)(\$900) =\$50{,}000+\$162{,}000+\$81{,}000 =\$293{,}000.

The separate design has $2(100)+90+90=380$ participants. Its control cost is $2(100)(\$500)=\$100{,}000$; its treatment costs are unchanged. Therefore,

C_{\text{separate}} =\$100{,}000+\$162{,}000+\$81{,}000 =\$343{,}000.

The shared design saves 100 participants and $\$50{,}000$, exactly $100(\$500)$, the cost of the 100 control participants no longer needed. The cost saving is $\$50{,}000/\$343{,}000=14.6\%$ of the separate-design cost. The differing treatment costs do not change the absolute saving here, because both treatment groups are unchanged; they do contribute to the total-cost denominator.

Building Costs From Recruitment and Follow-Up

A single per-participant figure can hide important details. If costs are recorded separately by activity, first add the relevant costs for each participant type, then multiply by the group size. For example, if a control participant costs $r_0$ to recruit and $f_0$ for follow-up, the total control cost per participant is $c_0=r_0+f_0$. Use the same accounting boundary for both designs: do not include follow-up for one design while omitting it from the other.

Worked Example: Combining Recruitment and Follow-Up Costs

Hypothetical trial planning data: A two-treatment comparison requires 80 controls and 80 participants in each treatment arm. Control recruitment costs $300 and control follow-up costs $700 per person. Treatment recruitment costs $500 and treatment follow-up costs $2,500 per person. Assume each separate comparison requires 80 controls, and the treatment groups are unchanged. Calculate the totals using both cost components.

The combined costs per participant are $c_0=\$300+\$700=\$1{,}000$ for control and $c_T=\$500+\$2{,}500=\$3{,}000$ for treatment. The shared-control design has $80+80+80=240$ participants, with cost

C_{\text{shared}} =(80)(\$1{,}000)+2(80)(\$3{,}000) =\$80{,}000+\$480{,}000 =\$560{,}000.

The separate design has $2(80)+2(80)=320$ participants, with cost

C_{\text{separate}} =2(80)(\$1{,}000)+2(80)(\$3{,}000) =\$160{,}000+\$480{,}000 =\$640{,}000.

Sharing saves $320-240=80$ participants and $\$640{,}000-\$560{,}000=\$80{,}000$. The participant reduction is $80/320=25.0\%$, while the cost reduction is $\$80{,}000/\$640{,}000=12.5\%$. The treatment groups account for most of the cost and are still required, so the budget saving is a smaller percentage than the headcount saving.

Assumptions, Comparisons, and Diagnostics

These calculations are accounting comparisons, not statistical estimates. They assume that the participant numbers being compared are appropriate for the same scientific objectives. If the shared design changes sample sizes, follow-up, or outcome collection, those changes must be represented in the totals rather than assumed away. The per-person costs should also be estimates for the relevant trial setting, not generic prices detached from the specified procedures.

The basic comparison is between one shared-control protocol and the sum of separate two-arm comparisons. Counting only participants is a useful first description of recruitment burden, but it is not a substitute for multiplying each group size by its cost. Similarly, reporting only total cost can conceal whether savings come from fewer controls, less follow-up, or some other change. State both totals and their difference, and identify which costs are included.

For the simple formula $(K-1)c_0n_0$ to describe the entire variable-cost saving, separate comparisons must have the same control requirement and per-person control cost, while treatment requirements and costs must remain unchanged. If separate comparisons have different control sizes or costs, calculate each total directly. If a shared protocol introduces an additional fixed cost $F$ not included in the per-participant costs, the net saving is the variable-cost saving minus $F$. A cost comparison that omits such a material item can give a misleading budget conclusion.

Check the units. Multiply participants by dollars per participant to obtain dollars; do not add a headcount directly to a monetary cost.
Check the accounting boundary. Ensure recruitment, intervention, monitoring, and follow-up are included consistently in both designs.
Check the groups counted. A shared control is counted once; separate comparisons each include their own control group.
Check the comparison basis. Make clear whether a reported percentage uses the separate-design participant total or separate-design cost as its denominator.

Key takeaway: A shared control reduces the number of control groups recruited, but the budget saving is the cost of the avoided control participants, not automatically the same percentage as the participant reduction. Calculate and report participant totals and cost totals separately.

Check Your Understanding

For each question, use the stated costs as variable costs and assume that treatment requirements are unchanged between designs.

Two separate comparisons each require 50 controls. A shared design requires 50 controls total. If a control participant costs $400, how many control participants and how much control cost does sharing save?
In Question 1, suppose the unchanged treatment groups cost $120,000 in total. What are the separate and shared total costs, and what percentage of separate-design cost is saved?
Why can a 30% reduction in participants correspond to a smaller percentage reduction in total cost?
A control participant costs $250 for recruitment and $450 for follow-up. What total control cost should be used per participant?

Solutions. (1) The shared design avoids $2(50)-50=50$ control participants, saving $50(\$400)=\$20{,}000$. (2) Separate control cost is $2(50)(\$400)=\$40{,}000$; adding treatment costs gives $\$160{,}000$. Shared control cost is $50(\$400)=\$20{,}000$, so total cost is $\$140{,}000$. The cost saving is $\$20{,}000/\$160{,}000=12.5\%$. (3) The participants avoided may be relatively inexpensive controls, while costly treatment groups remain in both designs; the percentage cost saving depends on the full separate-design cost. (4) Add the components: $\$250+\$450=\$700$ per control participant.