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Cocaine is a stimulant psychoactive drug. Comparisons of its population harm require exposure denominators and consistent definitions of drug-related outcomes, rather than death counts alone.

Use a concurrent comparison: test the same specimens for both cocaine and mephedrone, rather than treating the historical cocaine percentage as an exactly known 2010 parameter. Assume representative sampling of privates, effectively independent specimens, stable underlying rates during the sampling period, and sufficiently accurate assays. I use a two-sided 5% test of equal positive-test probabilities, with 80% statistical power at $p_C=0.010$ and $p_M=0.005$. This is a design to distinguish the rates at a twofold alternative; a significance test does not prove that their ratio is exactly two.

The paired design needs the joint positive-test distribution. For specimen $i$, write $C_i,M_i\in \{0,1\}$ and $D_i=C_i-M_i$. Put $q_{11}=P(C_i=M_i=1)$ andThen $\mathbb{E}{D}_i=\delta$ and $\mathrm{Var}(D_i)=q-{\delta }^2$. Under equal marginal rates, the two discordant outcomes have equal probabilities; conditional on the total number of discordant specimens, their split is a fair binomial distribution. This gives the McNemar test. Its large-sample version rejects for a sufficiently large absolute difference between the discordant counts, divided by their estimated standard deviation.

For planning, suppose simultaneous positives are negligible, so $q\simeq 0.015$. Under the alternative the difference in positive counts has mean $n\delta$ and standard deviation $\sqrt{n(q-{\delta }^2)}$; the approximate upper null rejection boundary is $z_{0.975}\sqrt{nq}$. Requiring 80% upper-tail rejection probability gives the paired binary sample size calculationAdd the mephedrone assay to about 5,000 existing tests, roughly ten weeks at 500 per week. An exact conditional-power calculation under the negligible-overlap model gives about $77.6\%$ at 4,707 specimens and $80.2\%$ at 5,000, so the rounding also compensates for the conservative discrete test. If positivity for the two drugs were independent within a specimen, $q_{11}=0.00005$, giving a very similar requirement of about 4,676. For the stated marginal rates, $q\le 0.015$, so negligible overlap is a conservative variance choice within this approximation. Substantial co-use reduces the discordant proportion and changes the necessary size. Repeated tests on the same person, unit-level clustered data or inaccurate assays can instead reduce effective information and require more specimens.

A pre-specified one-sided 5% comparison would use $1.645$ in place of $1.96$ and require about 3,708 specimens before allowing for discreteness under the negligible-overlap assumption. These are different testing conventions. Treating the historical 1% as fixed would give a one-sample calculation, but would ignore uncertainty or changes in the actual 2010 cocaine rate.

On the stipulated figures, a 20% decline from 200 cocaine-related deaths means about 40 fewer deaths, against about 10 attributed to mephedrone:That bookkeeping is relevant to a population-harm assessment only if the avoided deaths really result from substitution, the new deaths are counted comparably, and overlapping drug attributions are not counted twice. A change in the legality of one drug is an intervention affecting behaviour; the before-and-after association alone does not identify its causal effect.

Distinguish per-user danger from total population harm. More use can raise total deaths even for a less dangerous drug, and an increase can involve new users who would otherwise use no drug. Conversely, restricting a substitute may move users back to more dangerous alternatives. The relative fatality risks do not mechanically determine legal classification: nonfatal harm, dependence, dosage and purity, co-use, the composition of users, enforcement and supply effects, and uncertainty in the estimates all matter. Any policy assessment should compare plausible behavioural responses to the alternatives, including displacement of both cocaine and MDMA, rather than extrapolate from ten deaths alone.