Most of my litterature review started with Senn's
textbook, *Statistical Issues in
Drug Development* (Wiley, 2007, pp. 317-336). Contrary to *direct assays*
where we know what we want to achieve, say a given response to treatment,
and we adjust the dose until this goal is reached, in *indirect assays*
individual response is studied as a function of the dose and a 'useful dose'
is decided upon afterwards. Studies on dose finding are generally done
through between- or within-subject design. In within-patient design--dose
escalation or cross-over--doses are given in ascending order, keeping in
mind that within-patient titration share most of the problems of cross-over
trials (see below), with additional limitations (dose and period effects are
confounded) unless there's a parallel placebo group or an intervening
placebo treatment in the dose escalation sequence. In any case, there seems
to be some agreement on the fact that within-patient designs (cross-over or
dose escalation) usually perform better than any parallel-groups
design.^{(1)} However, the main difficulty with analyzing **dose
escalation** studies is that it generally requires complex non-linear
random-effects models which allow for drop-out to be used.

In **cross-over trials**, patients are randomly allocated to a sequence of
treatments where treatments are interleaved with (active or passive)
wash-out periods. Such a design is typical of a design where subject is
taken as his own control and cross-over trials are an example of a Latin
square design where treatments appear only once in each period and in each
sequence. A simple design is the AB/BA cross-over where the two treatments
under study are administered in both order: A then B, or B then
A. Carry-over effects are of much concerns in this approach, and even if
different weighting schemes have been proposed to eliminate or render them
innocuous it seems that the best is actually to take into account
pharmacokinetic and pharmacological theories when devising wash-out
period. In the special case of single-dose studies the wash-out period has
been proven to be effective in general.^{(5)}

Some references are given in the References section, but here is one good textbook by Stephen Senn himself:

Senn S.

Cross-over trials in clinical research(2nd ed.). Chichester, England: John Wiley & Sons; 2002.

As has been said, a **parallel-groups design** can also be used in effective
dose studies. Assuming 3 doses for the active group and a standard deviation
of the outcome (e.g., pain score) of 45 points, with a minimal clinical
important difference of 25 points, we would need 54 patients in each group
to ensure 80% power. However, titration assays are often done in
**two-stage**, with a first randomization of patients on dose sequence, and
a second random allocation of patients to effective dose group or a placebo,
see e.g. Davis (1992) and the following illustration.

**Free combination therapy** is another topic where complex designs might be
required (factorial or response surface with quadratic terms added) but it
is generally found in pre-clinical studies.^{(6,7)} Of note,
fixed-dose combinations have been shown to perform usually better than
free-drug combination, especially in terms of adherence (non-adherence
reduced by 25% according to (8)).

## References

- Sheiner LB, Hashimoto Y, and Beal SL. A simulation study comparing
designs for dose-ranging.
*Statistics in Medicine*. 1991; 10: 303–321. - Senn, S. Cross-over trials in Statistics in Medicine: The first '25'
years.
*Statistics in Medicine*. 2006; 25:3430-3442. - Senn, S. The AB/BA Cross-over: How to perform the two- stage analysis if you can’t be
persuaded that you shouldn’t. In
Hansen, B and De Ridder, M. (eds.)
*Liber Amicorum Roel van Strik*, Erasmus University, Rotterdam; 1996, pp. 93-100. - Senn, S, Lillienthal, J, Patalano, F, and Till,
D. An incomplete blocks cross-over in Asthma: A case study in
collaboration.
In Vollmar J and Hothorn, LA (eds).
*Biometrics in the pharmaceutical industry*, vol. 7, Stuttgart, Germany: Gustav Fischer; 1997, pp. 3–26. - D'Angelo G, Potvin D, and Turgeon J. Carryover effects in
bioequivalence studies.
*Journal of Biopharmaceutical Statistics*. 2001; 11: 27–36. - Machado SG, Robinson GA. A direct, general approach based on
isobolograms for assessing the joint action of drugs in pre-clinical
experiments.
*Statistics in Medicine*. 1994; 13:2289–2309. - Straetemans, R, O'Brien, T, Wouters, L, Van Dun, J, Janicot, V, Bijnens,
L, Burzykowski, T, Aerts, M. Design and Analysis of Drug Combination
Experiments.
*Biometrical Journal*. 2005; 47: 299-308. - Bangalore S, Kamalakkannan G, Parkar S, Messerli
FH. Fixed-Dose Combinations Improve Medication Compliance:
A Meta-Analysis.
*The American Journal of Medicine*. 2007; 120:713–719. - Davis, KL et al. A double-blind, placebo-controlled multicenter study of
Tacrine for Alzheimer's disease.
*New England Journal of Medicine*. 1992; 327: 1253-1259. - Dette, H, Bretz, F, Pepelyshev, A, and Pinheiro,
JC. Optimal Designs for Dose Finding Studies.
*Journal of the American Statisical Association*. 2008; 103: 1225-1237. See also the DoseFinding R package.