Comparing two treatments

The data of Table 2.4 are an example of the simplest kind of experiment. There is only one factor, the anal3d ical technique, and one response, the concentration obtained. The factor is being set at only two levels, represented by Arrhenius and Berzelius. Our objective is to discover if the response is affected by this change of level. 

We can solve this problem by adapting Eq. (2.17) to the difference between two averages. We start by substituting — xb for x and — jUg for fi in the numerator. In the denominator, we need the standard deviation of the difference between the two sample averages. Generalizing 

Comparison of results obtained by two chemists titrating vinegar samples from five different producers. Concentrations of acetic acid in % 

If we assume that s and s are estimates of the same population variance, we can combine them into a single estimate (with more degrees of freedom) and write 

To obtain a pooled estimate of the standard deviation of an observation, s, we take an average of the variances of the two samples, weighted by their respective number of degrees of freedom  

---

Consider the earlier example comparing two treatments for the reduction of blood pressure and suppose in this case i = 20 and 2 = 20 are the sample sizes in the two treatment groups. The means were ... 

For binary, categorical and ordinal data there is also an approach which is a further form of the Mantel-Haenszel chi-square test. You will recall that the MH test is used for ordinal responses comparing two treatments. Well, this procedure generalises to allow ordering across the treatment groups in addition, for each of... 

To explain in a little more detail, consider a parallel group trial in which we are comparing two treatment means using the unpaired t-test. The null hypothesis Hg p.1 = p.2 that the treatment means are equal is either true or not true God knows, we don t We mere mortals have to make do with data and on the basis of data we will see either a significant p-value (p < 0.05) or a non-significant p-value (p = NS ). The various possibilities are contained in Table 8.1. 

For comparing two treatments t and ti (such as tissue types or cell lines), both Kerr et al. (2000) and Hsu et al. (2002) recommended the design of two-channel microarray experiments as generalized Latin squares with an even number a of arrays and two dyes, as follows. 

Do simple statistical tests. Average food consumption for the 20-min periods on each day. Use Friedman s two-way analysis of variance for randomized blocks (the days are the blocks, constituting one factor, the treatments are the second factor) followed by pairwise comparisons. Compare two treatments of particular interest, such as lowest MA concentration vs. EtOH only. 

A trial which is somewhat in the spirit of the third strategy above is the so-called play the winner trial. Here one requires some definition of a successful treatment. The first patient to be treated can be allocated at random thereafter, the same treatment will be used until a failure is encountered. Thus in a trial comparing two treatments (A and B) in which the first patient had received B, the following sequence of successes (S) and failures (F) would be matched by the accompanying sequence of treatments ... 

Simpson s paradox is a phenomenon whereby an overall treatment effect in one direction is reversed in every stratum. It is named after a paper of 19 51 in which it was extensively examined by E.H. Simpson (Simpson, 1951), although a related phenomenon had been discussed at least as early as 1899 by Karl Pearson (Pearson et al., 1899). (See Aldrich (1995) for discussion.) A hypothetical example is given in Table 9.1, in which a trial has been run comparing two treatments in two strata of patients moderately ill and... 

Some of the issues which arise in connection with this general problem are discussed below. Unless explicitly stated otherwise, it will be assumed that the general set-up is that of a clinical trial comparing two treatments only, but for which a large number of measures may be taken. Occasionally the case of more than two treatments is discussed. 

As we have seen above, designs are possible in which there are more sequences than treatments. It is also not necessary for the number of periods to equal the number of treatments. For example, in a trial comparing two treatments we might decide to use four periods and two sequences as follows ABBA/BAAB. Here, each patient would receive each treatment for two periods. In a so-called incomplete blocks design we might have more treatments than periods. For example, we could have compared the doses of diclofenac to placebo using the sequences... 

The sign test to compare two treatments. We assume that there are several independent pairs of observations on the two treatments. The hypothesis to be tested states that each difference has a probability distribution having mean equal to zero. For each difference the algebraic sign is noted and then the number of times the less frequent sign is considered as the test statistic. There are speciahzed tables for the critical value of this quantity once a level of significance is chosen. 

The three most commonly used measures to compare two treatment groups are risk difference, risk ratio, and odds ratio. The estimate 0, and the Mantel-Haenszel estimate of Wj can be calculated for each measure as follows (Cochran, 1954 Mantel and Haenszel, 1959 Nurminen, 1981 Tanone, 1981) ... 

The purpose of the present study was to compare two treatment modalities to obtain diseased nail chemical avulsion in toenail onychomycosis. This was a multicentre, randomised, parallel-group, open-label, active controlled study. Male or female adult patients with distal-lateral or lateral subimgual dermatophyte onychomycosis on at least 12.5% of the great toenail were randomised either to a 40% urea ointment with plastic dressing group (n=53) or to a bifonazole urea ointment group (n = 52) [22 ]. 

Berber E, Herceg NL, Casto KJ, et al (2004) Laparoscopic radiofrequency ablation of hepatic tumors prospective clinical evaluation of ablation size comparing two treatment algorithms. Surg Endosc 18 390-396... 

The underlying aim of each mode of economic evaluation is to examine the efficiency with which resources are being utilized. If the evaluation is comparing two alternative treatments, the question to be addressed is whether one treatment achieves a better outcome for patients and families than the other treatment, relative to their respective costs. If the outcomes that follow from the two treatments are known or found to be identical, the economic question would be whether one treatment is less costly than the other. These are efficiency questions, and could be used to compare alternative accommodation settings, family support... 

It must be emphasized that a CBA seeks to put monetary values on one or more of the final or intermediate outcomes. It does not simply compare the amount spent with the amount saved as a result of a treatment the latter would be a cost ojfset analysisy which compares two different levels of expenditure. Many evaluators have carried out cost-offset analyses but erroneously given them the CBA label. Without outcome data an evaluation is certainly not worthless, but its relevance for decision-makers is generally reduced. 

In Connecticut in the USA, Essock and co-workers randomized 227 patients to treatment with clozapine or to usual care and observed treatment outcome for 24 months (Essock et al, 1996). At the end of this period 88 (64%) of the original clozapine group ( = 138) were still taking clozapine. All randomized participants were in-patients who were resistant to or intolerant of conventional neuroleptics. The authors presented only brief results. Discharge rates for the two treatment groups were similar, but stark differences were observed in readmission rates 3% of patients taking clozapine were readmitted within 6 months of discharge, compared with 29% of... 

Let s assume that you are comparing the two treatment groups of Active Drug and Placebo to see if they display different distributions for time to death. You can run this analysis with PROC LIFETEST as follows ... 

In case you think that six months may not be long enough, note that similar results were shown in a year-long industry-sponsored continuation trial comparing two different antidepressants (Seroxat and imipramine) to placebo. In that study, patients who had responded to either of the antidepressants or to the placebo during the initial six-week trial were kept on their treatment for an additional year. Patients in all three groups maintained their improvement. In fact, at the end of the one-year period, those who had been treated by placebos were the... 

E. Kerr, D. A. Stone, B. H. Nam, Irving Kirsch and R. H. Goldman, Sham Device Versus Inert Pill A Randomized Controlled Trial Comparing Two Placebo Treatments for Arm Pain Due to Repetitive Use , British Medical Journal 332 (2006) 391-97... 

Fig. 2. Mean number of unformed stools passed per day of study by subjects with travelers diarrhea taking rifaximin (400 mg twice a day) or ciprofloxain (500 mg twice a day). The mean values for the two treatment groups were comparable for each day of the study (from DuPont et al. [6]).

Having established that there is a significant difference between the two treatment groups for the number of events and the number of patients afflicted, the severity of the ADRs in the two groups should be compared. 

---