Matched pair control studies is an important epidemiological tool that allows associations between effects and its suspected causes to be tested. A typical example was in the search for a cause of newborn limb defects, when Thalidomide was suspected. For each case of limb defect, a number of matched babies with no limb defect was selected, and the mothers were asked for exposure to Thalidomide in early pregnancy, and it was found that mothers of babies with limb defects were much more likely to have been exposed to Thalidomide.

The matched pair controlled study allows each case with an indicated outcome to be matched by more than 1 case of control, thus increasing the statistical power and alleviates the problems associated with uncommon conditions. It also allows a retrospective examination of causes, using outcome to classify the groups.

The statistical method is usually the Odds Ratio, as the retrospective nature and the manner of case selection does not allow risks to be computed.

Sample size calculation during planning, and power analysis at the conclusion of studies are therefore important to ensure a robust and sensitive conclusion.

The model links outcomes backwards to causation. A case with an indexed outcome (e.g. fetal malformation) is matched with one or more normal cases (control), so that as many possible confounding variable as possible are matched (age, social class, and so on). The incidence of exposure to a specified suspected cause (e.g. exposure to a drug) in the two groups are then compared

The study unit is the matched unit, an index case and one or more controlled cases. Sample size and power calculations are based on the number of units.

As matched pair studies are focussed on identifying a cause of an outcome, the one tail model is usually used. The calculations and tables from StatTools are therefore all one tail models.

Please note the following examples used computer generated numbers to demonstrate the statistical procedures, and are not reflective of reality.

Sample size

We think taking a drug during pregnancy may cause the baby to develop an unusual malformation, and wish to test this. We think that 1% (p_i=0.01) of mothers who have malformed babies might have taken the drug, and 0.1% (p_c=0.001) of mothers with normal babies might have taken the drug.

For every mother with a malformed baby, we will pick 5 mothers (ratio n_c/n_i= 5) who are demographically similar but have normal babies, and we want to know how many units (1 index and 5 controls) we will need.

Using α = 0.05, power = 0.8, Proportion control p_c = 0.001, proportion index p_i= 0.01, ratio n_c/n_i= 5. The number of sets or units we will need is calculated to be 381. That is, 381 mothers with abnormal babies, and 5 x 381= 1905 mothers with normal babies.

Power calculation In the study of taking a drug during pregnancy and malformed babies, we actually managed to get 10 controls for each indexed case (r = 10), and we had 250 sets or units (250 indexed and 2500 control).

We found 5 of the 250 mothers of the abnormal babies group took the drug (2% or p_i=0.02), and 4 of the 2500 mothers from the normal babies group took the drug (0.15% or p_c0.0015) The power of the data is 0.85.

As a double check, we calculate the odds Ratio using the Unpaired Comparison of Two Proportions Program Page using the data obtained. Group 1 (with abnormality) had 5 mothers exposed to the drug (Pos1=5) and 245 mothers not exposed to the drug (Neg1=245). Group 2 (without abnormality) had 4 mothers exposed to the drug (Pos2=4) and 2496 mothers not exposed to the drug (Neg2=2496). The odds ratio is 12.73, with the 95% confidence interval 3.40 to 47.74.