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THE EXAMPLE BELOW WILL DEMONSTRATE HOW:

  1. Simple "arithmetic mean" pregnancy rates of two embryologists and of two catheters who were involved in embryo transfers (as examples) are NOT their "TRUE" pregnancy rates.

As a result, statistical differences in "arithmetic mean" pregnancy rates between the two embryologists as well as between the two catheters (even if detected by simple statistical tests) are NOT "TRUE" statistical differences.

  1. HOWEVER, analyzing the entire data in an advanced SINGLE STATISTICAL MODEL / ANALYSIS / TEST, by correcting (adjusting) those "arithmetic mean" pregnancy rates for the effect of the other factor (i.e., by correcting / adjusting the "arithmetic mean" pregnancy rate of each embryologist for the catheter effect as well as by correcting / adjusting the "arithmetic mean" pregnancy rate of each catheter for the embryologist effect) dramatically changes those pregnancy rates, and DETECTS "TRUE" pregnancy rates of embryologists and catheters.

As a result, the advanced SINGLE STATISTICAL MODEL / ANALYSIS / TEST dramatically changes the degree of statistical differences in pregnancy rates between the two embryologists as well as between the two catheters, and DETECTS the "TRUE" statistical differences among those "true" (corrected / adjusted) pregnancy rates.

  1. AND, even further correcting (adjusting) those pregnancy rates for the effect of patient's age dramatically changes those pregnancy rates even further and DETECTS further "TRUE" pregnancy rates of embryologists and catheters.

Before going through the example on this page step by step, let's have a look at the following table, which summarizes pregnancy rates of two embryologists and of two catheters who were involved in embryo transfers, showing (side by side) simple arithmetic means of pregnancy rates as well as corrected (adjusted) means of the same pregnancy rates, accompanied by their respective statistical differences (P values) (see below for the actual data and the statistical tests that generated the results in that table).

Embryologist (E)

OR Catheter (C)

Pregnancy (%)

(arithmetic mean)

Pregnancy (%)

(corrected for E/C)

Embryologist 1 (E1)

65

P=0.03

68

P=0.006

Embryologist 2 (E2)

27

18

Catheter 1 (C1)

36

P=0.26

25

P=0.04

Catheter 2 (C2)

56

61

Test Type

Simple Tests

(Chi-Square or T-Test)

Two-Way

Analysis of Variance

(Two-Way ANOVA)

The second column in the above table shows:

  • Simple "arithmetic mean" pregnancy rates of two embryologists and of two catheters (who were involved in embryo transfers) as well as

  • The degrees of statistical differences (P values) between those two embryologists and between those two catheters, calculated by simple statistical tests.

The third column in the above table shows:

  • Corrected (adjusted) "true" pregnancy rates of the same two embryologists and of the same two catheters, calculated by the more advanced / comprehensive Two-Way Analysis of Variance Test (Two-Way ANOVA), as well as

  • The corrected (adjusted) "true" degrees of statistical differences (P values) between the two embryologists and between the two catheters, calculated by the more advanced / comprehensive Two-Way Analysis of Variance Test (Two-Way ANOVA).

Note that, in the third column, the "arithmetic mean" pregnancy rates of the embryologists have been corrected (adjusted) for the effect of the catheter involved. Likewise, the "arithmetic mean" pregnancy rates of the catheters have been corrected (adjusted) for the effect of the embryologist involved.

As we see in the above table, after correcting (adjusting) the "arithmetic mean" pregnancy rates for the effect of the embryologist / catheter, each embryologist’s and catheter's “true” pregnancy rate has changed. AS A RESULT:

  1. The percentage-point difference between the two embryologists’ “true” pregnancy rates INCREASED FROM 38 (the difference between 65% & 27%) when using simple statistical tests TO 50 (the difference between 68% & 18%) when using the more advanced / comprehensive Two-Way Analysis of Variance Test (Two-Way ANOVA).

As a result, the more advanced / comprehensive Two-Way ANOVA Test detected a more significant difference between the two embryologists’ “true” pregnancy rates compared to the simple statistical tests (P=0.006 vs. P=0.03).

  1. The percentage-point difference between the two catheter's “true” pregnancy rates INCREASED FROM 20 (the difference between 36% & 56%) when using simple statistical tests TO 36 (the difference between 25% & 61%) when using the more advanced / comprehensive Two-Way Analysis of Variance Test (Two-Way ANOVA).

As a result, the more advanced / comprehensive Two-Way ANOVA Test detected a significant difference between the two catheters' “true” pregnancy rates, which was NOT detected by the simple statistical tests (P=0.04 vs. P=0.26).

NOW LET'S ANALYZE THE ACTUAL DATA, step by step, THAT GENERATED the results in the above TABLE.

ANALYZING your ENTIRE data in a SINGLE statistical model / analysis / test (as opposed to analyzing for factors separately) DETECTS "true means" and "true differences" among those "true means," BECAUSE:

  • It takes into account ALL the factors;

  • It corrects (adjusts) data for ALL the factors;

  • It removes the effects of the other factors from the effect of the factor investigated.

Clinical outcomes (such as pregnancy rate, fertilization rate, etc.) in ART / IVF programs are the results of NOT ONLY ONE factor but the results of MULTIPLE factors that are at work simultaneously, i.e., those outcomes are simultaneously affected by multiple factors.

Therefore, it is NOT sufficient to visually compare, or even statistically analyze, the arithmetic means of factors separately, i.e., by taking into account the effect of ONLY ONE factor at a time.

The examples below with a sample pregnancy data will illustrate why it is important to analyze your clinical outcomes (such as pregnancy rate, fertilization rate, etc.) in a SINGLE statistical model / analysis / test, by correcting (adjusting) those arithmetic means for the effects of ALL the factors involved, i.e., by taking into account the effects of ALL the factors involved.

This can only be achieved with advanced / comprehensive statistical knowledge, expertise and experience as well as with the use of advanced / comprehensive tests of statistical analyses, which is what the STATS OF THE ART is here to help you with.

Below is an example with a sample pregnancy data of 32 patients, with each embryo transfer procedure involving one of the two embryologists and one of the two catheters.

In other words, there were TWO FACTORS (embryologist and catheter), and TWO LEVELS within each factor (Embryologists 1 & 2; and Catheters 1 & 2, respectively).

These factors (and levels within) are only examples, so you can include as many important factors / levels as you wish.

In this example, you want to know the pregnancy rate of each embryologist, and the pregnancy rate of each catheter.

However, when you look at the "arithmetic mean" pregnancy rate of an embryologist, we know that, in each embryo transfer procedure performed by that embryologist, there was also one of the two catheters involved. So the "arithmetic mean" pregnancy rate of that embryologist is NOT the “true” pregnancy rate of that embryologist in its entirety. In other words, the "arithmetic mean" pregnancy rate of that embryologist is NOT entirely independent of the catheter effect.

Likewise, when you look at the "arithmetic mean" pregnancy rate of a catheter, we know that, in each embryo transfer procedure involving that catheter, there was also one of the two embryologists involved. So the "arithmetic mean" pregnancy rate of that catheter is NOT the “true” pregnancy rate of that catheter in its entirety. In other words, the "arithmetic mean" the pregnancy rate of that catheter is NOT entirely independent of the embryologist effect.

So because of this, you should not just want to know the "arithmetic mean" pregnancy rate of each embryologist and of each catheter, but you should want to know the “true” pregnancy rate of each embryologist independent of the catheter effect, and the “true” pregnancy rate of each catheter independent of the embryologist effect.

So in order to know the “true” pregnancy rate of each embryologist independent of the catheter effect, you need to correct (adjust) the "arithmetic mean" pregnancy rate of each embryologist for the catheter effect. In other words, you need to remove the catheter effect from the "arithmetic mean" pregnancy rate of each embryologist. In other words, you need to take into account the catheter effect.

Likewise, in order to know the “true” pregnancy rate of each catheter independent of the embryologist effect, you need to correct (adjust) the "arithmetic mean" pregnancy rate of each catheter for the embryologist effect. In other words, you need to remove the embryologist effect from the "arithmetic mean" pregnancy rate of each catheter. In other words, you need to take into account the embryologist effect.

In the example below:

  1. First, we will statistically analyze the "arithmetic mean" pregnancy rate within each factor at a time (within embryologists and within catheters) (i.e., running multiple statistical analyses / tests separately within factors, i.e., NOT correcting / adjusting for the effects of the other factors, i.e., WITHOUT taking into account the effects of the other factors, and so which will NOT yield the “true” effects of the factors).

  2. Then, in order to see the “true” effects of those factors (embryologists and catheters), we will statistically re-analyze the same pregnancy data within and across all factors (i.e., running one SINGLE statistical model / analysis / test, i.e., correcting / adjusting for the effects of the other factors, i.e., taking into account the effects of the other factors).

Now let’s look at, and statistically analyze, the (imaginary) pregnancy data below, involving 32 patients, with two embryologists (E1 & E2) and two catheters (C1 & C2) who were involved in embryo transfer procedures of those patients. Again, this is only an example, and you can include as many important factors and levels as you want in the statistical analysis of these data. Although the analyzed outcome in this example is “pregnancy,” the statistical analysis is applicable to other outcomes as well, such as live birth, fertilization rate, etc.

Patient

ID

Patient’s

Age

Embryologist

(E)

Catheter

(C)

Pregnancy

Patient 01

26

E1

C2

YES

Patient 02

27

E1

C1

NO

Patient 03

28

E2

C2

YES

Patient 04

29

E1

C1

NO

Patient 05

29

E1

C2

YES

Patient 06

30

E1

C1

YES

Patient 07

30

E1

C2

YES

Patient 08

30

E2

C2

YES

Patient 09

31

E1

C1

YES

Patient 10

31

E2

C1

YES

Patient 11

31

E2

C2

NO

Patient 12

31

E2

C2

NO

Patient 13

32

E1

C2

YES

Patient 14

33

E1

C2

YES

Patient 15

33

E2

C2

YES

Patient 16

34

E2

C2

NO

Patient 17

35

E1

C1

NO

Patient 18

35

E1

C1

NO

Patient 19

35

E2

C1

NO

Patient 20

36

E1

C1

YES

Patient 21

36

E2

C1

NO

Patient 22

36

E2

C2

NO

Patient 23

37

E1

C1

YES

Patient 24

37

E1

C1

NO

Patient 25

37

E1

C2

YES

Patient 26

37

E1

C2

YES

Patient 27

38

E1

C1

NO

Patient 28

38

E2

C1

NO

Patient 29

38

E2

C2

NO

Patient 30

38

E2

C2

NO

Patient 31

39

E2

P2

NO

Patient 32

40

E2

P2

NO

So now we have two “factors” (embryologist and catheter), and then we have two “levels” within each “factor.” We also have patient's age as “covariate.”

Factors

Levels of Factors

Embryologist

Embryologist 1 (E1)

Embryologist 2 (E2)

Catheter

Catheter 1 (C1)

Catheter 2 (C2)

The following table summarizes "arithmetic mean" pregnancy rate (WITHOUT any statistical analyses) for each embryologist (E1 & E2) and for each catheter (C1 & C2).

Embryologist (E)

OR Catheter (C)

Pregnancy (%)

(arithmetic mean)

E1

65 (11/17)

E2

27 (4/15)

C1

36 (5/14)

C2

56 (10/18)

 

 

More specifically, the data constitute a "two-by-two factorial design" as shown below.

 

   

FACTOR 2

Catheter

Pregnancy (%)

   

LEVEL 1

Catheter 1

LEVEL 2

Catheter 2

FACTOR 1

Embryologist

LEVEL 1

Embryologist 1

40% (4 / 10) 100% (7 / 7) 65% (11 / 17)

LEVEL 2

Embryologist 2

25% (1 / 4) 27% (3 / 11) 27% (4 / 15)

Pregnancy (%)

36% (5 / 14) 56% (10 / 18) 47% (15 / 32)

 

The following is the list of the steps we will go through (you can also click on them to go directly to each step):

 


STEP 1 - ARITHMETIC MEAN (UNTRUE) PREGNANCY RATES COMPARED BY SIMPLE STATISTICAL TESTS

Now we want to know the “overall” pregnancy rate for each embryologist (E1 & E2) and for each catheter (C1 & C2), who were involved in embryo transfers of those patients.

And we also want to know whether the pregnancy rates of embryologists are statistically different from one another. Likewise, we also want to know whether the pregnancy rates of catheters are statistically different from one another.

For this purpose, we will statistically analyze the pregnancy data within each factor at a time (i.e., running multiple statistical analyses / tests separately within factors, i.e., NOT correcting / adjusting for the effects of the other factors, i.e., WITHOUT taking into account the effects of the other factors, and so which will NOT yield the “true” effects of the factors).

Accordingly, using a statistics software, we will analyze the pregnancy data within embryologists, and then also within catheters, by Chi-Square Test, or alternatively by T-Test, both of which will generate the same results.

NOTE THAT: Chi-Square Test and T-Test are appropriate to compare "arithmetic means," when there is ONLY ONE factor, and ONLY TWO levels within that factor (such as two embryologists or two catheters). When there are more than two embryologists and/or catheters, those tests have to be repeated multiple times, i.e., between each pair of levels of the factor (i.e., between Embryologists 1 & 2; between Embryologists 1 & 3; between Embryologists 2 & 3; and so on), which makes these tests impractical, and so necessitates the use of a more advanced / comprehensive statistical analysis / test called One-Way ANALYSIS OF VARIANCE Test (One-Way ANOVA), although those simple tests still have to be repeated multiple times between each pair of levels of the factor, which will be illustrated in the next step. However, when there are more than ONE factor involved (e.g., two factors as "embryologist" and "catheter"), One-Way ANOVA has to be repeated for each factor. But even then, One-Way ANOVA Test still and only compares "arithmetic means," which are NOT "true means," as they are NOT corrected (adjusted) for all the factors. This necessitates the use of Two-Way ANOVA, Three-Way ANOVA, or Four-Way ANOVA, and so on, when there are two, three, or four factors involved, and so on, which will also be illustrated in the next step.

After analysis of the pregnancy data, now let’s update the above table by adding P values in the table, showing statistical differences in "arithmetic means" between the two embryologists as well as between the two catheters.

See below for the updated table, and let’s see whether those "arithmetic mean" pregnancy rates are different between the two embryologists as well as between the two catheters.

Embryologist (E)

OR Catheter (C)

Pregnancy (%)

(arithmetic mean)

E1 (n=17)

65

P=0.03

E2 (n=15)

27

C1 (n=14)

36

P=0.26*

C2 (n=18)

56

*Note: P=0.26 by Chi-Square Test; P=0.28 by T-Test.

As we see in the above table:

  1. There is a 38 percentage-point difference between the two embryologists (65% vs. 27%), which is statistically significant (P=0.03).

  2. There is a 20 percentage-point difference between the two catheters (36% vs. 56%), although statistically not significant (P=0.26).

However, the above comparisons cannot be conclusive, because, when we look at the "arithmetic mean" pregnancy rate of, say, Embryologist 1 (65%) who did the embryo transfers of those patients, we know that Catheter 1 or Catheter 2 was also involved in those embryo transfers performed by Embryologist 1, and so the two catheters (as independent factors) may have affected the "arithmetic mean" pregnancy rate of Embryologist 1 differently from one another.

So the 65% "arithmetic mean" pregnancy rate of Embryologist 1 is NOT the “true” pregnancy rate of Embryologist 1, as it is NOT corrected (adjusted) for different effects of Catheter 1 and Catheter 2, as some of those embryo transfers were performed by Catheter 1 and some others by Catheter 2, and those two catheters (as independent factors) may result in different pregnancy rates. The same is true for the "arithmetic mean" pregnancy rates of Embryologist 2, Catheter 1 and Catheter 2, and so their "arithmetic mean" pregnancy rates shown in the above table are NOT their “true” pregnancy rates.

The above necessitates the use of a more advanced / comprehensive statistical analysis / test, which is discussed in the next step.


STEP 2 - THE “TRUE” PREGNANCY RATES CALCULATED AND COMPARED BY A SINGLE ADVANCED STATISTICAL MODEL / ANALYSIS / TEST

That is, as opposed to "arithmetic means":

  • The “true” pregnancy rate of each embryologist corrected (adjusted) for the effect of the catheter; and

  • The “true” pregnancy rate of each catheter corrected (adjusted) for the effect of the embryologist.

As discussed in the previous step, when we look at the "arithmetic mean" pregnancy rate of, say, Embryologist 1 (65%) who did the embryo transfers of those patients, we know that Catheter 1 or Catheter 2 was also involved in those embryo transfers performed by Embryologist 1, and so the two catheters (as independent factors) may have affected the "arithmetic mean" pregnancy rate of Embryologist 1 differently from one another.

So the 65% pregnancy "arithmetic mean" rate of Embryologist 1 is NOT the “true” pregnancy rate of Embryologist 1, as it is NOT corrected (adjusted) for different effects of Catheter 1 and Catheter 2, as some of those embryo transfers were performed using Catheter 1 and some others using Catheter 2, and those two catheters (as independent factors) may result in different pregnancy rates. The same is true for the "arithmetic mean" pregnancy rates of Embryologist 2, Catheter 1 and Catheter 2, and so their "arithmetic mean" pregnancy rates shown in the above table are NOT their “true” pregnancy rates.

So now we want to know the “true” pregnancy rate of each embryologist when each embryologist’s pregnancy rate is corrected (adjusted) for the effect of the catheter factor (i.e., for the effect of the catheter that was used) (i.e., when the effect of the catheter factor is taken into account). Likewise, we want to know the “true” pregnancy rate of each catheter when each catheter's pregnancy rate is corrected (adjusted) for the effect of the embryologist factor (i.e., for the effect of the embryologist who was involved) (i.e., when the effect of the embryologist factor is taken into account.

And we also want to know whether the “true” (corrected / adjusted) pregnancy rates of embryologists are statistically different from one another. Likewise, we also want to know whether the “true” (corrected / adjusted) pregnancy rates of catheters are statistically different from one another.

So, in order to see the “true” pregnancy rate of each embryologist and of each catheter, let’s correct (adjust) each embryologist’s "arithmetic mean" pregnancy rate for the effect of the catheter that was used; and likewise, let’s correct (adjust) each catheter's "arithmetic mean" pregnancy rate for the effect of the embryologist who was involved.

For this purpose, instead of statistically analyzing the pregnancy data within each factor at a time (which was done in the previous step), we will statistically re-analyze the same pregnancy data within and across all factors (i.e., running one SINGLE statistical analysis / test, i.e., correcting / adjusting for the effects of the other factors, i.e., taking into account the effects of the other factors).

Accordingly, using a statistical analysis software that is more advanced / comprehensive than in the previous step, we will re-analyze the same pregnancy data, in a SINGLE statistical model / analysis / test, within and across embryologists and catheters at the same time, In other words, we will re-analyze the same pregnancy data by Two-Way ANALYSIS OF VARIANCE Test (Two-Way ANOVA) in a "two-by-two factorial design," with "embryologist" and "catheter" being FACTORS, and with "Embryologist 1", "Embryologist 2", "Catheter 1" and "Catheter 2" being LEVELS within those factors.

NOTE THAT: As discussed previously here, you can include in the same single statistical  model / analysis / test any number of factors you wish. Likewise, you can include any number of levels within each factor (e.g., two embryologists, three types of embryo transfer catheters, etc.). For example:

  • You can include two factors with two levels in each, and analyze them by "Two-Way Analysis of Variance"  in a "two-by-two factorial design."

  • You can include two factors with two and three levels, and analyze them by "Two-Way Analysis of Variance"  in a "two-by-three factorial design."

  • You can include three factors with two, three and four levels, and analyze them by "Three-Way Analysis of Variance"  in a "two-by-three-by-four factorial design."

For the sake simplicity, our example here involves only two factors with two levels in each, analyzed by "Two-Way Analysis of Variance"  in a "two-by-two factorial design."

 

After re-analysis of the same pregnancy data, now let’s update the above table by adding a third column, showing pregnancy rates for each embryologist and for each catheter corrected (adjusted) for the effect of embryologist / catheter AND showing P values (statistical differences) between the two embryologists as well as between the two catheters .

See below for the updated table, and let’s see whether those corrected (adjusted) pregnancy rates, and the corrected (adjusted) P values for the differences between the two embryologists as well as between the two catheters, have changed in comparison to the table in the previous statistical analysis.

Embryologist (E)

OR Catheter (C)

Pregnancy (%)

(arithmetic mean)

Pregnancy (%)

(corrected for E/C)

E1 (n=17)

65

P=0.03

68

P=0.006

E2 (n=15)

27

18

C1 (n=14)

36

P=0.26*

25

P=0.04

C2 (n=18)

56

61

Test Type

Simple Tests

(Chi-Square or T-Test)

Two-Way

Analysis of Variance

(Two-Way ANOVA)

*Note: P=0.26 by Chi-Square Test; P=0.28 by T-Test.

As we see in the above table, after correcting (adjusting) the pregnancy data for the effect of the embryologist / catheter (with Two-Way Analysis of Variance Test, or Two-Way ANOVA), each embryologist’s and catheter's “true” pregnancy rate has changed. AS A RESULT:

  1. The percentage-point difference between the two embryologists’ “true” pregnancy rates INCREASED FROM 38 (the difference between 65% & 27%) when using the simple Chi-Square or T-Test TO 50 (the difference between 68% & 18%) when using the more advanced / comprehensive Two-Way ANOVA Test.

As a result, the more advanced / comprehensive Two-Way ANOVA Test detected a more significant difference between the two embryologists’ “true” pregnancy rates compared to the simple Chi-Square or T-Test (P=0.006 vs. P=0.03).

  1. The percentage-point difference between the two catheters' “true” pregnancy rates INCREASED FROM 20 (the difference between 36% & 56%) when using the simple Chi-Square or T-Test TO 36 (the difference between 25% & 61%) when using the more advanced / comprehensive Two-Way ANOVA Test.

As a result, the more advanced / comprehensive Two-Way ANOVA Test detected a significant difference between the two catheters' “true” pregnancy rates, which was NOT detected by the simple Chi-Square or T-Test (P=0.04 vs. P=0.26).

However, the above comparisons still cannot be conclusive, because, we also know that patient’s age is an independent factor that adversely affects pregnancy rate, and that not all patients are of the same age in this sample data.

As a matter of fact, a separate statistical analysis of our sample data indicates that patients' pregnancy in our sample is inversely and significantly correlated to patient's age, with a correlation coefficient of –0.41 with the P value of 0.02.

So the pregnancy rate of each embryologist and of each catheter in the above table (already corrected / adjusted for the effect of embryologist / catheter) are still NOT the “true” pregnancy rate of each embryologist and of each catheter, as they are NOT corrected (adjusted) for the effect of patient's age.

The above necessitates the use of a more advanced / comprehensive statistical analysis / test, which is discussed in the next step.


STEP 3 - THE “TRUER” PREGNANCY RATES CALCULATED AND COMPARED BY A MORE ADVANCED STATISTICAL MODEL / ANALYSIS / TEST, TAKING INTO ACCOUNT PATIENT'S AGE

That is:

  • The “truer” pregnancy rate of each embryologist corrected (adjusted) for the effect of the catheter and for the effect of the patient's age; and

  • The “truer” pregnancy rate of each catheter corrected (adjusted) for the effect of the embryologist and for the effect of the patient's age.

We know that patient’s age is an independent factor that adversely affects pregnancy rate, and that not all patients are of the same age in this sample data.

As a matter of fact, a separate statistical analysis of our sample data indicates that patients' pregnancy in our sample is inversely and significantly correlated to patient's age, with a correlation coefficient of –0.41 with the P value of 0.02.

So the pregnancy rate of each embryologist and of each catheter in the above table (already corrected / adjusted for the effect of embryologist / catheter) are still NOT the “true” pregnancy rate of each embryologist and of each catheter, as they are NOT corrected (adjusted) for the effect of patient's age.

So, in order to see the “truer” pregnancy rate of each embryologist and of each catheter, let’s further correct (adjust) those (already-corrected / adjusted) pregnancy rates for the effect of patient’s age.

For this purpose, we will repeat the same statistical analysis as in the previous step (Two-Way ANOVA Test), but now we will include, in the statistical model / analysis / test, patient's age as additional factor (as COVARIATE) (i.e., now also correcting / adjusting for the effects of patient's age, i.e., taking into account the effects of patient's age as well).

Accordingly, using a statistical analysis software that is more advanced / comprehensive than in the previous step, we will re-analyze the same pregnancy data within and across embryologists and catheters, and while correcting / adjusting for the effects of patient's age as covariate at the same time, in a SINGLE statistical model / analysis / test, by what is called now ANALYSIS OF COVARIANCE Test.

After re-analysis of the same pregnancy data, now let’s update the above table by adding a fourth column, showing pregnancy rate for each embryologist and catheter corrected (adjusted) for the effect of embryologist / catheter as well as corrected for the effect of patient's age AND showing P values (statistical differences) between the two embryologists as well as between the two catheters.

See below for the updated table, and let’s see whether those pregnancy rates, and the P values for the differences between the two embryologists as well as between the two catheters, have changed even further in comparison to the table in the previous statistical analysis.

[ Of course, you also have the option to do these analyses within the age groups; however, correcting /adjusting for the age factor directly will still be useful. ]

Embryologist (E)

OR Catheter (C)

Pregnancy (%)

(arithmetic mean)

Pregnancy (%)

(corrected for E/C)

Pregnancy (%)

(corrected for E/C & Age)

E1 (n=17)

65

P=0.03

68

P=0.006

64

P=0.02

E2 (n=15)

27

18

23

C1 (n=14)

36

P=0.26*

25

P=0.04

28

P=0.07

C2 (n=18)

56

61

59

Test Type

Simple Tests

(Chi-Square or T-Test)

Two-Way

Analysis of Variance

(Two-Way ANOVA)

Analysis of Covariance

*Note: P=0.26 by Chi-Square Test; P=0.28 by T-Test.

As we see in the above table, after correcting (adjusting) the pregnancy data for the effect of the embryologist / catheter as well as further for the effect of patient's age (with Analysis of Covariance Test), each embryologist’s and catheter's “true” pregnancy rate has FURTHER changed. AS A RESULT:

  1. The percentage-point difference between the two embryologists’ “true” pregnancy rates INCREASED FROM 38 (the difference between 65% & 27%) when using the simple Chi-Square or T-Test TO 41 (the difference between 64% & 23%) when using the more advanced / comprehensive Analysis of Covariance Test.

As a result, the more advanced / comprehensive Analysis of Covariance Test detected a more significant difference between the two embryologists’ “true” pregnancy rates compared to the simple Chi-Square or T-Test (P=0.02 vs. P=0.03).

  1. The percentage-point difference between the two catheters' “true” pregnancy rates INCREASED FROM 20 (the difference between 36% & 56%) when using the simple Chi-Square or T-Test TO 31 (the difference between 28% & 59%) when using the more advanced / comprehensive Analysis of Covariance Test.

As a result, the more advanced / comprehensive Analysis of Covariance Test detected a more significant difference between the two catheters' “true” pregnancy rates compared to the simple Chi-Square or T-Test (P=0.07 vs. P=0.26).

So far, we have ONLY looked at, and analyzed, the “overall” pregnancy rate of each embryologist and of each catheter, corrected (adjusted) for the effect of embryologist or catheter as well as for the effect of patient's age.

However, we don’t know yet what the pregnancy rates of the four different combinations of embryologists and catheters are, AND how they are different from one another. In other words, we don’t know yet about the nature of the interaction between embryologists and catheters, with regard to pregnancy rates.

The above necessitates the use of a more advanced / comprehensive statistical analysis / test, which is discussed in the next step.


STEP 4 - PREGNANCY RATES OF COMBINATIONS OF EMBRYOLOGISTS AND CATHETERS CALCULATED AND COMPARED

So far, we have ONLY looked at, and analyzed, the “overall” pregnancy rate of each embryologist and of each catheter, corrected (adjusted) for the effect of embryologist or catheter as well as for the effect of patient's age.

However, we don’t know yet what the pregnancy rates of the four different combinations of embryologists and catheters are, AND how they are different from one another. In other words, we don’t know yet about the nature of the interaction between embryologists and catheters, with regard to pregnancy rates.

So now, we want to know the pregnancy rates of the four different combinations of “embryologist x catheter.” We also want to know whether those pregnancy rates are statistically different from one another.

So we will break the pregnancy rate of each embryologist down by catheters; and likewise, we will break the pregnancy rate of each catheter down by embryologists (i.e., break pregnancy results down by “embryologist x catheter” combinations).

After we break down the pregnancy data, we will re-analyze the pregnancy data:

  1. First, WITHOUT correcting (adjusting) pregnancy rates for the effect of patient's AGE (analyzing by Two-Way ANOVA Test), and

  2. Then, by CORRECTING (adjusting) them for the effect of patient's AGE (analyzing by ANALYSIS OF COVARIANCE Test; with patients’ age as covariate).

After re-analysis of the pregnancy data by Two-Way ANOVA Test (WITHOUT correcting / adjusting pregnancy rates for the effect of patient's AGE), the following table shows pregnancy rate (arithmetic mean) for each combination of “embryologist x catheter” AND shows P values (statistical differences) among those combinations.

Levels of Factors

 

Combinations of Levels (arithmetic means)

 

Comparisons among

Combinations

Difference

(P Value)

Embryologist 1 (E1)

 

E1-C1 = 40%

n=10

 

E1-C1 vs. E1-C2   (40% vs. 100%)

0.01

Embryologist 2 (E2)

 

E1-C2 = 100%

n=  7

 

E1-C1 vs. E2-C1   (40% vs. 25%)

0.57

Catheter 1 (C1)

 

E2-C1 = 25%

n=  4

 

E1-C1 vs. E2-C2   (40% vs. 27%)

0.51

Catheter 2 (C2)

 

E2-C2 = 27%

n=11

 

E1-C2 vs. E2-C1   (100% vs. 25%)

0.01

 

 

 

 

E1-C2 vs. E2-C2   (100% vs. 27%)

0.002

 

 

 

 

E2-C1 vs. E2-C2   (25% vs. 27%)

0.93

As we see in the above table:

The highest pregnancy rate resulted from the combination of E1-C2 (100%), whereas the lowest pregnancy rates resulted from the combinations of E2-C1 (25%) and E2-C2 (27%).

Statistically significant differences existed between combinations of:

E1-C1 vs. E1-C2   (40% vs. 100%)   (P=0.01)

E1-C2 vs. E2-C1   (100% vs. 25%)   (P=0.01)

E1-C2 vs. E2-C2   (100% vs. 27%)   (P=0.002)

Although not statistically significant:

There was a 15 percentage-point difference between E1-C1 and E2-C1 (40% vs. 25%) (P=0.57)

There was a 13 percentage-point difference between E1-C1 and E2-C2 (40% vs. 27%) (P=0.51)

After re-analysis of the same pregnancy data by ANALYSIS OF COVARIANCE Test (by correcting / adjusting pregnancy rates for the effect of patient's AGE), the following table shows pregnancy rate for each combination of “embryologist x catheter” AND shows P values (statistical differences) among those combinations.

Levels of

Factors

 

Combinations of Levels

(corrected for age)

 

Comparisons among

Combinations

Difference

(P Value)

Embryologist 1 (E1)

 

E1-C1 = 39%

n=10

 

E1-C1 vs. E1-C2   (39% vs. 94%)

0.01

Embryologist 2 (E2)

 

E1-C2 = 94%

n=  7

 

E1-C1 vs. E2-C1   (39% vs. 30%)

0.71

Catheter 1 (C1)

 

E2-C1 = 30%

n=  4

 

E1-C1 vs. E2-C2   (39% vs. 30%)

0.61

Catheter 2 (C2)

 

E2-C2 = 30%

n=11

 

E1-C2 vs. E2-C1   (94% vs. 30%)

0.03

 

 

 

 

E1-C2 vs. E2-C2   (94% vs. 30%)

0.005

 

 

 

 

E2-C1 vs. E2-C2   (30% vs. 30%)

1.00

As we see in the above table:

The highest pregnancy rate resulted from the combination of E1-C2 (94%), whereas the lowest pregnancy rates resulted from the combinations of E2-C1 (30%) and E2-C2 (30%).

Statistically significant differences existed between combinations of:

E1-C1 vs. E1-C2   (39% vs. 94%)   (P=0.01)

E1-C2 vs. E2-C1   (94% vs. 30%)   (P=0.03)

E1-C2 vs. E2-C2   (94% vs. 30%)   (P=0.005)

Although not statistically significant:

There was a 9 percentage-point difference between E1-C1 and E2-C1 (39% vs. 30%) (P=0.71)

There was a 9 percentage-point difference between E1-C1 and E2-C2 (39% vs. 30%) (P=0.61)

 


CONCLUSION

Clinical outcomes (such as pregnancy, live birth and fertilization rates) in ART / IVF programs are the results of NOT ONLY ONE factor but the results of MULTIPLE factors that are at work simultaneously, i.e., those outcomes are simultaneously affected by multiple factors.

Therefore, it is NOT sufficient to visually compare, or even statistically analyze by simple statistical tests, the arithmetic means of factors separately, i.e., by taking into account the effect of ONLY ONE factor at a time.

The above examples with a sample pregnancy data illustrates why it is important to analyze your clinical outcomes (such as pregnancy, live birth and fertilization rates) in a SINGLE statistical model / analysis / test, by correcting (adjusting) those arithmetic means for the effects of ALL the factors involved, i.e., by taking into account the effects of ALL the factors involved, AS OPPOSED TO simply calculating arithmetic means and simply comparing those arithmetic means by simple statistical tests.

This can only be achieved with advanced / comprehensive statistical knowledge, expertise and experience as well as with the use of advanced / comprehensive tests of statistical analyses, which is what the STATS OF THE ART is here to help you with.

 

 


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