Question

1. A questionnaire is used to screen for symptoms of anxiety and has a sensitivity of 60% and a specificity of 80%. Only those who receive a positive test result after completing the questionnaire are sent to be interviewed by a psychiatrist. The psychiatrist's interview has a sensitivity of 90% and a specificity of 90%. The prevalence of anxiety is 20% in this population of 1,000 persons.

d.) Describe what would happen if the order of the tests were reversed.

Answer 1

Solution-

According to question,

The prevalence of anxiety is 20% in this population of 1,000 persons.

Now, since prevalence of anxiety = 20% out of 1000 persons.

So, 1000×0.20 = 200 people actually have anxiet and

1000 -200 = 800 people actually do not have anxiety.

Now,

The questionnaire used to screen for symptoms of anxiety and has a sensitivity of 60% and a specificity of 80%.

So, 200×0.60 = 120 people having anxiety are tested positive and 200-120 =80 people having anxiety are tested negative.

Also 800×0.80 = 640 people not having anxiety are tested negative and 800-640 =160 people not having anxiety are tested positive.

So, total people who tested positive are 120 +160 = 280 .

Of those who receive a positive test result after completing the questionnaire (280 people out of which 120 people actualy have anxiety and 160 actually not have anxiety) are sent to be interviewed by a psychiatrist.

The psychiatrist's interview has a sensitivity of 90% and a specificity of 90%.

So, 120×0.90 = 108 are tested positive who actually have anxiety and 120-108 = 12 are tested negative who actually have anxiety.

Also, 160×0.90=144 are tested negative who actually do not have anxiety and 160-144 = 16 are tested positive who actually do not have anxiety.

The above information is summarize below-

Test-1 Questionnaire

Sensitivity 60% and specificity 80%

	Anxiety(+)	Anxiety(–)
Test Result (+)	120	160
Test Result (–)	80	240

Test-2 psychiatrist interview

Sensitivity = 90% and Specificity = 90%

	Anxiety (+)	Anxiety(–)
Test Result (+)	108	160
Test Result (–)	12	144

So,

Net Sensitivity = 108/200 = 0.54 or 54% and .....(1)

Net Specifically = (240+144)/800 = 384/800 = 0.48 or 48% ....(2)

Now,

If the order of the tests were reversed.It means if psychiatrist interview first then Questionnaire test.

Since 200 people actually have anxiety and 800 people actually do not have anxiety.

Now,

The psychiatrist interview used to screen for symptoms of anxiety and has a sensitivity of 90% and a specificity of 90%.

So, 200×0.90 = 180 people having anxiety are tested positive and 200-180 =20 people having anxiety are tested negative.

Also 800×0.90 = 720 people not having anxiety are tested negative and 800-720 =80 people not having anxiety are tested positive.

So, total people who tested positive are 180 +80 = 260.

Of those who receive a positive test result after completing the psychiatrist interview (260 people out of which 180 people actualy have anxiety and 80 actually not have anxiety) are sent for questionnaire.

Since the questionnaire has a sensitivity of 60% and a specificity of 80%.

So, 180×0.60 = 108 are tested positive who actually have anxiety and 180-108 = 72 are tested negative who actually have anxiety.

Also, 80×0.80=64 are tested negative who actually do not have anxiety and 80-64 = 16 are tested positive who actually do not have anxiety.

The above information is summarize below-

Test-1 psychiatrist interview

Sensitivity 90% and specificity 90%

	Anxiety(+)	Anxiety(–))
Test result(+)	180	80
Test Result(–)	20	720

Test-2 questionnaire

Sensitivity = 60% and Specificity = 80%

	Anxiety(+)	Anxiety(–)
Test Result(+)	108	16
Test Result (–)	72	64

Net Sensitivity = 108/200 = 0.54 or 54% and .....(3)

Net Specifically = (720+64)/800 = 384/800 = 0.48 or 48% .....(4)

From equations (1) and (3) & (2)and (4), we can observe that Net Sensitivity and Net Specifically are same even if order of test is reversed.

Hence, overall there will be no effect on number of people who are tested positive (finally after 2 tests) if the order of test were reversed.