Inferring… What?
Stefano Petti
Dept. Public Health & Infectious Diseases
Sapienza University
Rome
Italy
INFERENCE
comes from the Latin word
composed by
ferre = bring & in = in
and means
inferre
bring in
Thus, inference refers to
the process of drawing conclusions relative to the
underlying study population starting from a sample
which is subject to observational errors or sampling
variation
INFERENCE
A sinonymous of INFERENCE is INDUCTION
which comes from another Latin word
inducere
and means, once again,
bring in
When we make inference/induction we
BRING something IN the studypopulation
INFERENCE/INDUCTION VS.
DEDUCTION
INFERENCE is radically different from
DEDUCTION
Another Latin word composed by ducere + de
which means
bring out / extract
When we make deduction we bring something
out (from a sample), when we make inference
we bring something in (the study-population)
How do inference/induction and
deduction function? Which is the
process of knowledge (science)?
Two completely distinct parts
1-our deduction from our sample
2-our inference in the underlying study-population
Example (part 1 - DEDUCTION)
Gurbuz O, et al. Community Dent Health 2010;27:151-7
Prevalence of edentulousness in adult Turkish hospitalized
chronic psychiatric patients
Sample, 491 subjects, mean age 52.3 (sd, 12.3)
Number of edentulous patients, 89
We DEDUCE that 18.1% of the sampled
subjects were edentulous
Example (part 2 –
INFERENCE/INDUCTION)
Can we say that 18.1% of ALL adult Turkish institutionalized
psychiatric patients (the underlying study population) are
edentulous?
Sample prevalence IS NOT the population prevalence
We need to calculate the 95% confidence interval
14.7% to 21.5%
INFERENCE = We can say that a proportion between 14.7%
and 21.5% of ALL adult Turkish institutionalized psychiatric
patients are edentulous
How do inference/induction and
deduction function? Which is the
process of knowledge (science)?
Two completely distinct parts
1-we bring something out from our sample
(deduction)
2-we bring something in the study population
(inference/induction)
AFTER AN ADAPTATION PROCESS!!!
Which are the causes of wrong
inference?
wrong deductions
good deductions
lead to
wrong inference
mined by
wrong inference
biased study
wrong deductions
due to
incomplete deductions
Which are the causes of wrong
inference?
WRONG INFERENCE MAY ARISE FROM
STUDY DESIGN
DEDUCTION
INFERENCE
EXAMPLE-1 BIASED STUDY
Gomez I, et al. Eur J Oral Sci 2009;117:541-6
Is diagnostic delay related to advanced-stage oral cancer? A meta-analysis
OR advanced-stage cancer due to diagnostic delay = 1.32 [1.07 to 1.62]
Authors’ inference
The probability that delayed diagnosis patients present an
advanced stage tumour at diagnosis is approximately 30%
higher than for non-delayed diagnosis patients
There were several errors in the meta-analytic methods, the
Authors used the fixed-effect method, which does not apply in
MA of observational studies (confirmed by high between-study
heterogeneity) and did not study the effect of correction for
publication bias
EXAMPLE-1 BIASED STUDY
Petti S. Eur J Oral Sci 2010;118:210-1
Diagnostic delay is not associated with advanced-stage oro-pharyngeal cancer
Meta-analytic method
OR
95CI
Fixed-effect
1.32
1.07 to 1.62
Random-effect
1.15
0.89 to 1.48
Fixed-effect adjusted
for publication bias
1.08
0.87 to 1.34
Good inference: data do not allow to infer that patients with
diagnostic delay are at higher risk for oro-pharyngeal cancer at
an advanced stage
EXAMPLE-1 BIASED STUDY
Gomez I, et al. Eur J Oral Sci 2010;118:212
Diagnostic delay may be associated with
advanced-stage oro-pharyngeal cancer
This is a good inference!
EXAMPLE-2 INCOMPLETE DEDUCTION
Typical in observational studies, because authors may only
report the outcomes of interest, which may be a subset of all
the outcomes examined
Llena C, Forner L. Caries Res 2008;42:387-93.
Dietary habits in a child population in relation to caries experience
EXAMPLE-2 INCOMPLETE DEDUCTION
Llena C, Forner L. Caries Res 2008;42:387-93
Dietary habits in a child population in relation to caries experience
Authors’ inference
It can be concluded that the results of the present study
suggest that the intake frequency of foods rich in
semihydrolyzed starch (whether or not combined with sugar)
and of sugary drinks are factors which are positively
associated with caries experience in children from 6 to 10
years old, irrespective of age, sex and tooth-brushing
frequency.
Surprisingly… the average weekly consumption frequency of sticky sugar-rich foods is not a caries risk factor in the
population studied
EXAMPLE-2 INCOMPLETE DEDUCTION
Llena C, Forner L. Caries Res 2008;42:387-93
Dietary habits in a child population in relation to caries experience
Petti S. Caries Res 2009;43:78-9
Candies and jellies for caries prevention?
EXAMPLE-2 INCOMPLETE DEDUCTION
Petti S. Caries Res 2009;43:78-9
Candies and jellies for caries prevention?
Good Inference: Frequent intake of sticky sugar-rich
foods, such as jellies and candies, would help
prevent caries in primary schoolchildren
Llena C, Forner L. Caries Res 2009;42:79
Obviously not
This is not good inference
WRONG INFERENCE
TYPICAL OF CLINICAL TRIALS
RCCTs are more likely than other studies to be free of bias
Selected participants are enrolled to decrease the sources of
bias
DISTORTED ASSEMBLY
Only a small fraction of participants have co-morbidities
Most RCCTs do not/minimally involve women, older people and
minority ethnic groups
DECREASE OF EXTERNAL VALIDITY
Under-representation will bias absolute effect estimates
EXAMPLE-3 WRONG INFERENCE
Sankaranarayanan R, et al. Lancet 2005;365:1927-33
Effect of screening on oral cancer mortality in Kerala, India: a cluster-randomised
controlled trial
EXAMPLE-3 WRONG INFERENCE
Sankaranarayanan R, et al. Lancet 2005;365:1927-33
Effect of screening on oral cancer mortality in Kerala, India: a cluster-randomised
controlled trial
Authors’ inference: On the basis of our findings, oral visual screening has the potential to prevent at least 37 000 deaths
from oral cancer worldwide every year
If oral cancer kills 83 000 males annually
If ¾ cancer cases are attributable to tobacco and/or alcohol
Tobacco and/or alcohol would be responsible for 62 000 deaths
for oral cancer among males annually
If Mortality Rate Ratio among screened and not screened
smoking/drinking males is 0.57
The annual prevented number of oral cancer deaths would be
36 000
EXAMPLE-3 WRONG INFERENCE
Typical example of NO INFERENCE
The most favourable result obtained from a sample was simply
extended without adaptation to the study-population. In this
case to the world population
Situation regarding oral cancer in Kerala ≠ World
Mortality for oral cancer in Kerala 30-45 x100,000 annually
Global mortality for oral cancer [GLOBOCAN] 2.6 X100,000
Mortality in Kerala 10-20 times greater than in the rest of the
World!!!
Sensitivity of visual screening in the rest of the World
drastically reduced due to the increase in False Negatives
Mortality Rate Ratio in the World drops from 0.57 to ???
EXAMPLE-3 WRONG INFERENCE
Statistical Inference
Mortality Rate Ratio among screened and not screened is 0.57
in Authors’ sample
Then the 95% Confidence Interval of Mortality Rate Ratio is
0.35 to 0.93 [reported by Authors]
The annual prevented number of oral cancer deaths among
males ranges between 54 000 [concordant with the Authors’ sentence at least 37 000 deaths] and 5 800
Good Inference: oral visual screening has the potential to
prevent at least 5 800 deaths from oral cancer worldwide every
year
EXAMPLE-3 WRONG INFERENCE
Kujan O, et al. Lancet 2005;366:1265-6
Screening for oral cancer
Good Inference: The results of Sankaranarayanan and
colleagues’ study do not change the conclusion of our earlier Cochrane review that there is insufficient
evidence to support or refute the introduction of
population-based screening programmes for oral
cancer worldwide
Why do you see the speck in your
brother's eye but fail to notice the
beam in your own eye?
Petti S, Scully C. Oral Oncol 2005;41:828-34
Oral cancer: The association between nation-based alcohol-drinking profiles and oral
cancer mortality
Why do you see the speck in your
brother's eye but fail to notice the
beam in your own eye?
Petti S, Scully C. Oral Oncol 2005;41:828-34
Oral cancer: The association between nation-based alcohol-drinking profiles and oral
cancer mortality
Authors’ Inference: In conclusion, the results of the present study suggest that a high fraction of oral cancer deaths is
attributable to heavy alcohol consumption and that this effect
would be higher for spirit
Paper cited 27 times
Why do you see the speck in your
brother's eye but fail to notice the
beam in your own eye?
Petti S, Scully C. Odontology 2010;98:144-52
Determinants of oral cancer at the national level: just a question of smoking and
alcohol drinking prevalence?
Why do you see the speck in your
brother's eye but fail to notice the
beam in your own eye?
Petti S, Scully C. Odontology 2010;98:144-52
Determinants of oral cancer at the national level: just a question of smoking and
alcohol drinking prevalence?
Good Inference: oral cancer mortality may benefit from the
improvement of the efficiency of health-care systems, and of
the general economical, cultural, and social conditions of the
population, in line with the principles of the Ottawa Charter for
Health Promotion
CONCLUSIONS
Good Inference requires that
1.the study is well designed
2.the results are completely reported
3.the necessary limitations are adopted
before extending the results to the
general population